Keynote Lectures

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.

KEYWORDS: Residual stress, Analytical modelling, Load path, Incremental plasticity, History-dependent manufacturing processes, Laser powder bed fusion.

Residual stress plays a fundamental role in determining the structural integrity, dimensional accuracy, and fatigue performance of manufactured components. Depending on the manufacturing process, it evolves under thermal loading, mechanical loading, or their coupled interaction, making its prediction a major challenge in manufacturing science. While experimental characterization is costly and finite element analysis is computationally expensive for predictive applications, this keynote lecture presents an incremental physics-based analytical framework for predicting residual stress evolution by accounting for the entire loading history through sequential thermo-mechanical analysis. Owing to its general formulation, the framework is applicable to a broad range of manufacturing processes, including laser powder bed fusion, machining, burnishing, shot peening, and laser shock peening. The proposed methodology is demonstrated and verified through pulsed laser powder bed fusion as a representative case study, where the predicted residual stresses show good agreement with X-ray diffraction measurements.

Figure 1: Temperature history as load path for single-pulse, multi-pulse single track and multi-pulse multi-track pulsed laser powder bed fusion

ACKNOWLEDGEMENT: This work was supported by the FLAME project under Grant Agreement No. 101148340, funded by the European Research Agency through MSCA-PF program.

Dr. Hab. Eng. Reza Teimouri is a Researcher and Associate Professor of Mechanical Engineering in the field of Advanced Manufacturing. He is affiliated with the Faculty of Mechanical Engineering, Cracow University of Technology (Politechnika Krakowska im. Tadeusza Kościuszki), Poland, and is currently conducting research at Politecnico di Milano, Italy, under the Marie Skłodowska-Curie Postdoctoral Fellowship (MSCA-PF).
His research focuses on the application of computational solid mechanics to manufacturing-related processes, including additive manufacturing, machining, plastic deformation-based surface treatment, and fatigue performance assessment. His work integrates iterative-based analytical formulation and physics-enhanced machine learning approaches to establish process-structure-properties-performance relationships in engineering materials and components, which are fabricated by manufacturing processes.
Dr. Teimouri has received several prestigious international and national distinctions, including the Chinese Postdoctoral International Exchange Program Fellowship, NAWA Ulam Fellowship, the NAWA Bekker Fellowship, the Marie Skłodowska-Curie Postdoctoral Fellowship (MSCA-PF), the 2025 Award of Division IV (Technical Sciences) of the Polish Academy of Sciences (PAN), and the Scholarship for Outstanding Young Scientists (SMN 20) awarded by the Ministry of Science and Higher Education of Poland. He has also been recognized among the World's Top 2% Scientists in the annual ranking developed by Stanford University and Elsevier for five consecutive editions from 2021 to 2025.

KEYWORDS: EBM, additive manufacturing, TPMS structure, energy absorption, numerical modelling.

Cellular structures are the subject of many research works due to their high capacity to absorption mechanical energy. These meta-materials have been classified into two main groups: 2D and 3D [1]. One of the example of spatial 3D structures is Triply Periodic Minimal Surface (TPMS), which has been widely studied over last years with the most well-known architectures like diamond and gyroid structures [2].

In the present paper, the EBM method was used to produce specimens of TPMS structures, which were subsequently subjected to uniaxial compression tests under quasi-static loading conditions in order to characterize their deformation behavior and energy absorption capacity. Moreover, the material model calibration was performed in the LS-DYNA numerical environment based on the results of quasi-static uniaxial tensile tests conducted on dog-bone specimens. The purpose of this paper is to present the results of experimental and numerical studies of TPMS structures manufactured using EBM technology from Ti6Al4V titanium alloy and tested under quasi-static compression conditions for different wall thicknesses. The obtained results constitute a starting point for assessing the potential use of this type of structure as an element of a ballistic panel.

Figure 1. Deformation force vs. displacement curves from experimental test and simulations: a) Diamond structure, b) Gyroid structure.

The developed LS-DYNA numerical model accurately reproduced experimental behavior, with an overall discrepancy between numerical predictions and experiments within 6–10% for SEA. From the conducted studies it was demonstrated that gyroid structures shows progressive folding and stable plateau behavior, while diamond structures exhibits higher stiffness and peak force associated with shear-band dominated collapse. Furthermore, diamond architectures gave approximately 8% higher SEA than gyroid structures at comparable relative densities.

ACKNOWLEDGEMENT: The research was research was supported by the Military University of Technology under the research grant no: UGB: 000009-W100-22 and with the support of the Interdisciplinary center for Mathematical and Computational Modeling (ICM) of the University of Warsaw, under grant no GBE84-20. The numerical models were prepared using Altair® HyperMesh software and computed with Ansys LS-Dyna software.

1. Y. Hanfeng, Z. Wenzheng, Z. Liangcong, M. Fanbo, L. Jie, W. Guilin, Compos. Struct. 304, 116397, 2023. https://doi.org/10.1016/​j.compstruct.2022.116397
2. Z. Dong, X. Zhao, Eng. Regener. 2, 154–162, 2021. https://doi.org/10.1016/​j.engreg.2021.09.004

Lt Col Paweł Płatek, Ph.D., Eng., is an Assistant Professor at the Military University of Technology in Warsaw, Poland, and a Visiting Fellow of Mechanical Engineering at the University of Derby, UK. His research is centered on the design, manufacturing, and experimental testing of advanced regular cellular materials for energy absorption applications.

He employs Additive Manufacturing technologies (including PBF, DED, and MEX) in conjunction with experimental and numerical methods to evaluate material behavior under dynamic loading. His current research focuses heavily on applying advanced cellular structures to the development of novel, highly effective ballistic armor systems and protective materials for the defense sector.

KEYWORDS: Physical Vapor Deposition, PVD, Direct Simulation Monte Carlo, Multiscale Simulation.

Physical Vapor Deposition (PVD) is an essential industrial process characterised by the physical sputtering of a target material and the subsequent deposition of the particles onto a substrate, such as a semiconductor wafer. This technique allows for the precise control of composition, thickness, and microstructure of the deposited materials.

The optimisation of semiconductor thin films necessitates a comprehensive understanding of how macro-scale operational parameters ultimately determine the final deposited film properties. This requires a computational framework capable of resolving phenomena across an enormous dynamic range, linking the ∼50 cm scale of the entire deposition chamber (where boundary conditions are applied) through the ∼1 mm shadow mask structural dimensions and further down to feature level of ∼50 nm, where deposition spots evolve. This endeavour involves bridging approximately 9 orders of magnitude in volume.

In this talk a multiscale simulation framework (Fig. 1 left) that connects the scale of the deposition chamber with the feature scale will be presented, explicitly accounting for shadowing effects and the role of the background gas (Fig. 1 right). Rarefied transport is modelled using Direct Simulation Monte Carlo (DSMC) to obtain energy- and angle-resolved particle fluxes at the substrate, which then serve as boundary conditions for level-set based feature-scale simulations. The framework is used to analyse not only local deposition profiles and step coverage, but also the spatial evolution of film composition across the wafer and within individual features.

ACKNOWLEDGEMENT: The authors gratefully acknowledge the financial support provided by the Sächsische Aufbaubank (SAB) and the European Union for funding this research project.

1. E.E. Lorenz et al., Film Growth from Particle Raytracing: A Simulation Method for Vapor Deposition Processes with Changing Surface Topographies, IEEE Materials for Advanced Metallization Conference, Dresden, Germany, 2023, pp. 1–3, https://doi.org/10.1109/IITC/​MAM57687.2023.10154705
2. J. Gehre, Coupling between stochastic particle transport models and topographic thin film growth, Master thesis, Chemnitz University of Technology, 2022.

Dr. Tomasz Bednarek is a Senior Researcher and Project Officer at Fraunhofer ENAS and Chemnitz University of Technology, Germany. He is a computational scientist specialising in multiscale numerical modelling, scientific software development, and high-performance computing for advanced manufacturing processes.

Dr. Bednarek received his Ph.D. in Computational Mechanics from the Institute of Fundamental Technological Research of the Polish Academy of Sciences (IPPT PAN). During his career he has worked at IPPT PAN, Kazimierz Wielki University, and the European Commission's Joint Research Centre (JRC), where he led the development of advanced multiphysics simulation models for proton exchange membrane (PEM) fuel cells and designed the JRC ZERO∇CELL reference testing hardware.

His current research focuses on the computer simulation of Physical Vapor Deposition (PVD) processes for semiconductor manufacturing. He is one of the developers of the GeoSect simulation software, a multiscale computational platform for modelling thin-film growth on complex three-dimensional structures. His research combines Direct Simulation Monte Carlo (DSMC), level-set methods, and high-performance computing to bridge multiple length scales in thin-film deposition. Particular emphasis is placed on phase-change materials, including GeTe and Ge-Sb-Te alloys, for next-generation memory and neuromorphic computing applications.

Dr. Bednarek's research interests include multiscale and Multiphysics modelling, computational materials science, semiconductor process simulation, thin-film deposition, rarefied gas dynamics, finite element methods and computational fluid dynamics, and scientific computing for advanced manufacturing.

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.

KEYWORDS: Chemical bonding, contact mechanics, coupled problems, implant osseointegration, nonlinear finite element analysis.

This work presents a general contact formulation for coupled chemical, mechanical and thermal contact. It is derived from the balance laws of mass, momentum and energy at the contact interface, thus exposing the general coupling between the different fields [1]. Chemical bonding and debonding is assumed to occur between bonding sites following a kinetic reaction equation. A quadratic contact potential is used to describe the free energy of contact, bonding and debonding. The proposed formulation corresponds to the known thermomechanical contact equations [2] extended to chemical contact, see Fig. 1.

Figure 1. Thermo-chemo-mechanical contact [1]: Bodies in contact with their chemical, mechanical and thermal contact fields (left). Exemplary evolution of the contact bonding state for various initial conditions (right).

The formulation is discretized and implemented in the 3D nonlinear finite element framework of [3] using a fully monolithic coupling formulation. Implicit time integration is used of the chemical and thermal evolution equations. The formulation is illustrated by several applications. A particular focus is placed on implant osseointegration [4] and thermo-chemo-mechanical bonding.

1. R.A. Sauer, T.X. Duong and K.K. Mandadapu, A chemo-mechano-thermodynamical contact theory for adhesion, friction and (de)bonding reactions, Math. Meth. Solids., 27(4):711–745, 2022.
2. T.A. Laursen, Computational Contact and Impact Mechanics: Fundamentals of modeling interfacial phenomena in nonlinear finite element analysis, Springer, Berlin, 2002.
3. R.A. Sauer, and L. De Lorenzis, An unbiased computational contact formulation for 3D friction, Int. J. Numer. Meth. Engng., 101(4):251–280, 2015.
4. K. Immel, V.-H. Nguyen, G. Haïat and R.A. Sauer, Modeling the debonding process of osseointegrated implants due to coupled adhesion and friction, Biomech. Model. Mechanobiol., 22:133–158, 2023.

Prof. Dr. Roger A. Sauer heads the Institute of Structural Mechanics at Ruhr University Bochum, Germany, since 2024. Before this he held professor positions at Gdansk University of Technology, Poland, IIT Kanpur, India, and RWTH Aachen University, Germany. His research focuses on developing advanced theories and computational methods for structural mechanics, contact and related multifield problems. Dr. Sauer was awarded an Emmy-Noether fellowship from the German Research Foundation (2009), he was member of the Junges Kolleg of the North-Rhine-Westphalian Academy of the Sciences and Arts (2012-2014), he was a J. Tinsley Oden fellow at ICES at the University of Texas at Austin (2016), and he is honorary professor at IIT Guwahati since 2021. He has supervised more than 25 PhD students and post-docs, (co)authored 11 book chapters and 106 peer-reviewed journal publications and has a current h-index of 33 (according to Scopus).

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).

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.

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.

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).

KEYWORDS: Geometric Nonlinearities, Multistable Structures, Nonlinear Dynamics, Energy Harvesting.

Growing demand for self-powered sensors and autonomous monitoring systems has increased the need for robust vibration energy harvesters capable of operating under broadband and variable excitation (in both frequency and amplitude). However, classical linear resonant harvesters, such as cantilever beams or plates, suffer from narrow bandwidth and high sensitivity to frequency detuning, limiting their effectiveness in realworld conditions. To address these limitations, nonlinear approaches can be exploited, including nonlinear resonances, parameter tuning, and multistable designs. In this context, orthotropic multistable shells proposed in [1], characterized by one-sided clamped boundary conditions are promising. The shell mid-surface is defined in the \((x_1,x_2,x_3)\) domain using two pseudo-radii \(r_0(x_1 = 0)\) and \(r_f (x_1 = L_1)\), see Fig. 1 and Eq. (1).

Figure 1. The shell geometry definitions (left), stable configurations for prototype A (center), and prototype B (right).

\begin{equation} w_0(x_1,x_2) = \left[\frac{1}{r_0}+\left(\frac{1}{r_f}-\frac{1}{r_0}\right)\frac{x_1}{L_1} \right] \frac{x^2_2}{2},\quad\\ 0 \leq x_1 \leq L_1, \quad -\frac{1}{2}L_2 \leq x_2 \leq \frac{1}{2}L_2. \end{equation}

Energy harvesting from an MFC patch embedded in a bistable shell of type A \( (r_0 = 0.1045 \text{m}, r_f = 0.08493 \text{m}, L_1 = 0.18 \text{m}, L_2 = 0.15 \text{m}) \) is experimentally investigated [2]. The structure exhibit two distinct configurations I and C with significantly different natural frequencies in the linear regime. For moderate response amplitudes, the system shows nearly linear behavior in configuration C and pronounced softening behavior in the configuration I during in-well oscillations. At higher amplitudes, reversible snap-through transitions occur, significantly enhancing energy harvesting performance. In the second case, nonlinear dynamics and energy harvesting performance of a pentastable shell of type B \( (r_0 = 0.114 \text{m}, r_f = -0.07 \text{m}, L_1 = 0.45 \text{m}, L_2 = 0.15 \text{m}) \) are presented [3]. The latter sheds the light on effective placement of a piezoelectric transducer location based on criteria: stress distribution, strain distribution, frequency bandwidth, excitation framework and MFC patch integration in the structure. The results are summarized in maps of RMS power versus excitation frequency, highlighting the advantages of cross-well oscillations. A reduced-order model capturing both local and global dynamics of the multistable structure, including the piezoelectric coupling, is currently under development.

ACKNOWLEDGEMENT: This research was funded in whole or in part by National Science Centre, Poland 2021/41/B/ST8/03190.

1. M. Brunetti, A. Vincenti, S. Vidoli, Int. J. Solids Struct 194, 388–397, 2018. https://doi.org/10.1016/​j.compstruct.2018.04.009
2. A. Mitura, M. Brunetti, L. Kloda, F. Romeo, J. Warminski, Mech. Syst. Signal Process 206, 110890, 2024. https://doi.org/10.1016/​j.ymssp.2023.110890
3. L. Kloda, Mech. Syst. Signal Process 244, 113825, 2026. https://doi.org/10.1016/​j.ymssp.2025.113825

Łukasz Kłoda is an Assistant Professor at the Lublin University of Technology (LUT), Lublin, Poland. He received his PhD in Civil, Environmental and Building Engineering and Architecture from the Polytechnic University of Marche, Ancona, Italy, in March 2020. His doctoral dissertation, Coupled Longitudinal–Transversal Vibrations of Nonlinear Planar Timoshenko Beams with an Axial End Spring, was awarded the Doctor Europaeus distinction.

His research interests include nonlinear dynamics, nonlinear vibrations and stability of continuous structures, particularly beams and composite shells, with an emphasis on multistable and morphing structures, nonlinear modal interactions, energy harvesting, and reduced-order modeling. His work integrates analytical, numerical, and experimental approaches, including asymptotic methods, particularly the Multiple Time Scales Method, finite element modeling, and experimental modal analysis.

Dr. Kłoda is the author or co-author of over 25 peer-reviewed scientific publications (ORCID: 0000-0001-7029-5885). He actively collaborates with research institutions and groups in Italy and Bulgaria on topics related to nonlinear structural dynamics. He is a member of the Dynamics Section of the Committee of Mechanics of the Polish Academy of Sciences (PAN) and the Lublin Branch of the Polish Society of Theoretical and Applied Mechanics (PTMTS). In recognition of his scientific achievements, Dr. Kłoda received the Second Scientific Award of the Committee of Mechanics of the Polish Academy of Sciences, named after Professor Michał Życzkowski.

KEYWORDS: Semi-Active Modal Control, Lockable Joints, Modal Energy Transfer, Robust Vibration Control, Experimental Validation, Model Updating.

Vibration remains one of the key challenges across mechanical engineering, motivating ongoing advances in damping and control. Since dissipated energy is typically lost as heat, recent research increasingly explores the integration of vibration suppression with energy harvesting [1].

This work proposes a semi-active modal control strategy that enables precise energy transfer between selected vibration modes by locking or unlocking rotational joints (see: Fig. 1a), effectively switching the structural stiffness. This induces modal coupling and imposes directed energy flow. Such an approach can be employed for two functional objectives: damping, by shifting energy from low-frequency modes to higher, more strongly damped ones (see: Fig. 1b), and energy harvesting, by concentrating energy in a target mode tuned to a harvester. The approach shows excellent performance in simulations and experiments [2]. Here, the focus is placed on robustness with respect to modeling errors, demonstrating that the controller remains effective despite substantial stiffness deviations. Experimental results are compared with those obtained using a finely calibrated model with 17 adjusted stiffness parameters.

Results demonstrate that, despite substantial changes in natural frequencies (up to 80 %) due to stiffness errors in the model used by the controller, the control performance is nearly the same as for the controller based on the calibrated model. Due to these advantages and the high control performance, the proposed control strategy has broad applicability to real engineering structures and is robust to changes in structural properties caused by operational wear.

1. T. Yang, S. Zhou, G. Litak, X Jing, Recent advances in correlation and integration between vibration control, energy harvesting and monitoring. Nonlinear Dyn. 111, 20525–20562, 2023. https://doi.org/10.1007/​s11071-023-08999-2
2. M. Ostrowski, Semi-Active Control of Energy Transfer Between Vibration Modes in Mechanical Structures, Institute of Fundamental Technological Research, Polish Academy of Sciences, IPPT Reports 2/2025. https://doi.org/10.24423/​9788365550644

Dr. Mariusz Ostrowski is an Assistant Professor at the Institute of Fundamental Technological Research, Polish Academy of Sciences (IPPT PAN). He is affiliated with the Department of Intelligent Technologies and focuses on structural control, structural health monitoring, model updating, optimal sensor placement, vibration-based energy harvesting, and computer vision. He received his PhD with distinction in Mechanical Engineering from IPPT PAN in 2025. He was awarded the Third Award of the Committee on Mechanics of the Polish Academy of Sciences for his scientific achievements. In 2022 he placed sixth in “The 2nd International Competition for Structural Health Monitoring” (IC-SHM 2021), organized by five international universities and featuring 167 teams from 20 countries. He has also worked on modeling electromechanical systems and industrial multiphysics problems using MATLAB and similar tools. His interest in structural dynamics and control began during his undergraduate and master's studies at Lublin University of Technology (2011–2016) and continues to the present.

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.