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.

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.

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.

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 G_c independent of mode-mixity.
2. Again that of a mode I+III loading, but with a mode-mixity-dependent G_c .
3. That of a general mixed-mode I+II+III loading, with a mode-mixity-dependent G_c .

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)

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.