Scipedia: XVIII International Conference on Computational Plasticity (COMPLAS 2025)

Recent advances in the development of reliable neural simulators based on graph architectures

Jesús Sánchez Pinedo — Thu, 09 Oct 2025 10:46:59 +0200

Of all the contributions that AI is making to computational mechanics, the possibility of developing learned simulators is one of the most interesting. Of course, there is a whole ecosystem of techniques that can be used for this purpose, but the use of geometric deep learning is perhaps one of the most promising. Of particular interest is the so-called graph neural network architecture, since traditional finite element meshes can themselves be considered a graph. Thus, it is very convenient to train such architectures with synthetic data obtained by high-fidelity simulation. As will be seen in our presentation, graph networks (possibly informed by physics) allow a very high degree of generalization, as well as the level of accuracy they provide. In this talk we will show details about the inner workings of such networks, particularly the message passing scheme, and we will see how reliable they are for use in problems involving plasticity.

Variational Phase-Field Modeling of Fracture: Towards Second-Generation Models

Jesús Sánchez Pinedo — Thu, 09 Oct 2025 11:04:55 +0200

Strain ageing phenomena in metallic alloys: Experiments and modelling

Jesús Sánchez Pinedo — Thu, 09 Oct 2025 11:10:29 +0200

Static and dynamic strain ageing phenomena induced by the interaction between dislocations and solute atoms, are ubiquitous in engineering metallic alloys. In Nickel-based superalloys used for turbine disks in jet engines, negative strain rate sensitivity is observed at service tempature and results in the devlopment of Portevin-Le Chatelier bands. A viscoplastic constitutive model will be presented which captures the serrations in tensile notch samples and biaxial tension specimens. Finite element simulations then show the impact of DSA on the burst of turbine disks [1]. Static strain ageing is associated to the formation of L¨uders bands in steel sheets. We illustrate the impact of their propagation on the viscoplastic behaviour of zinc coatings on galvanized steel sheets, by means of crystal plasticity applied to zinc grains

AI-accelerated computational multiscale modeling

Jesús Sánchez Pinedo — Thu, 09 Oct 2025 11:17:44 +0200

Multiscale modeling is the branch of computational mechanics that has suffered from the limits imposed by computational costs probably the most, owing to computations being performed on more than one scale. Consequently, the use of machine learning (ML) methods to bypass costly lower-scale or scale-bridging simulations has tremendous potential to accelerate multiscale modeling and provide new opportunities for simulating the complex mechanics of materials and structures. We will discuss a few recent applications of ML to the field of computational mechanics, all united by the ambition to accelerate simulations across scales. One example is ML-based surrogate material modeling to bypass expensive material point calculations, e.g., by using Recurrent Neural Operators (RNOs) as surrogates for computationally expensive constitutive laws. This is demonstrated for finite-strain crystal plasticity models for magnesium, which are typically too expensive to be used in a multiscale setting. Similarly, FE2 simulations can be considerably accelerated when replacing the microscale boundary value problem by an efficient ML-based surrogate model [1] – as we will show for multiscale simulations of beam-based metamaterials, accelerated by a Kolmogorov-Arnold (KAN) network. Another example are constitutive artificial neural networks for architected materials, which learn the complex constitutive response as a function of the underlying structural architecture [2] for use as surrogate models in macroscale boundary value problems. Overall, we demonstrate how the integration of the principles of mechanics and thermodynamics with ML tools can result in (sufficiently) accurate and efficient AIaccelerated solutions for computational multiscale modeling. We close by highlighting the potential of such tools also for design optimization, e.g., of architected materials.

Recent developments in detecting and localizing weaknesses in structures for high-fidelity digital twins

Jesús Sánchez Pinedo — Thu, 09 Oct 2025 11:21:35 +0200

Given that all materials exposed to the environment and/or undergoing loads eventually age and fail, the task of trying to detect and localize weaknesses in structures is common to many fields. Traditionally, manual inspection was the only way of carrying out this task, aided by ultrasound, X-ray, or vibration analysis techniques. The advent of accurate, abundant and cheap sensors, together with detailed, high-fidelity computational models in an environment of digital twins has opened the possibility of enhancing and automating the detection and localization of weaknesses in structures. The procedures proposed here are based on measured forces and displacements/strains, and formulate the determination of material properties (or weaknesses) as an optimization problem for the strength factor. These procedures belong to the more general class of inverse problems where structural properties are sought based on a desired cost functional. The use of adjoint formulations and smoothing of gradients to quickly localize damaged regions makes the problem tractable. Recent developments include: extension to nonlinear materials, incorporation of uncertainty, and transient problems. Several examples show the viability, accuracy and efficiency of the proposed methodology and its potential use for high fidelity digital twins.

Front tracking with a twist: the eXtreme mesh deformation approach (X-MESH)

Jesús Sánchez Pinedo — Thu, 09 Oct 2025 11:24:12 +0200

The arbitrary Eulerian Lagrangian (ALE) formulation is a common approach for tracking fronts in finite element simulations. It is, however, difficult to track fronts over long distances because the mesh quality becomes poor on one side of the front. Moreover, traditional ALE front tracking cannot cope with changes in the front topology. To remedy the above problems (at least the first one), remeshing is required from time to time to maintain correct mesh approximation capability on both sides of the front. This remeshing requires projection of the field and updating of the database in the simulation, which is detrimental to the speed and accuracy. We introduce a new approach in which the set of nodes located on the front evolves over time allowing the front to migrate through the mesh. Topological changes are easily considered. For example, a front can nucleate, propagate and merge with other fronts as it propagates. For the new approach to work properly, we must accept that some elements become very small and possibly of zero measure. This means that the elements can deform in extreme ways, hence the acronym X-MESH. Surprisingly, as we shall show, this situation does not prevent simulations from being carried out. In short, X-MESH simply uses node movements to propagate fronts over long distances, even in the event of topological changes. The mesh topology remains unchanged during simulation. The size and sparsity of the finite element matrices are therefore fixed throughout the simulation, and no field projection is required. As the simulation progresses, nodes arrive and depart from the front. X-MESH's capability will be demonstrated for several important applications in mechanics and physics, such as front tracking in the Stefan phase change model or the simulation of immiscible two-phase flows. The work is funded by a European Research Council (ERC) Synergy Grant whose co-pI is Professor J-F. Remacle also at UCLouvain

A coupled Multiscale Model of the Human Cornea Accounting for the Collagenous Microstructure and the Extracellular Matrix

Jesús Sánchez Pinedo — Thu, 09 Oct 2025 11:28:42 +0200

The human cornea is a complex, highly specialized structure necessary for the vision function of the Eye. The cornea, due to its shape and transparency, refracts and transmits the light to the retina. Cornea's mechanical properties, critical for maintaining corneal shape and function under intraocular pressure, arise from the composition of a hydrated proteoglycan-rich extracellular matrix (ECM) reinforced by an intricate network of collagen fibrils organized into lamellae. Despite extensive research, existing biomechanical models often fall short of capturing the coupled interplay between the ECM and collagen reinforcements, especially under physiological and pathological conditions. This work seeks to address this gap by proposing a novel computational model that integrates a continuum representation of the ECM with a discrete collagencrosslinking network. The continuum approach for the ECM is chosen to represent its viscoelastic behavior and interaction with fluid flow, critical for corneal hydration and load transmission. Conversely, the collagen network is modeled as a discrete, anisotropic reinforcement system, capturing the directional stiffness imparted by the collagen fibrils and their crosslinking. The model is developed to account for the influence of enzymatic degradation, age-related changes, and disease processes such as keratoconus, where alterations in the ECM-collagen coupling are known to drive structural instability. The innovation of this approach lies in its multiscale integration, bridging the molecular mechanics of collagen crosslinking with macroscopic corneal behavior. By explicitly linking the continuum matrix with a collagen-reinforced network, the model offers some possibility to deepen our understanding of corneal mechanics. The inclusion of experimentally derived parameters for collagen alignment, crosslink density, and ECM properties, will make the model predictive in the simulation of physiological responses to intraocular pressure and external mechanical perturbations.

Recent advances in the particle finite element method for fluid-structure interactions and multi-physics problems

Jesús Sánchez Pinedo — Thu, 09 Oct 2025 12:37:25 +0200

Particle Finite Element Method (PFEM) is a still rather young discretization method that seeks to merge the advantages of the classical FEM with those of modern particle-based methods, such as SPH. To this end, PFEM is designed as a Lagrangian method that combines computations over one time step using FEM with a fast remeshing algorithm, thereby avoiding mesh distortions consequent to very large deformations, such as those encountered in fluid flow with free surfaces. The method is thus quite flexible and can be applied to both solid and fluid material behavior (see e.g. [1] as a sample of the state of the art). PFEM has proven to be a very versatile method that not only allows tracking free evolving boundaries but also take into account thermo-mechanical coupling and thus tackle more complex multi-physics problems. For instance, thanks to its Lagrangian character and its ability to automatically track evolving free surfaces and interfaces, PFEM allows handling phase change due to solidification, melting and vaporization, as well as capillary and Marangoni effects from surface tension [2]. These physical ingredients are highly valuable for simulating melt pool dynamics, for example, in the context of additive manufacturing. Multiphysics problems can lead to models that are inherently incompatible or highly difficult to combine within the same numerical implementation. In such a case, it is convenient to split the physical models and solve them separately using dedicated software. Although this approach has been used mostly to address fluid-structure interaction problems in PFEM, it has also been used to couple thermo-mechanical models, for example, in the simulation of welding processes. This work gathers recent advances in the PFEM with special attention to the incorporation of multi-physics models and their applications. In addition, numerical examples of the PFEM will illustrate fluid-structure interaction problems including contact between different solid parts and plastic deformation of some components of the system. These advances will be complemented by new remeshing proposals to further improve the PFEM strategy, which aim at reducing numerical artifacts and improving the continuity and smoothness of the free surface on which complex physical phenomena take place.

Advances and structural applications of Isogeometric Analysis

Jesús Sánchez Pinedo — Thu, 09 Oct 2025 12:41:57 +0200

Isogeometric Analysis (IGA) is a successful simulation framework originally proposed by T.J.R. Hughes et al., in 2005, with the aim of bridging Computational Mechanics and Computer Aided Design. In addition to this, thanks to the high-regularity properties of its basis functions, IGA has shown a better accuracy per degree-of-freedom and an enhanced robustness with respect to standard finite elements in many contexts - ranging from solids and structures to fluids, as well as to different kinds of coupled problems – opening also the door for the approximation in primal form of higher-order partial differential equations. After a concise introduction of the basic isogeometric concepts, this lecture aims at presenting some IGA recent advances with a special focus on interesting structural applications in several fields where the characteristics of IGA seem to be of great advantage. In particular, applications that will be discussed include the simulation of fluid-structure interaction in different situations, studies on the effect of mechanicallyinduced stresses on prostate cancer growth, thermo-mechanical simulations of additive manufacturing processes, electro-mechanical simulations for biological tissues, and the use of phase-field modeling of fracture and other problems.

Surrogate computational homogenization for inelastic composites and room for quantum acceleration strategies

Jesús Sánchez Pinedo — Thu, 09 Oct 2025 12:44:18 +0200

We have recently proposed a class of data-centric methods for computational homogenization (CH) using radial basis function (RBF) interpolation, which substitutes for the microscopic analysis for inelastic composites at small-strain and finite-strain [1,2,3]. This approach, which is referred to as RBF-based surrogate CM, has been applied to elastoplastic composite materials at small strain [1] and finite strain [2], and viscoelastic composite materials [3] to demonstrate the capability in overcoming the difficulty of conventional multiscale analysis methods. However, the computational cost of the process of obtaining the weights of RBFs by solving linear equations with the kernel matrix as coefficients is high, and this approach has been applied only to twodimensional (2D) problems. To address the problem that comes from the sheer volume of data, in this study, various measures can be taken to extend the RBF-based surrogate CH to 3D problems from a practical perspective. For example, a limited number of combinations of the six components of macroscopic strain are randomly selected on the hypersphere to perform numerical material tests to generate a set of macroscopic stresses and macroscopic strain histories. After that, the procedure should be the same as the one we have developed so far. The present study particularly focusses on a partitioned RBF interpolation with the help of decision-tree-based partitioning of the data space. Optimizing the partitioning of the hyperspace, consisting of macrostrain and historydependent variables in the input data, allows for low-cost and efficient RBF interpolation approximation. Several numerical examples are presented to demonstrate the promise and performance of the proposed method. The RBF-based surrogate model thus created can be applied to several engineering problems. For example, its convenience can be used for topology optimization, and we will also briefly discuss its potential for combination with quantum algorithms for nonlinear multiscale analysis.

Plasticity and the airframe -- aircraft structure from birth to ultimate state

Jesús Sánchez Pinedo — Thu, 09 Oct 2025 12:48:48 +0200

From the beginning of metallic airframes in the 1930's until today, it has always been required to have a thorough understanding of the plastic behaviour of aircraft structure. Nowadays, advanced models of plasticity are used along the entire design and development process: they are needed to compute the ultimate state of the structure for certification, and also to simulate the manufacturing of the often complex, double-curved components. Mastery of this chain has helped to create the safest mode of transport humankind has known so far. This talk will recap some of the history that got us to where we are today, to help understand current practice, and it will sketch future needs and possibilities. As in the past, the collaboration between academic research and the aerospace industry will continue to be the key to safety, comfort and sustainability.

Constitutive Laws as Generative Graphs and Trees

Jesús Sánchez Pinedo — Thu, 09 Oct 2025 12:57:37 +0200

This talk explores the various ways high-fidelity constitutive laws for a wide range of solids, such as soil, rock, alloys, and polymer composites, can be represented and how the choice of representations influences the accuracy, robustness, and data/computational efficiency for computer simulations of solids. To represent material models as points, we adopt a model-free approach that enables physical simulations of material behaviors without a smooth constitutive law. In this case, pointwise stress-strain pairs are selected in Gauss points of finite elements to be compatible with the conservation laws. To represent material models as meshes, we introduce a latent diffusion model where previous material models and experimental data are used to guide the reverse generation of models. This mesh-based material model is particularly efficient for non-smooth plasticity, where projection on segments can lead to significantly faster simulations. To represent material models as expression trees, we use the neural additive model in the projected space of strain measures. This technique enables us to search for hyperelasticity in high-dimensional space without sacrificing the expressivity of neural networks. We show that the proposed model may reproduce any polynomial of arbitrary orders and dimensions and thus achieve the universal approximation through the StoneWeierstrass theorem. Through a series of 1D post-hoc symbolic regressions, we obtain symbolic material models that significantly reduce the inference time for hydrocodes [1]. The pros and cons of these techniques for various practical applications will be discussed.

On the application of the virtual element method for problems with inelastic material behaviour

Jesús Sánchez Pinedo — Thu, 09 Oct 2025 12:53:34 +0200

Personalized design and reconstruction for the defect bone based on data driving and mechanics modelling

Jesús Sánchez Pinedo — Thu, 09 Oct 2025 13:01:10 +0200

Human periarticular bone defect is a difficult disease in orthopedics. There is challenge issue to recognize anisotropy, heterogeneity of bone tissue structure and graphics by low resolution clinic-CT image. In collaboration with clinical medicine, the data-driven and mechanics modeling technique for bone defect reconstruction is proposed. Data driven micro-CT and clinical-CT images are used to obtain the characteristics of cancellous bone structure and graphics. The experimental technology and numerical method are developed for predicting the mechanics parameters of animal specimen on the multi-axial stress state. The constitutive model of heterogeneous anisotropy of bone tissue is established and the parameters are deduced by Bayesian inference using the data given by numerical simulation and experiment. For designing the robust cancellous prosthesis bone, a kind of spinodal lattice is designed with random, indeterminate, aperiodic, asymmetry, irregular, large space for mechanical and biological function. The digital triplets with physical scanning CT image, virtual equivalent modulus and additive manufacturing lattice design are created to guide the clinical treatment of personalized bone defects. This work has been demonstrated in some clinical applications to the benefit of patients.