arXiv subjects

Nikolaos Bouklas

Publications and source records attributed to Nikolaos Bouklas.

At least 19 recordsLinked to original sources

arXiv2026

Mixture of Polyconvex Neural Potentials for Parametric Hyperelasticity: Towards Foundation Material Models

Hyperelastic constitutive models enable modeling large deformations in elastic solids. In common practice, a strain energy density function is prescribed in advance and model-specific parameters are calibrated from experiments. However, many applications require constitutive models for a family of related materials whose mechanical behavior varies with composition. A fixed constitutive model-form may not capture the full range of behavior across the family, while fitting separate forms does not provide a direct way to predict the response of new compositions. Recent work has developed data-driven constitutive models that learn flexible strain energy functions while incorporating key physical constraints. In this work, we propose using mixtures of convex neural potentials based on input convex neural networks as a modular and data efficient approach to modeling material families. Each potential is convex and monotonic with respect to polyconvex strain invariants, while a conditioning network maps material descriptors to mixture weights. We compare the approach with a monolithic partially input-convex neural network using experimental data from PolyJet 3D-printed materials and a synthetic Gent-type benchmark. Across both benchmarks, the mixture architecture generalized better to material descriptors not seen during training. In the PolyJet experimental benchmark, we showed that the mixture architecture is less sensitive to model hyperparameters, while in the Gent-type benchmark it generalized more reliably with sparse data in the material-descriptor space. These results suggest that representing a material family through a small set of shared convex neural potentials provides a useful structural prior for learning descriptor-dependent constitutive behavior from limited data.

physics.comp-ph↗

arXiv2026

Read, Write, Relax: Why Neural PDE Surrogates Need Both Global and Local Processing

Recent mesh-based simulation advances have, in no small part, relied on neural surrogates of two distinct families: global models that route information through a small set of latent tokens, and local models that perform message passing across mesh edges. Consistent with both classes is the inability to perform beyond low-dimensional problems and small-scale or oversimplified meshes, the simulation regimes where industrial problems reside. Our work shows this explicitly and presents a unified formulation. In global approaches, latent-token attention acts as a spatial low-pass filter, while local message passing lacks the global reach necessary to propagate information across large mesh spaces. Viewed through the error, the two operators are the halves of a multigrid cycle: one corrects errors at the lower end of the spectrum, the other at the higher end, and neither can do the other's job. We introduce Read-Write-Relax (RWR), which interleaves latent attention with message-passing relaxation under a unified formulation. The interleaved processor lowers error across the entire spectrum, making RWR the most accurate model in nearly every comparison across our industrial and public benchmarks. It is also markedly data-efficient in the scarce-data regimes, accurate on the engineering quantities of interest, and scales full-field predictions to challenging, large-scale problems.

cs.LG↗

arXiv2026

Interval and fuzzy physics-augmented neural networks (iPANN and fPANN) for uncertainty quantification and propagation in constitutive modeling

Constitutive modeling under uncertainty remains a central challenge for reliable mechanics simulations, particularly when the available stress-deformation data are sparse, noisy, or heterogeneous. We propose interval and fuzzy physics-augmented neural networks (iPANNs and fPANNs) for uncertainty-aware hyperelastic constitutive modeling. iPANNs learn sparse lower, mean, and upper free energy density branches whose stresses, obtained by automatic differentiation, ultimately enclose noisy stress observations. In contrast to this deterministic interval description, fPANNs embed the learned iPANN branches into a fuzzy-set representation through alpha-cut interpolation, yielding a nested family of admissible responses. iPANNs and fPANNs encode mechanistic constraints - preserving objectivity, consistency and promoting polyconvexity - and smoothed L0 regularization promotes interpretable energy representations. The bound models are trained through a two-stage transfer-learning procedure in which a sparse mean constitutive response is learned first and then fine-tuned into lower and upper energy branches. We evaluate the framework on synthetic isotropic hyperelastic data with heteroscedastic noise, varying random realizations, shifted noise means, and varying noise magnitudes. The results show that the learned bounds enclose noisy stress observations while generalizing to the test set. Further, we examine the propagation of uncertainty through the mean, upper and lower bound predictions of the learned iPANN models in a finite element setting. The proposed framework provides a compact, physics-consistent route for distribution-free aleatoric uncertainty quantification in hyperelastic constitutive modeling, and propagation in downstream finite element simulations.

cs.LG↗

arXiv2026

Towards end-to-end optimization in multimaterial 3D printing

Multimaterial 3D printing enables the fabrication of functionally graded components, but optimizing their spatial material distribution alongside structural topology remains a formidable challenge due to high-dimensional design spaces and complex constitutive modeling. This paper presents an end-to-end computational framework integrating sparsified physics-augmented neural networks with finite-element-based topology optimization. By extracting closed-form, composition-aware hyperelastic constitutive laws from experimental data, this approach facilitates exact symbolic differentiation via the adjoint state method implemented with FEniCSx, efficiently circumventing the bottlenecks of applying neural network constitutive models. This pipeline is deployed on soft robotic gripper applications, demonstrating continuous composition optimization for highly anisotropic contact responses, and the concurrent optimization of macroscopic topology and material distribution under non-failure stretch constraints. This methodology could replace laborious empirical prototyping, establishing interpretable machine-learning models as practical, robust design primitives for advanced multimaterial additive manufacturing.

physics.comp-ph↗

arXiv2026

How do 3M Command strips work? A fracture mechanics approach

Removable adhesive systems such as 3M Command strips are designed to support substantial loads while allowing clean, damage-free removal from the substrate. These systems rely on a highly extensible adhesive strip that bonds strongly during use but releases when stretched, causing the adhesive layer to elongate and progressively debond from the surfaces. A central challenge in the design of stretch-release adhesives is therefore to maximize load-bearing capacity while minimizing the force required for removal. This study investigates the finite-deformation mechanics governing both load support and tape release in a hyperelastic stretch-release adhesive system, with particular focus on the 3M Command tape geometry. Explicit analytical expressions are derived for the energy release rate of interfacial cracks under both load-bearing and release conditions and are validated against $J$-integral evaluations from finite element simulations. The results show that the ratio of maximum supported load to release force scales linearly with the ratio of bonded length to adhesive thickness, which is typically very large. We also investigate geometry-driven alternating crack propagation between the backing and substrate interfaces, governing tape removal, by analytical solutions and simulations. Parametric studies of competing interfacial fracture toughnesses produce failure envelopes that provide a predictive framework for estimating release forces and unstable crack propagation in multilayer stretch-release adhesive systems.

cond-mat.soft↗

arXiv2026

Courant: a State-Adaptive Perceiver-Based Neural Surrogate with Local Support and Interpretable Field Decomposition

We introduce "Courant", a Perceiver-based encoder-processor-decoder surrogate model that has latent features exhibiting adaptive specialization and local support in the physical space, enabling functionality akin to an adaptive hp-refinement scheme, an attribute that is highly desirable in traditional numerical solvers and scientific machine learning broadly. The proposed architecture combines a shared random Fourier feature coordinate embedding, state-adapted latent queries, and a light-weight decoder. Courant is trained end-to-end with steady or transient simulation data and only a standard L_2 prediction loss in the physical space, achieving competitive accuracy on benchmarks. We demonstrate that Courant's inductive biases yield latents that are interpretable by design: they develop multiscale geometric specialization in the simulation domain and track coherent structures in the time-dependent case, acting analogously to time-evolving spatial basis functions and allowing for decoding a compact, geometry-anchored, partition-of-unity-like decomposition of the simulated field.

cs.LG↗

arXiv2026

Influence of Heterogeneity on the Response of Architected Metamaterials

Architected metamaterials like foams and lattices exhibit complex responses governed by microstructural instabilities, localization, and phase-transition-like phenomena. Their behavior is further affected by heterogeneities inherent in their microstructure often caused through manufacturing processes. In this study we extend a gradient-enhanced, nonlocal continuum formulation to incorporate stochastic material heterogeneity through Gaussian random fields imposed on selected constitutive parameters. The framework enables independent control of both the amplitude and spatial correlation of material fluctuations while preserving thermodynamic consistency and regularization of localization. It also introduces a characteristic lengthscale ratio between the nonlocal and correlation lengthscales, that enables modeling at the limit of random or spatially correlated microstructures. Finite element simulations of confined compression and indentation show that heterogeneity fundamentally alters phase nucleation, localization morphology, and macroscopic response. Overall, the proposed framework provides a unified approach for linking stochastic material variability to instability-driven mechanics in architected metamaterials, enabling improved understanding of imperfection sensitivity, stability and design. It showcases how heterogeneity alone can influence characteristic features of the response, such as stability, slope of the plateau region, and elimination of the initial elastic regime.

cond-mat.mtrl-sci↗

arXiv2026

Towards Rapid Constitutive Model Discovery from Multi-Modal Data: Physics Augmented Finite Element Model Updating (paFEMU)

Recent progress in AI-enabled constitutive modeling has concentrated on moving from a purely data-driven paradigm to the enforcement of physical constraints and mechanistic principles, a concept referred to as physics augmentation. Classical phenomenological approaches rely on selecting a pre-defined model and calibrating its parameters, while machine learning methods often focus on discovery of the model itself. Sparse regression approaches lie in between, where large libraries of pre-defined models are probed during calibration. Sparsification in the aforementioned paradigm, but also in the context of neural network architecture, has been shown to enable interpretability, uncertainty quantification, but also heterogeneous software integration due to the low-dimensional nature of the resulting models. Most works in AI-enabled constitutive modeling have also focused on data from a single source, but in reality, materials modeling workflows can contain data from many different sources (multi-modal data), and also from testing other materials within the same materials class (multi-fidelity data). In this work, we introduce physics augmented finite element model updating (paFEMU), as a transfer learning approach that combines AI-enabled constitutive modeling, sparsification for interpretable model discovery, and finite element-based adjoint optimization utilizing multi-modal data. This is achieved by combining simple mechanical testing data, potentially from a distinct material, with digital image correlation-type full-field data acquisition to ultimately enable rapid constitutive modeling discovery. The simplicity of the sparse representation enables easy integration of neural constitutive models in existing finite element workflows, and also enables low-dimensional updating during transfer learning.

cs.LG↗

arXiv2026

Rethinking failure in polymer networks: a probabilistic view on progressive damage

The mechanics of single-chain stretching and rupture are central to understanding the resilience of biological polymers and designing strong and tough soft materials such as double-network gels and multi-network elastomers. In this work, we develop a statistical mechanics based model that enables one to determine the distribution of forces along the chain segments. By combining the force distribution with a tilted bond potential that captures the stretch energy stored in these bonds, we calculate the corresponding activation energy required for bond dissociation. This allows us to determine the probability of bond (and consequently chain) failure. The proposed approach is simple, direct, and readily adaptable for constructing higher-level coarse-grained descriptions of damage and fracture in polymer networks. We demonstrate this by applying the theory to two problems of practical interest: (1) toughening networks via sacrificial bond rupture in polymer chains and (2) incorporation of the local chain model into a 3-dimensional constitutive relation that captures damage in elastomers. The latter was implemented through the micro-sphere framework, which accounts for different chain orientations, as well as the computationally inexpensive eight chain model. The findings from this work provide a physically-based model to quantify the stretching and failure of a single chain and pave the way to the integration of local damage models into 3-dimensional networks.

cond-mat.soft↗

arXiv2026

Modeling cavitation and fibrillation in elastomers and adhesives. Part I: Cohesive instability

Cavitation in soft elastomers and adhesives is often viewed as an elastic instability, commonly tied to the study of incompressible solids. It is the first step prior to fibrillation and ultimate failure in adhesives. Building on the work of Lamont et al. (2025), elastomeric materials are treated as a crosslinked van der Waals fluid. The van der Waals contribution, capturing excluded volume and cohesive forces, is non-(poly)convex, readily providing an intrinsic analytical criterion for cavity nucleation. This work introduces a gradient-enhanced continuum framework that examines the emergence of cavity formation from the perspective of a cohesive instability and corresponding phase transition without requiring a pre-existing defect. The corresponding thermodynamically consistent derivation includes the introduction of a relevant material length scale as well as viscous dissipation associated with polymer chain disentanglement during the cohesive instability. This work does not study the impending damage that the material undergoes during the cohesive instability and transition from a dense to a rare phase. Interestingly, it is shown that for both strain stiffening and strain softening models (in terms of their shear response), an instability reminiscent of what is expected in the case of cavitation is recapitulated. Simulations reproduce key experimental trends, including the aspect ratio-driven transition from a few large to many small cavities depending on the thickness of an adhesive layer. The framework offers a robust, physically grounded basis for the cohesive instability that drives cavity nucleation, enabling future integration with damage, fracture, and dissipation models to capture the complete cavitation, fibrillation, and failure process.

cond-mat.soft↗

arXiv2025

Instabilities and Phase Transformations in Architected Metamaterials: a Gradient-Enhanced Continuum Approach

Architected metamaterials such as foams and lattices exhibit a wide range of properties governed by microstructural instabilities and emerging phase transformations. Their macroscopic response--including energy dissipation during impact, large recoverable deformations, morphing between configurations, and auxetic behavior--remains difficult to capture with conventional continuum models, which often rely on discrete approaches that limit scalability. We propose a nonlocal continuum formulation that captures both stable and unstable responses of elastic architected metamaterials. The framework extends anisotropic hyperelasticity by introducing nonlocal variables and internal length scales reflective of microstructural features. Local polyconvex free-energy models are systematically augmented with two families of non-(poly)convex energies, enabling both metastable and bistable responses. Implementation in a finite element framework enables solution using a hybrid monolithic--staggered strategy. Simulations capture densification fronts, forward and reverse transformations, hysteresis loops, imperfection sensitivity, and globally coordinated auxetic modes. Overall, this framework provides a robust foundation for accelerated modeling of instability-driven phenomena in architected materials, while enabling extensions to anisotropic, dissipative, and active systems as well as integration with data-driven and machine learning approaches.

physics.comp-ph↗

arXiv2025

Capturing the fractocohesive length scale through a gradient-enhanced damage model for elastomers

This study aims to unravel the micro-mechanical underpinnings of the emergence of the fractocohesive length scale as a central concept in modern fracture mechanics. A thermodynamically consistent damage and fracture model for elastomers is developed, incorporating elements of polymer chain statistical mechanics. This approach enables the direct incorporation of polymer chain response into a continuum gradient enhanced damage formulation, that in turn allows a physically meaningful description of diffuse chain damage and corresponding fracture events. Through a series of numerical experiments, we simulate crack propagation and extract the fracture energy as an output of the model, while keeping track of the micromechanical signatures of diffuse chain damage that accommodate fracture propagation. Furthermore, we investigate flaw sensitivity and demonstrate that when flaw sizes are smaller than a critical length scale, the material response becomes largely insensitive to notch size. Finally, by combining the fracture toughness and the work to rupture, we identify a fractocohesive length of the material, corresponding to the full width of the damage zone and representing the region where the irreversible dissipation process (i.e., bond scission) is happening. As this region is dictated in the proposed FED model through the introduction of a length scale associated with the non-local nature of the damage and fracture process, the emerging relationship of the two length scales is discussed, effectively connecting the microscopic characteristics of damage to the effective macroscopic response.

cond-mat.soft↗

arXiv2025

The effect of fiber plasticity on domain formation in soft biological composites -- Part II: An imperfection analysis

The main objective of this work is to numerically investigate the effect of geometric imperfections on the macroscopic response and domain formation in soft biological composites that exhibit plasticity in the stiff (fiber) phase.This work builds on the corresponding bifurcation analysis in Part I of this study for simple laminates with perfectly flat layers under plane strain, nonmonotonic loading conditions, aligned with the layer direction. The post-bifurcation solution obtained in Part I for these materials corresponds physically to the formation of twin lamellar domains perpendicular to the loading axis, which is consistent with the chevron like deformation patterns that develop in tendons under cyclic loading. As biological materials are highly imperfect, and specifically tendons exhibit a high degree of so called crimp in the collagen fibers, in this study the effect of imperfections to the response is explored. For all composites with small initial imperfections that have been considered, the results of this work have been found to be in complete agreement with the corresponding analytical results of Part I, and, domains have been found to emerge at a macroscopically compressive state. However, as the imperfection amplitude is increased and becomes of the order to the layer width, or greater, domains begin to develop at macroscopically tensile stresses, which is in agreement with the fact that the loading of soft biological materials such as tendons and ligaments is tensile in nature. Thus, the findings of this work suggest strongly that plasticity and geometric imperfections of collagen fibers may play a key role on the onset and evolution of domains in actual soft biological composites.

cond-mat.soft↗

arXiv2025

The effect of fiber plasticity on domain formation in soft biological composites -- Part I: a bifurcation analysis

The main objective of this work is to shed light on the effect of fiber plasticity on the macroscopic response and domain formation in soft biological composites. This goal is pursued by analyzing the plane-strain response of two-phase laminates. In the context of this problem, the effect of fiber plasticity is accounted for by allowing the elastically stiffer layers (``fiber'' phase) to also yield plastically and by taking the soft layers (``matrix'' phase) to be purely elastic solids. The analysis is carried out at finite elastic and plastic strains, but it is restricted to unidirectional, non-monotonic loading paths, applied by initially increasing the macroscopic stretch along the direction of the layers up to a prescribed maximum value and then decreasing the same stretch down to a minimum value. A simple expression is derived for the critical conditions at which the homogenized behavior of the laminate loses strong ellipticity for the first time along the loading path. The relevance of this result stems from the fact that the loss of macroscopic ellipticity of these composites is known to coincide with the onset of bifurcations of the long-wavelength type. It follows from this result that, just like hyperelastic laminates, elastoplastic laminates may lose macroscopic ellipticity whenever their incremental strength in shear perpendicular to the layers vanishes for the first time. For situations in which loss of macroscopic ellipticity does take place, a corresponding post-bifurcation solution for the homogenized behavior of the laminate is computed. The deformed state of the material described by this solution is characterized by twin lamellar domains that are formed at a length scale much larger than the width of the original, microscopic layers, but still much smaller than the overall dimensions of the macroscopic specimen under consideration.

cond-mat.soft↗

arXiv2025

Physics Augmented Machine Learning Discovery of Composition-Dependent Constitutive Laws for 3D Printed Digital Materials

Multi-material 3D printing, particularly through polymer jetting, enables the fabrication of digital materials by mixing distinct photopolymers at the micron scale within a single build to create a composite with tunable mechanical properties. This work presents an integrated experimental and computational investigation into the composition-dependent mechanical behavior of 3D printed digital materials. We experimentally characterize five formulations, combining soft and rigid UV-cured polymers under uniaxial tension and torsion across three strain and twist rates. The results reveal nonlinear and rate-dependent responses that strongly depend on composition. To model this behavior, we develop a physics-augmented neural network (PANN) that combines a partially input convex neural network (pICNN) for learning the composition-dependent hyperelastic strain energy function with a quasi-linear viscoelastic (QLV) formulation for time-dependent response. The pICNN ensures convexity with respect to strain invariants while allowing non-convex dependence on composition. To enhance interpretability, we apply $L_0$ sparsification. For the time-dependent response, we introduce a multilayer perceptron (MLP) to predict viscoelastic relaxation parameters from composition. The proposed model accurately captures the nonlinear, rate-dependent behavior of 3D printed digital materials in both uniaxial tension and torsion, achieving high predictive accuracy for interpolated material compositions. This approach provides a scalable framework for automated, composition-aware constitutive model discovery for multi-material 3D printing.

cs.LG↗

arXiv2025

Multiphysics Modeling of Surface Diffusion Coupled with Large Deformation in 3D Solids

We present a comprehensive theoretical and computational model that explores the behavior of a thin hydrated film bonded to a non-hydrated / impermeable soft substrate in the context of surface and bulk elasticity coupled with surface diffusion kinetics. This type of coupling can manifests as an integral aspect in diverse engineering processes encountered in optical interference coatings, tissue engineering, soft electronics, and can prove important in design process for the next generation of sensors and actuators, especially as the focus is shifted to systems in smaller lengthscales. The intricate interplay between solvent diffusion and deformation of the film is governed by surface poroelasticity, and the viscoelastic deformation of the substrate. While existing methodologies offer tools for studying coupled poroelasticity involving solvent diffusion and network deformation, there exists a gap in understanding how coupled poroelastic processes occurring in a film attached to the boundary of a highly deformable solid can influence its response. In this study, we introduce a non-equilibrium thermodynamics formulation encompassing the multiphysical processes of surface poroelasticity and bulk viscoelasticity, complemented by a corresponding finite element implementation. Our approach captures the complex dynamics between the finite deformation of the substrate and solvent diffusion on the surface. This work contributes valuable insights, particularly in scenarios where the coupling of surface diffusion kinetics and substrate elasticity is an important design factor.

cond-mat.soft↗

arXiv2025

A chain stretch-based gradient-enhanced model for damage and fracture in elastomers

In this study, we introduce a novel stretch-based gradient-enhanced damage (GED) model that allows the fracture to localize and also captures the development of a physically diffuse damage zone. This capability contrasts with the paradigm of the phase field method for fracture, where a sharp crack is numerically approximated in a diffuse manner. Capturing fracture localization and diffuse damage in our approach is achieved by considering nonlocal effects that encompass network topology, heterogeneity, and imperfections. These considerations motivate the use of a statistical damage function dependent upon the nonlocal deformation state. From this model, fracture toughness is realized as an output. While GED models have been classically utilized for damage modeling of structural engineering materials, they face challenges when trying to capture the cascade from damage to fracture, often leading to damage zone broadening. This deficiency contributed to the popularity of the phase-field method over the GED model for elastomers and other quasi-brittle materials. Other groups have proceeded with damage-based GED formulations that prove identical to the phase-field method (Lorentz et al., 2012), but these inherit the aforementioned limitations. To address this issue in a thermodynamically consistent framework, we implement two modeling features (a nonlocal driving force bound and a simple relaxation function) specifically designed to capture the evolution of a physically meaningful damage field and the simultaneous localization of fracture, thereby overcoming a longstanding obstacle in the development of these nonlocal strain- or stretch-based approaches. We discuss several numerical examples to understand the features of the approach at the limit of incompressibility, and compare them to the phase-field method as a benchmark for the macroscopic response and fracture energy predictions.

cond-mat.soft↗

arXiv2024

Condensed Stein Variational Gradient Descent for Uncertainty Quantification of Neural Networks

We propose a Stein variational gradient descent method to concurrently sparsify, train, and provide uncertainty quantification of a complexly parameterized model such as a neural network. It employs a graph reconciliation and condensation process to reduce complexity and increase similarity in the Stein ensemble of parameterizations. Therefore, the proposed condensed Stein variational gradient (cSVGD) method provides uncertainty quantification on parameters, not just outputs. Furthermore, the parameter reduction speeds up the convergence of the Stein gradient descent as it reduces the combinatorial complexity by aligning and differentiating the sensitivity to parameters. These properties are demonstrated with an illustrative example and an application to a representation problem in solid mechanics.

cs.LG↗