SolMech 2026

44th Solid Mechanics Conference

September 7–10, 2026, Kraków, Poland


Keynote Lectures

Session TS1:  Advanced continuum theories

Prof. Yifei Sun

Taiyuan University of Technology, China

KEYWORDS: Nonlocal Regularization, Fractional Plasticity, Fabric Anisotropy, Numerical Methods.

Stress-Fractional and non-orthogonal plasticity models are capable of capturing the state-dependent nonassociated behaviour of soil without using additional plastic potential or even state index in some circumstances; however, their performances in finite element analysis involving softening and strain localization can be highly sensitive to mesh discretization, thereby compromising the reliability and accuracy of the results. To this end, a nonlocal regularised two-surface stress-fractional plasticity model is proposed, where a basic simplification criterion for the practical modelling in general stress condition is suggested. Given the critical role of plastic volumetric strain in simulating strain softening, its evolution is assumed to be governed by increments at both local and neighbouring integration points. The regularization method is implemented via a user-defined subroutines using an explicit stress integration scheme, where the nonlocal model is applied to simulate boundary value problems involving over-consolidated clay under biaxial compression, cut slope, and strip footing bearing capacity. When compared to the original model, the nonlocal model substantially reduces mesh sensitivity in the load-displacement response and produces more consistent soil failure patterns, validating the effectiveness of the nonlocal approach.

  1. W. Sumelka and M. Nowak. Non-normality and induced plastic anisotropy under fractional plastic flow rule: a numerical study. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 40(5), pp. 651–675, 2016.
  2. Y. Sun, Y. Gao, and Q. Zhu. Fractional order plasticity modelling of state-dependent behaviour of granular soils without using plastic potential. International Journal of Plasticity, Vol. 102, pp. 53–69, 2018.


Yifei Sun is a Professor of Geotechnical Engineering at the College of Civil Engineering, Taiyuan University of Technology (TYUT), China. He received his PhD in Geotechnical Engineering from the University of Wollongong, Australia, in 2017. Prior to his current appointment, he held academic positions at Hohai University, Ruhr University Bochum, and Poznan University of Technology.

His research focuses on advanced elastoplastic constitutive modeling of geomaterials, computational geomechanics, and soil–structure interaction. He has been awarded several competitive international fellowships and research grants, including the Alexander von Humboldt Fellowship (Germany), the Ulam Programme (Poland), and a joint NCN–NSFC collaborative project.



Session TS2:  Atomistic and nanoscale modeling

Prof. Piotr Chudziński

Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland

KEYWORDS: Nanostructures, Moire bilayers, correlated electron-ion dynamics, anharmonicity.

In my talk I will give a general introduction to vibrational properties, and their coupling to electron liquid, in nanostructures. In the first part I wish to provide a brief and accessible explanation on what happens when a characteristic size of a device reaches an order of nanometers. I shall introduce concepts such as energy level quantization, surface-to-volume ratio, anharmonicity and non-adiabaticity to discuss their implications and range of applicability. To be specific I shall focus on one- and two-dimensional systems where collective phenomena definitely determine the physics of the material. These are the systems that are at present at the forefront of materials science such as nanotubes, nanorods, stepped surfaces, but also topological states on crystal dislocations. One particular example that I will explore in more detail are Moire bi-layers.

The reason why Moire bi-layers are special is because at a finite twist angle, in a single sample one obtains a set of atoms with varying degrees of anharmonicity and non-adiabaticity. Indeed, several exotic orderings have been detected in this platform within the last decade of intense research, which has lead to numerous publications in the highest level journals. Thus, in the second part of my talk I will show how to incorporate such extraordinary lattice dynamics within a full microscopic quantum mechanical description: the method of effective correlated electron-ion dynamics (ECEID). I will present the ECEID equation (together with a sketch of their derivation) and compare the results with simpler methods for instance Ehrenfest dynamics.

In the last part of my talk I will show how these microscopic results can be employed into a field theoretical description of nanostructures at the mesoscopic scale. It is at this scale that the collective phenomena play a crucial role and ought to be captured. In this way measurable quantities can be obtained. Overall, the aim of this talk is to show that a description of materials that include the quantum mechanical effects is entirely possible already with a current state of knowledge. Importantly, up to large extend it does not require a heavy numerical effort, but it is a description that uses analytical methods.

ACKNOWLEDGEMENT: We acknowledge financial support of NCN under OPUS grant no.2021/43/B/ST8/03207



Piotr Chudziński is an Associate Professor at Institute of Fundamental Technological Research, Polish Academy of Sciences (IPPT PAN), Warsaw, Poland. He obtained his PhD in Paris in the field of theoretical physics of materials and then worked on nanostructures is several universities across Europe: Geneve, Ratisbonne, Utrecht and Belfast. In 2021 he won PASIFIC fellowship and came back to Poland. His expertise is in the collective phenomena dominating low dimensional systems – he made several contribution in the field of unconventional superconducting and charge density wave's materials, and non-equilibrium light-matter interaction. At present he is an acting head of Analytical Mechanics and Field Theory Lab in the Department of Theory of Continuous Media and Nanostructures, IPPT PAN.



Session TS3:  Biomechanics and biomaterials

Igor Ważydrąg

Cracow University of Technology, Poland

KEYWORDS: Aortic Valves, Ogden model, FEM, FGM

Cardiovascular diseases are the leading cause of death worldwide. Among them, aortic valve (AV) disorders characterized by abnormal function manifesting as regurgitation or limited leaflets movement become more prominent [1]. Current treatment methods involving the implantation of an artificial valve, despite continuous advances in engineering and medical sciences, are still far from achieving an optimal solution in terms of balancing the implant's cyclic deformation with its fatigue strength. The aim of this study was to investigate the effect of using functionally graded materials (FGM) on the working cycle of the considered synthetic tricuspid AV geometries. A homogeneous reference AV model was also considered [see Fig. 1a]. Using ANSYS Mechanical software (ANSYS Inc., US) and the finite element method (FEM), dynamic simulations were performed under loading conditions corresponding to the isovolumetric contraction phase of the left ventricle with a maximum pressure of 120 [mmHg] and an aortic pressure of 80 [mmHg] [2]. Four conical curve-based rho-driven leaflet geometric variants were considered, with the coefficient ranging from 0.3 to 0.6. Using experimental data obtained from mSLA printed resins, hyperelastic material models were adopted, to which a second-order Ogden model was fitted. Within each geometry, the structure was divided into 4, 6, and 8 sections with varying mechanical properties, assuming a stepwise reduction in material stiffness along the free-edge direction of the valve leaflets [see Fig. 1b].


Figure 1. a) 3D-printed homogeneous AV. b) 0.4-rho AV model with six material sections. c) Total deformation [mm] of a one-third section before and after loading (isometric view). d) Top view of the deformation field.

The results of the simulations allowed the estimation of equivalent stress values, leaflet's buckling pressure as well as the displacements of the elements [see Fig. 1c, d], thereby enabling the calculation of both, the cross-sectional areas of the valve at the characteristic points required for Gorlin's equation and the assessment using clinically applied indicators. An additional outcome of this work is the development of a framework that provides a way to tailor the properties of the functionally graded material along the structure to achieve more balanced ratio between the strength of synthetic AVs and their ability to undergo elastic deformation.

ACKNOWLEDGEMENT: Presented research is an extension of the FutureLab PK founded project nr 187.

  1. S. Parness, J.T. Womble, T.E. Hester, P. Tasoudis, A.E. Merlo, Aortic Valve Replacement in the Current Era, J. Clin. Med. 14(5), 1447, 2025. https://doi.org/10.3390/jcm14051447
  2. YD. LaFlamme, Cardiology: A Practical Handbook, Editions Frison–Roche, Paris, France, 2nd Edition, 2020


Igor Ważydrąg is a Phd student in the discipline of mechanical engineering at the Cracow University of Technology Doctoral School at the Faculty of Mechanical Engineering. He graduated with honors in 2025 with a master's degree in medical engineering, specializing in biomechanics, and a bachelor's degree with a specialization in clinical engineering from the Faculty of Mechanical Engineering at the Cracow University of Technology. In his research, he focuses on the biomechanics of the heart and arteries, particularly on modelling and experimental studies using a hybrid cardiovascular simulation system. Recently, he has been focusing on research related to artificial aortic valves and the application of additive manufacturing methods for composites in the context of polymer heart valves.



Session TS5:  Computer methods in solid mechanics

Dr. Marcin Łoś

AGH University of Kraków, Poland

KEYWORDS: Physics-Informed Neural Networks, Collocation Methods, Robust Discrete Formulations.

Physics-informed Neural Networks (PINNs) have been introduced by G. Karniadakis [1] as a way to apply Deep Learning methods to solving partial differential equations (PDEs). Unlike the more common data-driven approaches, PINNs operate by minimizing a loss function based on the residual of the strong formulation of the PDE, evaluated on a set of collocation points. Because of that, PINNs fail to provide accurate solutions in some problems with low regularity of the data, since the solution only makes sense in a variational form. A natural way to overcome this limitation is to build the loss function using the residual of the variational formulation of the underlying PDE – an approach known as Variational PINN (VPINN) [2].

While the VPINNs have been successfully applied in a number of areas, they have a considerable drawback in that the loss is sensible to the choice of basis functions, and may not be robust, that is, the loss value can tend to zero, while tue true error in a relevant Sobolev norm does not. To mitigate that problem, Robust Variational PINN (RVPINN) has been proposed [3], which follows the core ideas introduced in Minimum Residual (MinRes) methods. The RVPINN loss function is constructed as the dual norm of the residual of the variational (Petrov-Galerkin) form of a PDE. As long as the variational formulation satisfies the assumptions of the Babuška theorem (continuity and inf-sup stability of the bilinear form), such loss function constitutes an efficient and reliable estimator of the true error. More precisely, the norm of the true error is bounded from below and above (up to an oscillation term) by the square of the loss.

Unfortunately, to compute the weak residuals, RVPINNs require expensive numerical integration. We proposed an alternative combining their robustness with the efficiency of standard PINN – Collocation-based Robust Variational PINN (RVPINN) [3]. The continuous spatial domain and integral forms are replaced with a discrete set of collocation points and discrete weak formulation, mimicking the properties of the continuous, Sobolev space-based theory, similar to the finite difference method. The result is a robust loss function, which does not require integration.

ACKNOWLEDGEMENT: This work was supported by the program “Excellence initiative – research university” for the AGH University of Krakow. This project has received funding from the European Union's Horizon Europe research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101119556.

  1. M. Raissi, P. Perdikaris, G.E. Karniadakis, J. Comput. Phys. 378 (2019) 686–707. https://doi.org/10.1016/j.jcp.2018.10.045
  2. E. Kharazmi, Z. Zhang, G.E. Karniadakis, Variational physics-informed neural networks for solving partial differential equations, 2019, arXiv:1912.00873.
  3. S. Rojas, P. Maczuga, J. Muñoz-Matute, D. Pardo, M. Paszyński, Robust Variational Physics-Informed Neural Networks, Computer Methods in Applied Mechanics and Engineering 425 (May 2024): 116904. https://doi.org/10.1016/j.cma.2024.116904
  4. M. Łoś, T. Służalec, P. Maczuga, A. Vilkha, C. Uriarte, M. Paszyński, Collocation-based robust variational physics-informed neural networks (CRVPINNs), Computers & Structures 316, 107839 (2025). https://doi.org/10.1016/j.compstruc.2025.107839


Marcin Łoś is an adjunct at the Faculty of Computer Science at the AGH University of Kraków. His research interests are focused on the isogeometric finite element method, applications of the Alternating Directions Solver (ADS), and Physics-informed Neural Networks (PINNs). His contributions include creating time marching schemes for non-stationary iGA simulations, and efficient solvers and residual minimization-based stabilization algorithms (iGRM) for various PDEs. More recently, his work focuses on incorporating the residual minimization stabilization into PINNs.



Session TS6:  Contact and interface mechanics

Prof. Francesco Maresca

University of Groningen, Netherlands

KEYWORDS: Twinning, Shape Memory Alloys, NiTi, Atomistic modelling

Shape memory alloys (SMAs) possess unique properties that make them suitable for various applications, including energy-efficient actuators, biomedical devices for minimally invasive surgery, and aircraft morphing. Their distinct behaviour involves the recovery of large strains under stress or thermal cycles, and it is well-known that microstructural twinning governs this exotic mechanism. However, it is crucial to understand the structure and mobility of twin systems in martensite microstructures to determine why specific twinning systems arise more frequently than others [1].

In this study [2,3], we demonstrate with the prototypical NiTi SMA that twin interface mobility can strongly influence twin emergence. We employ an integrated methodology that combines crystallographic theory [4], state-of-the-art atomistic modelling, topological model [5], and validation using high-resolution transmission electron micrographs [6]. Our atomistic model is based on a machine learning Atomic Cluster Expansion (ACE) interatomic potential trained on an extensive density functional theory (DFT) database, and tested on key benchmark properties of B2 and B19' phases in NiTi.

Our atomistic simulations reveal that twinning stress, rather than interfacial energy, determines the occurrence of twins. Moreover, our simulations address long-standing questions by explaining the atomistic structure and propagation mechanisms of twin interfaces at zero and finite temperatures, which established theories of martensite crystallography cannot explain. This mechanistic understanding of the role of interface mobility in twin formation can help predict variant selection and inform the design of SMAs with enhanced functional performance. Moreover, our predictions of twin interface energetics and kinetics can inform higher scale models of microstructure formation (e.g. phase-field).

ACKNOWLEDGEMENT: F. Maresca acknowledges the support of the Startup Budget of the Faculty of Science and Engineering at the University of Groningen.

  1. Nishida, M., Ohgi, H., et al. Acta Metall. et Mater. (1995) 43:1219–1227.
  2. La Rosa, L., and Maresca, F. Communications Mater. (2024) 5(1):142.
  3. Ţurcan, E., La Rosa, L., Fioravanti, D. and Maresca, F. (2026) Acta Mater. 303:121651
  4. Ball, J.M. and James, R.D. Arch. Ration. Mech. Anal. (1987) 100:13–52.
  5. Pond, R.C. and Hirth, J.P. Acta Mater. (2018) 151:229–242.
  6. Nishida, M., Yamauchi, K., et al. Acta Metall. et Mater. (1995) 43:1229–1234.


Francesco Maresca is Associate Professor in Engineering Mechanics and Materials Science, and Chair of the Mechanics of Materials research group at the Engineering and Technology Institute Groningen, Faculty of Science and Engineering of the University of Groningen, the Netherlands.

Francesco received both his Bachelor (2008) and Master (2011) in Civil Engineering cum laude, at the University of Florence (Italy). In 2015 he defended cum laude his PhD in Mechanical Engineering at the Eindhoven University of Technology (the Netherlands), working on Multi-scale modeling of plasticity and damage of lath martensite in multi-phase steels, under the supervision of professor Marc Geers and professor Varvara Kouznetsova. From 2015 to 2019, Francesco has been working as a postdoctoral researcher at EPFL (Switzerland), under the supervision of Professor William Curtin. During his postdoctoral activity, Francesco used both molecular dynamics and continuum modelling to develop a new theory of martensitic phase transitions in steels as well as a new theory of solute strengthening of dislocations in bcc alloys, from dilute to high entropy alloys.

Francesco's research aims at the fundamental, multi-scale understanding (from atomistics to continuum) of plasticity, phase transitions and failure in alloys, to develop predictive theories that can be used to guide materials design in uncharted regions of the material properties space.



Session TS7:  Experimental mechanics

Prof. José A. Rodríguez-Martínez

Charles III University of Madrid, Spain

KEYWORDS: Planar plate impact, Spall fracture, Split Hopkinson pressure bar, Shear fracture, X-ray phase-contrast imaging, X-ray tomography, Porous microstructure, Additively manufactured metals

Recent advances in high-energy X-ray imaging enable real-time, in-situ observation of dynamic deformation and fracture processes in metals subjected to extreme loading. This lecture presents results from impact experiments conducted at the ID19 beamline of the European Synchrotron Radiation Facility, where ultra-high-speed detectors resolve damage evolution over nanosecond to microsecond time scales. The study focuses on additively manufactured Ti6Al4V and AlSi10Mg specimens with controlled porosity, exhibiting void volume fractions from 0.04% to 0.77% and broad pore size distributions spanning a few micrometers to more than 180 μm. Dynamic shear fracture is investigated through impact loading of shear–compression specimens in Split Hopkinson Pressure Bar experiments, while spallation is examined through planar plate impact tests performed with a single-stage helium-driven gas gun. These two complementary loading configurations allow the influence of porosity on shear- and tension-dominated failure regimes to be explored within a consistent experimental framework and a wide range of loading rates. Time-resolved radiographic measurements provide direct insight into porosity evolution during dynamic deformation and the formation of shear bands and spall planes. These in-situ observations are complemented by extensive post-mortem X-ray computed tomography, enabling the contribution of individual voids to shear fracture and spallation to be identified. Together, the measurements clarify the interplay between pore collapse, void growth, strain localization, and crack initiation, and distinguish damage mechanisms governed by pre-existing pores from those associated with sub-resolution or dynamically nucleated defects. The lecture concludes with a brief outlook on current limitations and future directions, including three-dimensional time-resolved tomography, higher repetition rates, and tighter integration with physics-based modeling approaches.

ACKNOWLEDGEMENT:

The research leading to these results has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Project PURPOSE, Grant Agreement No. 758056).

Financial support from the Spanish Ministry of Science, Innovation and Universities through project UNCLOAK (Grant No. PID2022-137559NB-I00) is acknowledged.



J. A. Rodríguez-Martínez is Professor in the Department of Continuum Mechanics and Structural Analysis of UC3M. His research focuses on the dynamic behavior of materials. He has led and coordinated several competitive projects, including a MSCA-ITN-ETN, a MSCA-RISE, an ERC grant, a USAF-AFRL grant, and multiple national projects funded by the Spanish Ministry of Science, as well as the Spanish Network on Multiscale Mechanics of Engineering Materials. He also serves as Director of the Hypervelocity Center at UC3M. The total funding secured through these projects exceeds €5M. He has published >90 scientific papers in international journal and is a member of the Editorial Board of International Journal of Plasticity, Journal of Dynamic Behavior of Materials, Engineering Fracture Mechanics, and Mechanics of Materials. He is also Secretary of the Spanish Society of Theoretical and Applied Mechanics. Dr. Rodríguez-Martínez has organized six international conferences and supervised 10 PhD students and 4 postdoctoral researchers.



Dr. Ved Prakash Dubey

Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland

KEYWORDS: Additive manufacturing, Laser powder bed fusion (LPBF), Yield surface, Multiaxial loading.

The rapid adoption of laser powder bed fusion (LPBF) for stainless steel 316L (SS316L) components necessitates a deeper understanding of anisotropic plasticity under complex loading conditions [1]. This study presents a comprehensive experimental investigation of the initial and evolving yield surfaces of LPBF-fabricated SS316L, explicitly addressing the influence of printing orientation and plastic pre-deformation. Tubular specimens were manufactured in three orientations (XY, ZX45 and Z) and subjected to multiaxial loading using a single-specimen probing methodology, enabling efficient and precise yield surface characterization in axial–shear stress space.

Yield surfaces were determined using Szczepiński anisotropic yield criterion at initial state and subsequently tracked after controlled tensile plastic pre-strain equal to 0.35%, 0.5% and 0.8%. The results reveal pronounced anisotropy in LPBF specimens, strongly governed by build orientation. The Z-oriented samples exhibit reduced yield strength and enhanced softening in yield loci, while XY and ZX45 orientations demonstrate comparatively higher yield strength under selected loading paths. Additionally, specimens exhibit orientationdependent yield surface translation and rotation, indicating complex interactions between strain-induced hardening/softening mechanisms and inherent microstructural anisotropy [2].


Figure 1. Initial yield surfaces at 10με offset definition of yield and IPF maps of three printing orientations.

Microstructural analysis using electron backscatter diffraction (EBSD) establishes a strong correlation between grain morphology and mechanical anisotropy. Columnar grains aligned along the build direction in Z-oriented samples promote directional deformation and strain localization, whereas more equiaxed structures in XY and ZX orientations contribute to improved mechanical uniformity. Despite weak crystallographic texture, melt pool geometry and interlayer boundaries emerge as primary drivers of anisotropic plastic response.

ACKNOWLEDGEMENT: This work was funded by the National Science Centre, Poland through the grant no. 2023/51/B/ST8/01751.

  1. V.P. Dubey, D. Przygucka, M. Pawlik, Z.L. Kowalewski, P. Wood and M. Kopec, Materials Today Communications 50, 114531, 2026. https://doi.org/10.1016/j.mtcomm.2025.114531
  2. V.P. Dubey, M. Kopec, D. Przygucka, M. Pawlik, P. Wood and Z.L. Kowalewski, Int. J. Adv. Manuf. Technol. 140, 313–334, 2025. https://doi.org/10.1007/s00170-025-16296-y


Ved Prakash Dubey received his PhD degree with distinction in Mechanical Engineering in 2025 from the Institute of Fundamental Technological Research, Polish Academy of Sciences (IPPT PAN), Warsaw, Poland. He is currently working in the Department of Experimental Mechanics at the same institute. His research focuses on the mechanical behaviour of materials under complex loading and multiaxial stress states. His experimental work emphasizes pre-deformation effects, cyclic loading and yield surface evolution in both conventional and additively manufactured materials. His research combines fundamental mechanics with practical engineering applications, aiming to contribute to the development of advanced constitutive models, improved failure criteria and reliable structural integrity assessment of engineering materials.



Session TS8:  Geomechanics and granular materials

Prof. Stanisław Pietruszczak

McMaster University, Canada

KEYWORDS: Salt crystallization, Capillary uptake, Localized damage, Structural masonry.

Salt crystallization is a primary factor contributing to the deterioration of porous building materials, including masonry, concrete, and natural stone. Salt damage occurs when a porous medium contains both soluble salts and moisture. Dissolved ions, such as chlorides, nitrates, and sulfates, are transported by liquid water through the interconnected pore network via capillary flow. Moisture ingress can result from hygroscopic absorption, rainwater infiltration, condensation, or capillary rise from the ground, the latter being particularly common and difficult to mitigate. Under conditions that promote evaporation or temperature fluctuations, supersaturation may develop, leading to the nucleation and growth of salt crystals within the pore structure.

Salt crystallization can induce surface exfoliation or the development of microcracks due to crystallization pressure. The latter process, referred to as subflorescence, is particularly damaging, as crystal growth within pores generates expansive forces that lead to the initiation and propagation of internal damage within the material.

This paper focuses on the mechanical analysis of the effects of salt crystallization in porous materials, with primary emphasis on structural masonry components. In the first part of the study, inelastic constitutive relations governing deformation in the presence of salt crystallization are presented. Instead of explicitly modeling crystallization pressures, which are difficult to quantify due to complex pore geometry, the approach extends classical rate-independent plasticity by introducing an additional internal variable, viz. the pore volume fraction occupied by crystallized salt, defined as an explicit function of time. Subsequently, a coupled hydro–chemo–thermal framework for modeling salt crystallization in porous masonry materials is outlined. The formulation integrates moisture transport, dissolved salt advection–iffusion, temperature-dependent solubility, and kinetic crystallization laws within a finite element framework. The evolution of porosity and permeability induced by salt precipitation is explicitly incorporated, enabling reliable prediction of transport–crystallization interactions under transient environmental conditions.

Two independent benchmark problems are analyzed first to validate the transport formulation. These involve (i) a cooling–warming simulation focused on the evolution of dissolved salt concentration and crystallization dynamics under cyclic thermal loading, and (ii) the simulation of a drying process that captures evaporationdriven supersaturation and surface-dominated precipitation. The mechanical effects of crystallization are examined by analyzing a masonry specimen subjected to tension parallel to the bed joints. The spatial distribution of precipitated salt obtained from the transport analysis is incorporated into the mechanical model, and the localized fracture mechanism is analyzed by employing a constitutive law with embedded discontinuity. The crystallization effects are introduced through degradation of strength parameters at the brick–mortar interfaces. In addition, another heuristic example is provided, in which a masonry triplet is subjected to a sustained lateral load under a prescribed temporal history of salt deposition. This loading scenario leads to a spontaneous loss of stability of the specimen.



Prof. S. Pietruszczak's research interests are focused mainly on the description of the hydro-mechanical behaviour of various engineering materials. These include geomaterials (soils and rocks), structural materials (concrete, masonry, reinforced composites), as well as biomaterials. He has written over 190 technical papers on these and related topics. He is also the author of a monograph on ‘Fundamentals of Plasticity in Geomechanics’ and the co-author of the proceedings of 12 different International Symposia that he organized (in collaboration with Prof. G.N. Pande, University of Swansea, U.K.) in various European/North American cities. He was the North American Editor of the Intern. Journal ‘Computers and Geotechnics’, Elsevier Science Ltd. (1989–2011) and is presently on the Editorial Board of several other international journals. He also served on various Advisory Boards (e.g., European Research Council – International Panel of Experts) and was the Vice-President of the International Centre for Computational Engineering (IC2E).



Session TS10:  Micromechanics of heterogeneous and multi-component materials

Prof. Bernhard A. Schrefler

University of Padua, Italy

Classical fracture mechanics predicts an upper bound on crack propagation speed, typically the Rayleigh wave speed for mode I fractures and the shear wave speed for mode II ruptures. Beyond these limits, tensile and shear fracture are traditionally considered energetically forbidden. However, experimental observations, field evidence from large earthquakes, and recent numerical studies increasingly demonstrate the existence of sub-, inter-, and supershear rupture regimes. In this study, we investigate the dynamic propagation of mode I and mode II fractures in dry and fluid-saturated media using multiple numerical frameworks, including the Extended FEM (XFEM), peridynamics (PD), and hybrid FEM/PD formulations.

For mode I fracture, simulations reveal a systematic transition in fracture behavior with increasing mechanical or hydraulic loading. Crack propagation evolves from smooth steady growth to stepwise regime, and ultimately to previously undocumented forerunning characterized by the nucleation of cracks ahead of the main tip. This progression is observed in both dry and saturated porous media, under mechanical loading and fluid injection. Notably, forerunning is shown to occur not only at supershear speeds but also under subsonic crack advance, as demonstrated in a beam on an elastic foundation subjected to sinusoidal loading. In saturated media, increased injection rates strongly promote the transition to stepwise and forerunning behavior, enabling crack speeds that exceed both shear and dilatational wave velocities.

For mode II fracture, we employ a newly developed 2-D hybrid FEM/PD model to study the transition from sub-Rayleigh to supershear rupture in dry and fluid-saturated media. The model reproduces laboratory observations of direct and indirect (mother-daughter crack or Burridge-Andrews) transitions and captures the formation of shear Mach cones. In fluidsaturated media, poroelastic coupling near the rupture front favors direct transitions to supershear fracturing, even in the absence of daughter cracks.

The consistency of these results across distinct numerical methods and constitutive descriptions supports the robustness of supersonic fracture and rupture in both tensile and shear modes. The findings have direct implications for earthquake dynamics, fluid-rich fault zones, and geophysical processes involving rapid fracture acceleration (slab tearing, volcanic systems).



Prof. Bernhard Schrefler, educated at the University of Padua (MSc), and at the University of Wales (PhD and DSc), Professor (1980-2013) and currently Professor emeritus at the University of Padua, Affiliated Professor at the Institute of Academic Medicine, Houston, TX and Hans Fischer Senior Fellow Alumnus of the Institute for Advanced Study, Technical University of Munich. Honorary Fellow of the University of Swansea, Honorary Professor of the Dalian University of Technology, and Fellow of IACM (International Association for Computational Mechanics). Knighted by the French Republic in the Order of Academic Palms. Five honorary doctorates (St. Petersburg State Technical University, the University of Technology of Lodz, the Leibniz University of Hannover, the Russian Academy of Sciences, and the Ecole Normale Supérieure at Cachan); Biot, Euler, Gauss-Newton, Zienkiewicz Medals; Computational Mechanics and IACM Awards, ICCES Lifetime Achievement Award, INTERPORE Lifetime Honorary Membership Award, Fry International Sustainability Award. Member of the Pre-Selection Committee for the Nobel Sustainability Trust (NST) Awards (2023, 2024). He was inducted to the National (Italian) Academy of Sciences (“dei XL”), Galileian Accademy, Istituto Veneto and Istituto Lombardo di Scienze, Lettere ed Arti.

Professor Schrefler's research interests are in porous media mechanics applied to geomaterials, such as rocks, concrete and bricks, environmental geomechanics, soil mechanics and reservoir engineering; in bio-medical engineering; in structural and materials engineering; and in thermomechanical problems in controlled thermonuclear fusion technology.



Dr. Renald Brenner

CNRS, Sorbonne Université, France

KEYWORDS: FFTsolvers, mechanical field fluctuations, interphase properties, composites, polycrystals.

This work addresses the description of the spatial distribution of mechanical fields for elastic heterogeneous materials by using the fast Fourier transform (FFT) numerical method [1]. It relies on the resolution of the elastostatic boundary value problem with the Green functions method. By using a classical approach in micromechanics, the original elastic heterogeneous media is replaced by an homogeneous elastic media with a heterogeneous polarization field to be determined. This leads to a Lippmann-Schwinger equation which can be efficiently solved by a FFT-based iterative scheme on a regular grid. This approach has been the subject of numerous developments and is now widely used in micromechanics [2]. However, this reformulation of the local problem, based on Fourier series, can lead to spurious oscillations on local fields. This phenomenon emerges when (i) the polarization field has some discontinuities and (ii) pseudo-spectral differentiation is used [3]. To tackle this problem, modified Green operators and interface spreading approaches have been proposed. The latter consist in the introduction of an interphase, whose properties have to be defined, between domains with different elastic properties. This approach can be performed locally using composite voxel techniques [4], or globally using smoothing techniques [3]. By reducing material discontinuities, it improves consistency with the Fourier-series representation of the local fields.

Building on the previous work of Morin et al. [3], the present contribution aims at presenting two improvements: first, to provide a smoothing of elastic properties which is invariant when applied to stiffness or compliances, and second, to consider general anisotropic elastic properties. To do so, use is made of the logarithm of elasticity tensors following ideas of Moakher and Norris [5] to define an invariant distance between tensors. Numerical experiments are performed on elasticity problems involving isotropic and anisotropic phases, for composites and polycristals. A significant reduction of spurious oscillations is observed on the local fields.

  1. H. Moulinec, P. Suquet, Comput. Methods Appl. Mech. Eng. 157, 69–94, 1998. https://doi.org/10.1016/S0045-7825(97)00218-1
  2. M. Schneider, Acta Mech. 232, 2051–2100, 2021. https://doi.org/10.1007/s00707-021-02962-1
  3. L. Morin, R. Brenner, K. Derrien, K. Dohrmi, Comput. Methods Appl. Mech. Eng. 373, 113549, 2021. https://doi.org/10.1016/j.cma.2020.113549
  4. L. Gélébart, F. Ouaki, J. Comput. Phys. 294, 90–95, 2015. https://doi.org/10.1016/j.jcp.2015.03.048
  5. M. Moakher, A.N. Norris, J. Elast. 85, 215–263, 2006. https://doi.org/10.1007/s10659-006-9082-0



Renald Brenner is a senior researcher at Sorbonne Université in Paris. He received his PhD in Mechanics of Materials at Université Paris Nord in 2001 and became CNRS researcher in 2002. He obtained his Habilitation in 2011 and joined the D'Alembert Institute at Sorbonne Université in 2012. He was then head of the Solid Mechanics group from 2019 to 2025. The main focus of his research is the relationship between microstructure and effective properties of heterogeneous materials. He develops micromechanical models to describe the mechanical fields heterogeneity and the constitutive behaviour of polycrystals, composite and architectured materials.



Dr. Witold Ogierman

Silesian University of Technology, Poland

KEYWORDS: Micromechanics, Effective properties, Mori–Tanaka method, Discontinuous reinforcement.

Discontinuously reinforced composites, comprising particles or short fibres, represent an important class of engineering materials. Their effective properties are governed by both the intrinsic properties of the constituent phases and key microstructural characteristics, including reinforcement shape, spatial orientation, and distribution. Numerical homogenization methods (full-field approaches) enable the prediction of these effective properties by analysing representative volume elements (RVEs) that capture the composite's heterogeneous microstructure. Among full-field approaches, the most widely used methods rely on the finite element method (FEM) or the fast Fourier transform (FFT) to resolve stress and strain fields. In general, fullfield models provide high accuracy and broad modelling capabilities. Nonetheless, in practical applications, numerical homogenization can be highly time-consuming, which limits its applicability. A computationally efficient alternative is offered by mean-field models, such as the Mori–Tanaka method, which generally provide good predictive capability but have certain limitations. In its basic form, the modelling capabilities are limited, among other factors, to the ellipsoidal shape of inclusions, and the accuracy of the results decreases with increasing volume fraction of the reinforcing phase.

To overcome these limitations, a data-driven mean-field homogenization framework is developed by combining the physics-based foundations of the Mori–Tanaka method with data obtained from the full-field simulations [1, 2]. Following the concept presented in [2], the original strain concentration tensor is modified by fitting it to RVE-based data as a function of the volume fraction of inhomogeneities. Results reported in [2], associated with the case of composites reinforced with spherical particles, demonstrate very good agreement with full-field predictions across a wide range of stiffness contrasts and volume fractions. This study aims to extend the model to account for different shapes of the reinforcing phase, including those not captured by analytical solutions. In this case, both the strain concentration tensor and Eshelby's tensor are modified using data-driven corrections. The coefficients associated with the modified tensors are computed using a genetic algorithm. The proposed approach is expected to provide predictions comparable to those of full-field homogenization, while retaining the computational efficiency of mean-field models. During the conference, details of the database generation, the proposed numerical procedures, the obtained results, and future research directions will be presented.

ACKNOWLEDGEMENT: This work was supported by a statutory subsidy from the Faculty of Mechanical Engineering, Silesian University of Technology.

  1. W. Ogierman, A data-driven model based on the numerical solution of the equivalent inclusion problem for the analysis of nonlinear short-fibre composites, Compos. Sci. Technol. 250, 110516, 2024. https://doi.org/10.1016/j.compscitech.2024.110516
  2. W. Ogierman, Data-Driven Mean-Field Homogenization : Enhancing the accuracy of the Mori–Tanaka method, Compos. Struct. 358, 118985, 2025. https://doi.org/10.1016/j.compstruct.2025.118985



Witold Ogierman received his PhD in Mechanics in 2017 from the Silesian University of Technology (Gliwice, Poland), where he is currently an Assistant Professor at the Faculty of Mechanical Engineering. His research focuses on the micromechanics of materials, with particular emphasis on discontinuously reinforced composites. His recent work aims to bridge the gap between highly accurate but computationally demanding full-field models and computationally efficient but less accurate mean-field approaches by incorporating data-driven strategies. He has received several awards, including the Polish Ministry of Education and Science scholarship for outstanding young scientists (2022) and the Prof. Michał Życzkowski Awards from the Committee on Mechanics of the Polish Academy of Sciences (2019, 2025).



Session TS11:  Multiphysics and coupled problems

Prof. Laurence Brassart

University of Oxford, UK

KEYWORDS: Hydrolysis, Reaction, Diffusion, Viscoplasticity, Constitutive modelling.

Biodegradable polymers are materials designed to degrade and ultimately disappear after having completed their structural function. They are increasingly developed for engineering and biomedical applications, where simultaneous control over mechanical performance and degradation behaviour is critical. Many biodegradable polymers primarily degrade via hydrolysis, in which water molecules react with susceptible backbone bonds (e.g. esters), leading to chain scission. Chain scission in turn impacts the thermo-mechanical properties and causes mass loss. Conversely, mechanical stress can also impact the degradation kinetics [1].

In this talk, I will describe our recent experimental and modelling efforts to investigate the coupled chemo-mechanical behaviour of various degradable polymer systems in aqueous environments, including glassy polymers, semi-crystalline polymers, and biodegradable hydrogels. In particular, I will present a constitutive modelling framework for amorphous polymers, incorporating a mechanistic description of the chain scission process and its influence on the elasto-viscoplastic behaviour through the concept of effective temperature [2, 3]. We show that the behaviour of wet, degraded polymer can be accurately captured by evaluating the response of the dry, undegraded polymer evaluated at an elevated temperature and reflecting the reduction in glass transition temperature due to chain scission and water uptake.

ACKNOWLEDGEMENT: This research is supported by a Future Leaders Fellowship of UK Research and Innovation (MR/W006995/1).

  1. H. Chen, Z. Pan, G.S. Sulley, C.K. Williams, L. Brassart, Polym. Degrad. Stab. 243, 111751, 2026. https://doi.org/10.1016/j.polymdegradstab.2025.111751
  2. Z. Pan, L. Brassart, Acta Biomater. 167, 361–373, 2023. https://doi.org/10.1016/j.actbio.2023.06.021
  3. Z. Pan, H. Chen, L. Brassart, Int. J. Plasticity 178, 103996, 2024. https://doi.org/10.1016/j.ijplas.2024.103996


Laurence Brassart is an Associate Professor in the Department of Engineering Science at the University of Oxford. She received her PhD in Engineering Sciences from the University of Louvain in 2011. She then successively held postdoctoral positions at Harvard University and the University of Louvain. From 2015 to 2019, she was a Senior Lecturer in the Department of Materials Science and Engineering at Monash University, Australia. She is the recipient of an EPSRC New Investigator Award (2021) and a UKRI Future Leaders Fellowship (2022). Her research focuses on the development of micromechanical and constitutive modelling approaches for engineering materials, including polymers, composites, soft materials, and energy materials, with emphasis on multiscale and multiphysics aspects.



Prof. Mahmood Jabareen

Israel Institute of Technology, Israel

KEYWORDS: Thermodynamic regularization, Strain-induced crystallization, Loss of ellipticity.

Strain-induced crystallization (SIC) represents a type of phase transition in natural rubbers triggered by deformation. This is evident from the heterogeneities in temperature distribution observed in unfilled natural rubbers subjected to homogeneous uniaxial tension [1], as temperature variations in natural rubber are attributed to SIC. These heterogeneities become pronounced following the onset of SIC, particularly within the stretch ratio range of 4 ⪅ Λ ⪅ 5.5 (see Fig. 1). Interestingly, prior to the onset of SIC (Λ1 ⪅ 4) and following the stress upturn (Λ1 ⪆ 6), the temperature distribution remains homogeneous. This observation further implies that this behavior does not stem from coupling instabilities, as observed in electroactive elastomers, but rather from the loss of ellipticity associated with phase transitions.

In this contribution, we extend the recently developed thermodynamic regularization technique [2] to the context of strain-induced crystallization in natural rubbers and formulate a novel computational framework based exclusively on the laws of thermodynamics and a single thermodynamic potential. The predictions of the computational framework with the four coupled fields (displacement, temperature and two nonlocal interactions) is then demonstrated through multiple numerical benchmarks and comparison with experimental data. Specifically, the average nominal stress, calculated from the ratio of force and initial cross-sectional area, is demonstrated in Fig. 1 (left). In can be seen a good agreement with the experimental data and also there is no stress plateau observed after the onset of SIC due to regularization. The predicted heat source at the center of the specimen is plotted versus time in Fig. 1 (right). It can be observed that, initially, the heat source increases with crystallinity. Near the end of the loading phase, the heat source decreases due to the inflection point in the evolution of crystallinity.

Figure 1: Left: Average nominal stress in the uniaxial tension; Right: Heat source evolution at the center of the specimen.

  1. J.B. Le Cam, A. Tayeb, S. Charlè, Polymer 255, 125120, 2022. https://doi.org/10.1016/j.polymer.2022.125120
  2. V.N. Khiêm, M. Jabareen, R. Poudel, X. Tang, M. Itskov, J. Mech. Phys. Solids 193, 105874, 2024. https://doi.org/10.1016/j.jmps.2024.105874


Mahmood Jabareen is an Associate Professor at the Faculty of Civil and Environmental Engineering, Technion – Israel Institute of Technology. He received his Ph.D. degree in 2005 from the Technion – Israel Institute of Technology, and joined the Technion as an Assistant Professor in 2009 after two successively held postdoctoral positions at Technion and the Swiss Federal Institute of Technology – ETH. Mahmood is currently serving as the President of the Israel Association for Computational Methods in Mechanics (IACMM). His main research interest is developing advanced finite element formulations and computational methods for modeling solids and structures at different scales. Specifically, Mahmood is working on a variety of topics in computational mechanics, including Cosserat point element, modeling of electroactive polymers, biomechanics, failure modeling and crack propagation in soft materials. His research has been funded by grants from the Israel Science Foundation, The Ministry of Housing and Construction, and other resources.



Session TS13:  Plasticity, damage and fracture mechanics

Prof. Jean-Baptiste Leblond

Sorbonne Université, France

KEYWORDS: 3D elastic body, arbitrary crack, out-of-plane perturbation, extended Bueckner-Rice theory, mixed-mode propagation.

The aim of this work is to propose a new, simple and efficient method for solving problems of 3D elastic bodies containing cracks slightly perturbed out of their original plane or surface. It is divided into three parts.

We begin, in a first part, by defining a suitable extension of Bueckner-Rice's theory of 3D weight functions. Rice (1985, 1989)'s re-formulation of Bueckner (1987)'s theory provided the first-order variation of the elastic fields (displacements, strains, stresses) arising from an in-plane or tangential perturbation of the crack front, for an arbitrary crack in an arbitrary body. This result is extended here to arbitrary geometric perturbations of the crack front and surface, including an out-of-plane or normal component to the crack surface. The basis of the treatment is a new, general formula providing the variation of the total energy of the body arising from such an arbitrary crack perturbation. This formula is obtained by adapting and extending reasonings and results of deLorenzi (1982) and Destuynder et al. (1983). It is then used to derive the first-order expression of the full displacement field everywhere in the body. The reasoning here basically follows and extends that in the works of Rice (1985, 1989), which was limited to in-plane or tangential perturbations of the crack front.

In a second part, we illustrate the possible use of the formalism thus defined for the treatment of elastic problems of out-of-plane or out-of-surface crack perturbations. This is done by considering the simplest possible case of out-of-plane perturbation of a semi-infinite plane crack embedded in some infinite body. This problem was solved by Movchan et al. (1998), using an elaborate method specific of the special, infinite geometry considered. In constrast, the method of solution proposed here is general and potentially applicable to any cracked geometry. The derivation involves two steps:

  1. In the general formula providing the variation of the displacement at any point of the body, we let this point of observation go to an arbitrary point on the crack surface, so as to get the variation of the displacement discontinuity there.
  2. In the formula thus obtained, we let the point of observation on the crack surface go to some arbitrary point on the crack front, so as to get the variations of the stress intensity factors there.

The results obtained in this way fully confirm, and somewhat extend, those derived by Movchan et al. (1998) using a more complex and specific method.

We finally expound, in a third part, the possible applications of these results to the theoretical prediction of crack paths in 3D bodies loaded in mixed-mode conditions. We especially focus on the interpretation of the experimentally well-documented out-of-plane instability of crack fronts loaded in mode I+III. Three cases are considered, in order of increasing complexity:

  1. That of a mode I+III loading, with a critical energy-release-rate Gc independent of mode-mixity.
  2. Again that of a mode I+III loading, but with a mode-mixity-dependent Gc .
  3. That of a general mixed-mode I+II+III loading, with a mode-mixity-dependent Gc .

The results suggest interesting interpretations of both old and recent experiments.



Born in 1957, Jean-Baptiste Leblond studied physics in Ecole Normale Superieure and Universite Pierre et Marie Curie, where he got his PhD in 1984. He then switched to mechanics of deformable solids. He became Associate Professor at Ecole Polytechnique in 1985, then Full Professor at Universite Pierre et Marie Curie (now part of Sorbonne Universite) in 1988. He was elected a Corresponding Member in 1997, and a full Member in 2005, of the Academie des Sciences, Section des Sciences Mecaniques et Informatiques. He became an Emeritus Professor at Sorbonne Universite in 2021, but continues his research activities in this new position. In addition, he has always pursued, since the beginning of his career, close cooperations with the mechanical and metallurgical industries.
He is best known for his works on transformation plasticity of metals and alloys, brittle fracture and ductile fracture, but his research interests also include phase transformations of steels, finite element simulations of thermomechanical treatments (welding, quenching, tempering), problems of nonlinear diffusion in solids (including internal oxidation of metals and alloys), and advanced numerical methods in solid mechanics.

Honors received:

3rd prize, International Mathematical Olympiads (Deutsche Demokratische Republik, 1974)
3rd prize, International Mathematical Olympiads (Bulgaria, 1975)
“Jeune Chercheur” Prize, DRET (1987)
Jean Mandel Prize, Ecole des Mines de Paris (1989)
Fourneyron Prize, Academie des Sciences (1993)
Junior Member of the Institut Universitaire de France (1993 – 1998)
Corresponding Member of the Academie des Sciences, Section des Sciences Mecaniques et Informatiques (1997 – 2005)
Member of the Academie des Technologies (since 2000)
Member of the Academie des Sciences, Section des Sciences Mecaniques et Informatiques (since 2005)
Senior Member of the Institut Universitaire de France (2007 – 2017)
Chevalier de l'Ordre des Palmes Academiques (since 2011)
Fellow of the European Mechanics Society (since 2012)
Koiter Medal of the American Society of Mechanical Engineers (ASME) (2025)



Dr. Hossein Darban

Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland

KEYWORDS: Crack, Fracture Toughness, Molecular Dynamics Simulations, Size Effect.

This presentation addresses the following question: Can the available analytical or numerical solutions for stress intensity factors (SIFs), derived from classical continuum mechanics, accurately define SIFs in specimens with micro- or nanoscale dimensions?

This question arises because, at such small length scales, interactions between atoms on opposing crack surfaces may become significant and influence the deformation field at the crack tip. The extent to which these atomistic interactions affect the validity of classical SIF solutions remains unclear in the literature.

In this work, we aim to provide insight into this issue by investigating the problem using molecular dynamics (MD) simulations. The SIFs will be determined from MD simulations employing an interatomic potential that is carefully validated against Density Functional Theory (DFT) calculations and available experimental data.

The SIFs will be evaluated using two complementary approaches:

  1. A global method based on a discretized atomistic formulation of the J-integral, and
  2. A local method based on a least-squares fitting of the crack-tip displacement/stress fields.

Finally, the SIFs obtained from the MD simulations will be compared with those predicted by classical continuum solutions.

ACKNOWLEDGEMENT: The financial support provided by the National Science Centre (NCN) in Poland through the grant agreement No: UMO-2022/47/D/ST8/01348, is gratefully acknowledged.



Hossein Darban is an Assistant Professor at the Institute of Fundamental Technological Research, Polish Academy of Sciences (IPPT PAN). During his PhD (2014–2018), he contributed to research on the delamination of composite laminates using homogenized structural theories. Since then, he has applied experimental and numerical techniques, including phase-field methods, to study fracture in metal-ceramic composites. He has also contributed to modeling miniaturized structures using nonclassical, continuum-mechanics-based formulations. More recently, he has used atomistic simulations to study the physical integrity and mechanical stability of materials at small scales under various physical fields.



Session TS14:  Structural optimization and optimum material design

Dr. Marek Tyburec

Czech Technical University in Prague, Czech Republic

KEYWORDS: Free Material Optimization, Orthotropic Materials, Hashin–Shtrikman Bounds, Sequential Global Programming, Sequential Laminates

Free material optimization treats the elasticity tensor field itself as the design variable. In classical compliance minimization, admissibility is usually enforced by positive semidefiniteness together with resource constraints expressed in terms of tensor invariants, typically of trace or Frobenius norm type. These constraints control the overall amount of stiffness, but they do not guarantee that an admissible tensor can be realized as the effective property of a composite made from prescribed constituent phases. This work narrows that gap for two-dimensional plane-stress problems with two well-ordered isotropic phases by introducing a hierarchy of realizability-aware admissible sets based on zeroth-order, Voigt, and Hashin–Shtrikman energy bounds.

The proposed hierarchy has several notable structural properties. In the convex setting, the Voigt admissible set is strictly tighter than the zeroth-order one for intermediate phase volume fractions, while the two coincide at the pure-phase endpoints; moreover, the Voigt model reduces to an isotropic variable-thickness-sheet formulation. For the Hashin–Shtrikman model, the energy upper bound can be written as a Voigt term minus a nonnegative correction, which explains both the strict tightening of the admissible set and the loss of joint convexity in the effective tensor and the local volume fraction. In the single-loadcase continuum setting, the resulting relaxation is tight with the classical Allaire–Kohn relaxed problem and is attained in the relaxation sense by orthotropic sequential laminates. In generic multi-loadcase settings, by contrast, it should be interpreted as a lower bound on compliance minimization over general microstructures.

Computationally, the resulting nonconvex free orthotropic material optimization problem is solved by sequential global programming. Numerical experiments illustrate the expected compliance ordering induced by the zeroth-order, Voigt, and Hashin–Shtrikman models and show that the Hashin–Shtrikman formulation remains close to finite-rank laminate reference designs while staying computationally tractable. Overall, these results connect classical homogenization bounds with free material optimization and show how realizability-aware energy bounds can inform structural design.

ACKNOWLEDGEMENT: We acknowledge financial support from the European Union through the ROBOPROX project (reg. no. CZ.02.01.01/00/22_008/0004590) and from the mobility project 8J24DE005, funded jointly by the Ministry of Education, Youth and Sports of the Czech Republic (MŠMT) and the German Academic Exchange Service (DAAD).

  1. M. Tyburec, M. Stingl, S. Ma, Hierarchy of bounds in free orthotropic material optimization: From convex relaxations to Hashin–Shtrikman via sequential global programming, arXiv:2602.23180, 2026.
  2. G. Allaire, R.V. Kohn, Explicit optimal bounds on the elastic energy of a two-phase composite in two space dimensions, Quart. Appl. Math. 51(4), 675–699, 1993. https://doi.org/10.1090/qam/1247434
  3. K. Burazin, I. Crnjac, M. Vrdoljak, Optimality criteria method in 2D linearized elasticity problems, Appl. Numer. Math. 160, 192–204, 2021. https://doi.org/10.1016/j.apnum.2020.10.002


Marek Tyburec is an Assistant Professor at the Faculty of Civil Engineering, Czech Technical University in Prague. His research lies at the interface of computational mechanics, structural optimization, material design, and mathematical optimization. His work includes topology optimization of modular structures and mechanisms, free material design, polynomial optimization methods for structural design, and applications to composite structures and additive manufacturing. In 2022, he received the Joseph Fourier Prize—Special IT4Innovations Award.



Session TS15:  Shells, plates, and lattices as macroscopic or microscopic structures

Dr. Agnieszka Sabik

Gdańsk University of Technology, Poland

KEYWORDS: Multilayered plates and shells, 2D models, Finite element method, Failure

Over the past decades, numerous theoretical approaches have been proposed to model mechanical behaviour of composite laminated plates and shells. Among the various models developed, two-dimensional Equivalent Single Layer models (ESL) are particularly attractive due to their relatively low computational cost. Being two-dimensional, these models are generally based on theories of homogeneous plates and shells; however, their application to laminated composite structures requires appropriate modelling strategies to capture characteristic phenomena such as high transverse shear flexibility and the variation of stiffness through the thickness [1–3]. In addition, individual layers in laminated composite structures exhibit orthotropic behaviour, leading to markedly different mechanical responses depending on the direction of the applied loading. Variations in stiffness and strength along the fibre direction, transverse to the fibres, and in shear result in distinct deformation patterns and load-transfer mechanisms under different loading conditions. This imposes the use of appropriate constitutive models and failure criteria capable of capturing the direction-dependent, anisotropic response of individual layers.

This keynote lecture provides a comprehensive overview of the current state of the art in ESL modelling of laminated plates and shells, drawing on key contributions from the composite structures' community [1–2] as well as selected developments proposed by the author's research group. Different kinematics descriptions adopted within ESL formulations are examined and their implications for mechanical response prediction are discussed [3]. Particular attention will then be devoted to the capabilities and limitations of ESL models in the analysis of damage and failure in laminated shell structures, including the application of different failure criteria [4].

  1. E. Carrera, Compos. Struct., 50, 183–198, 2000. https://doi.org/10.1016/S0263-8223(00)00099-4
  2. A. Tessler, M. Di Sciuva, M. Gherlone, J. Mech. Mater. Struct., 5, 341–367, 2010. https://doi.org/10.2140/jomms.2010.5.341
  3. I. Kreja, A. Sabik, Acta Mech. 230, 2827–2851, 2019. https://doi.org/10.1007/s00707-019-02434-7
  4. J. Chróścielewski, A. Sabik, B. Sobczyk. W. Witkowski, Compos. Struct. 261, 1–15, 2021. https://doi.org/10.1016/j.compstruct.2020.113537


Agnieszka Sabik is an Associate Professor at Gdańsk University of Technology. Her primary expertise lies in finite element modeling, with applications spanning structural mechanics, biomechanics, and mechanobiology. Within structural mechanics, her research is particularly focused on the theoretical and computational modeling of laminated composite plates and shells, including Equivalent Single Layer (ESL) theories, refined kinematic descriptions, stability and damage and failure analysis of layered shell structures and finite elements development. Her work combines advanced mechanical modeling with efficient numerical implementations, bridging fundamental theory and engineering applications.