arXiv subjects

Hagen Holthusen

Publications and source records attributed to Hagen Holthusen.

At least 19 recordsLinked to original sources

arXiv2026

Component-wise hyperreduction for nonlinear solid mechanics problems

Hyperreduced nonlinear solid-mechanics components can be generated offline and reused as transferable building blocks across different assemblies, boundary conditions, meshes, material parameters, and constitutive models. We use proper orthogonal decomposition (POD) and energy conserving sampling and weighting (ECSW) on the component level and connect the substructures by mortar mesh tying. The POD modes and the ECSW weights and elements are computed offline from simulations of single components and the finite rigid body motions are treated by 12 additional rigid body modes per substructure. The numerical examples demonstrate errors below 1 \% for large quasi-static assemblies while evaluating less than 10 \% of the elements. The same component bases and ECSW elements are successfully reused for finite-strain viscoelastic dynamics, although they were trained only on elastic Neo-Hookean component simulations. These results indicate that component-wise hyperreduction can provide reusable reduced building blocks for modular nonlinear solid-mechanics simulations.

cs.CE↗

arXiv2026

Benchmarking data-driven material models on the classic Treloar dataset

Machine learning is rapidly reshaping constitutive modeling, offers new ways to learn material behavior directly from experimental data, and challenges long-established modeling paradigms. But with a growing number of machine-learning-based approaches available, how do they compare in practice? In this paper, we use the classic experimental data of Treloar to benchmark popular frameworks for hyperelasticity: (Generalized-Invariant) Constitutive Artificial Neural Networks, Physics-Augmented Neural Networks, (Adaptive) Material Fingerprinting, and Efficient Unsupervised Constitutive Law Identification & Discovery. We compare their fitting performance, computational cost, hyperparameter sensitivity, and ease of implementation. Furthermore, we discuss the trade-offs between predictive accuracy and model complexity. The latter is assessed by quantifying both the number of material parameters in the discovered models and the computational time required to evaluate the constitutive model and its derivatives. The results show that all methods can reproduce the benchmark data remarkably well. Rather than identifying a single winner, we highlight the strengths and limitations of each approach and provide practical guidance for their use. The source code for all six methods, including the training and comparison scripts, as well as all results and data used in this study, is publicly available via https://doi.org/10.5281/zenodo.21915635.

cs.AI↗

arXiv2026

Adaptive Material Fingerprinting for the fast discovery of polyconvex feature combinations in isotropic and anisotropic hyperelasticity

We recently proposed a method called Material Fingerprinting for the rapid discovery of mechanical material models that avoids solving continuous optimization problems. Material Fingerprinting assumes that each material exhibits a unique response when subjected to a standardized experimental setup, which is interpreted as the material's mechanical fingerprint. If a database of fingerprints is generated in an offline phase, a model for an unseen experimental measurement can be discovered in real time by comparing the experimentally measured fingerprint to the fingerprints in the database. In our original contributions, the database comprised a fixed number of material models, each with a fixed number of parameters. To increase the fitting flexibility of Material Fingerprinting, we propose an adaptive model database coupled with an iterative pattern recognition algorithm that refines the material model in each step. This strategy enables Material Fingerprinting to discover arbitrary linear combinations of material models from the database, rather than being restricted to selecting a single model from a predefined set. In comparison to previous works on Material Fingerprinting, this enables the discovery of more complex models, such as multi-term Ogden models or the anisotropic Holzapfel-Gasser-Ogden model. To design the adaptive database, we leverage sums of strain energy density feature functions that depend on isotropic and anisotropic invariants. All modeling features satisfy fundamental physical constraints, and polyconvexity can be optionally enforced via a simple user-controlled switch. We test the method on experimental data stemming from mechanical tests of isotropic rubber materials and anisotropic animal skin tissue.

cs.CE↗

arXiv2026

Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models

A key problem of solid mechanics is the identification of the constitutive law of a material, that is, the relation between strain history and stress. Machine learning has lead to considerable advances in this field lately. Here we introduce inelastic Constitutive Kolmogorov-Arnold Networks (iCKANs). This novel artificial neural network architecture can discover in an automated manner symbolic constitutive laws describing both the elastic and inelastic behavior of materials. That is, it can translate data from material testing into corresponding elastic and inelastic potential functions in closed mathematical form. We demonstrate the advantages of iCKANs using both synthetic data and experimental data of the viscoelastic polymer materials VHB 4910 and VHB 4905. The results demonstrate that iCKANs accurately capture complex viscoelastic behavior while preserving physical interpretability. It is a particular strength of iCKANs that they can process not only mechanical data but also arbitrary additional information available about a material (e.g., about temperature-dependent behavior). This makes iCKANs a powerful tool to discover in the future also how specific processing or service conditions affect the properties of materials.

cond-mat.mtrl-sci↗

arXiv2026

A Convex Route to Thermoelasticity: Learning Internal Energy and Dissipation

We present a physics-based neural network framework for the discovery of constitutive models in fully coupled thermomechanics. In contrast to classical formulations based on the Helmholtz energy, we adopt the internal energy and a dissipation potential as primary constitutive functions, expressed in terms of deformation and entropy. This choice avoids the need to enforce mixed convexity--concavity conditions and facilitates a consistent incorporation of thermodynamic principles. In this contribution, we focus on materials without preferred directions or internal variables. While the formulation is posed in terms of entropy, the temperature is treated as the independent observable, and the entropy is inferred internally through the constitutive relation, enabling thermodynamically consistent modeling without requiring entropy data. Thermodynamic admissibility of the networks is guaranteed by construction. The internal energy and dissipation potential are represented by input convex neural networks, ensuring convexity and compliance with the second law. Objectivity, material symmetry, and normalization are embedded directly into the architecture through invariant-based representations and zero-anchored formulations. We demonstrate the performance of the proposed framework on synthetic and experimental datasets, including purely thermal problems and fully coupled thermomechanical responses of soft tissues and filled rubbers. The results show that the learned models accurately capture the underlying constitutive behavior. All code, data, and trained models are made publicly available via https://doi.org/10.5281/zenodo.19248596.

cs.CE↗

arXiv2026

Reduced integration with scaled boundary parametrization for virtual elements at finite strains

This contribution presents an alternative stabilization technique for the virtual element method (VEM) based on reduced integration combined with a scaled boundary parametrization. To this end, a Taylor series expansion of the constitutive quantities with respect to the sectional center is carried out, enabling analytical integration of the weak form and reducing the need for integration points to only one per section. The accuracy of the proposed formulation is shown by several numerical examples, including a non-linear patch test. Different loading, e.g. compression under large deformations, and material conditions, such as hyperelastic anisotropy and elasto-plasticity, are considered. The biquadratic serendipity finite element formulation (Q2) and the low-order finite element formulation with hourglass stabilization (Q1STc+) are used for comparison. While the patch test was not fulfilled using higher order shape functions, the formulation led to good results and was able to capture the structure's response accurately. Furthermore, the formulation performed better when the physical element resembled the pre-assigned parent elements. The example of the asymmetrically notched specimen under elasto-plastic material behavior showed that the proposed formulation is able to capture inelasticities.

cs.CE↗

arXiv2026

Watching Physics: the Generative Science of Matter and Motion

Can we learn the physics of matter in motion directly from images and video--and trust it? Answering this question requires integrating experiments, physics-based simulation, and data across traditionally separate disciplines. Much of this knowledge is visual and temporal rather than textual: images and videos encode structure, dynamics, and causality that equations alone cannot fully capture. Recent generative models produce compelling visual content, yet they rely on observational data and often lack physical validity. Here we show that generative video models gain scientific value when they couple visual data with experiments and high-fidelity simulations. Using deformation mechanics as a testbed, we study three systems of increasing complexity--rubber compression, can crushing, and cardiac motion--and identify regimes in which visual learning succeeds, fails, and requires mechanistic supervision. When physics manifests in visible kinematics, generative models recover measurable quantities such as surface strain; when internal state variables dominate, visual plausibility no longer ensures physical admissibility. We propose that this convergence defines a new frontier, the Generative Sciences of Matter and Motion, which unifies Simulogenics, Physiogenics, and Materiogenics. These physics-grounded foundation models can turn visual generation into a scientific instrument for inference, prediction, and design of matter in motion.

cs.CE↗

arXiv2026

Influence of the geometry on the mechanical performance of tubular interlockings: A study of the Sine Block

Topological interlocking assemblies (TIA) are arrangements of blocks such that rigid-body motions of the blocks are fully constrained by their neighbours and a fixed frame. In this work, we investigate tubular interlocking structures derived from the sine curve and parametrised by several geometric design parameters. We analyse the behaviour of these parametrised tubular interlockings under various boundary conditions and examine how our proposed parameters influence the mechanical response. For this purpose, we first develop a simplified multibody dynamics formulation that enables an efficient exploration of how the design parameters of the block influence the load transfer within the assembly. To further corroborate these results, we perform several finite element simulations, which give insights into the mechanical behaviour of our proposed TIA. Our results show that the block geometry plays a decisive role in the mechanical performance of the corresponding TIA. We additionally discuss the problem of exploding TIAs and demonstrate that the TIA resulting from our Sine Block does not exhibit this behaviour. Lastly, we provide evidence that non-exploding TIAs possess better mechanical properties than exploding ones.

cs.CE↗

arXiv2025

A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strains

We propose a complement to constitutive modeling that augments neural networks with material principles to capture anisotropy and inelasticity at finite strains. The key element is a dual potential that governs dissipation, consistently incorporates anisotropy, and-unlike conventional convex formulations-satisfies the dissipation inequality without requiring convexity. Our neural network architecture employs invariant-based input representations in terms of mixed elastic, inelastic and structural tensors. It adapts Input Convex Neural Networks, and introduces Input Monotonic Neural Networks to broaden the admissible potential class. To bypass exponential-map time integration in the finite strain regime and stabilize the training of inelastic materials, we employ recurrent Liquid Neural Networks. The approach is evaluated at both material point and structural scales. We benchmark against recurrent models without physical constraints and validate predictions of deformation and reaction forces for unseen boundary value problems. In all cases, the method delivers accurate and stable performance beyond the training regime. The neural network and finite element implementations are available as open-source and are accessible to the public via https://doi.org/10.5281/zenodo.17199965.

cs.CE↗

arXiv2025

Autoencoder-based non-intrusive model order reduction in continuum mechanics

We propose a non-intrusive, Autoencoder-based framework for reduced-order modeling in continuum mechanics. Our method integrates three stages: (i) an unsupervised Autoencoder compresses high-dimensional finite element solutions into a compact latent space, (ii) a supervised regression network maps problem parameters to latent codes, and (iii) an end-to-end surrogate reconstructs full-field solutions directly from input parameters. To overcome limitations of existing approaches, we propose two key extensions: a force-augmented variant that jointly predicts displacement fields and reaction forces at Neumann boundaries, and a multi-field architecture that enables coupled field predictions, such as in thermo-mechanical systems. The framework is validated on nonlinear benchmark problems involving heterogeneous composites, anisotropic elasticity with geometric variation, and thermo-mechanical coupling. Across all cases, it achieves accurate reconstructions of high-fidelity solutions while remaining fully non-intrusive. These results highlight the potential of combining deep learning with dimensionality reduction to build efficient and extensible surrogate models. Our publicly available implementation provides a foundation for integrating data-driven model order reduction into uncertainty quantification, optimization, and digital twin applications.

cs.CE↗

arXiv2025

Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networks

In this work, we extend the existing framework of inelastic constitutive artificial neural networks (iCANNs) by incorporating plasticity to increase their applicability to model more complex material behavior. The proposed approach ensures objectivity, material symmetry, and thermodynamic consistency, providing a robust basis for automatic model discovery of constitutive equations at finite strains. These are predicted by discovering formulations for the Helmholtz free energy and plastic potentials for the yield function and evolution equations in terms of feed-forward networks. Our framework captures both linear and nonlinear kinematic hardening behavior. Investigation of our model's prediction showed that the extended iCANNs successfully predict both linear and nonlinear kinematic hardening behavior based on experimental and artificially generated datasets, showcasing promising capabilities of this framework. Nonetheless, challenges remain in discovering more complex yield criteria with tension-compression asymmetry and addressing deviations in experimental data at larger strains. Despite these limitations, the proposed framework provides a promising basis for incorporating plasticity into iCANNs, offering a platform for advancing in the field of automated model discovery.

cs.LG↗

arXiv2025

A Comprehensive Framework for Predictive Computational Modeling of Growth and Remodeling in Tissue-Engineered Cardiovascular Implants

Developing clinically viable tissue-engineered cardiovascular implants remains a formidable challenge. Achieving reliable and durable outcomes requires a deeper understanding of the fundamental mechanisms driving tissue evolution during in vitro maturation. Although considerable progress has been made in modeling soft tissue growth and remodeling, studies focused on the early stages of tissue engineering remain limited. Here, we present a general, thermodynamically consistent model to predict tissue evolution and mechanical response throughout maturation. The formulation utilizes a stress-driven homeostatic surface to capture volumetric growth, coupled with an energy-based approach to describe collagen densification via the strain energy of the fibers. We further employ a co-rotated intermediate configuration to ensure the model's consistency and generality. The framework is demonstrated with two numerical examples: a uniaxially constrained tissue strip validated against experimental data, and a biaxially constrained specimen subjected to a perturbation load. These results highlight the potential of the proposed model to advance the design and optimization of tissue-engineered implants with clinically relevant performance.

cs.CE↗

arXiv2025

An enhanced single Gaussian point continuum finite element formulation using automatic differentiation

This contribution presents an improved low-order 3D finite element formulation with hourglass stabilization using automatic differentiation (AD). Here, the former Q1STc formulation is enhanced by an approximation-free computation of the inverse Jacobian. To this end, AD tools automate the computation and allow a direct evaluation of the inverse Jacobian, bypassing the need for a Taylor series expansion. Thus, the enhanced version, Q1STc+, is introduced. Numerical examples are conducted to compare the performance of both element formulations for finite strain applications, with particular focus on distorted meshes. Moreover, the performance of the new element formulation for an elasto-plastic material is investigated. To validate the obtained results, a volumetric locking-free element based on scaled boundary parametrization is used. Both the implementation of the element routine Q1STc+ and the corresponding material subroutine are made accessible to the public at https://doi.org/10.5281/zenodo.14259791

cs.CE↗

arXiv2025

A generalized dual potential for inelastic Constitutive Artificial Neural Networks: A JAX implementation at finite strains

We present a methodology for designing a generalized dual potential, or pseudo potential, for inelastic Constitutive Artificial Neural Networks (iCANNs). This potential, expressed in terms of stress invariants, inherently satisfies thermodynamic consistency for large deformations. In comparison to our previous work, the new potential captures a broader spectrum of material behaviors, including pressure-sensitive inelasticity. To this end, we revisit the underlying thermodynamic framework of iCANNs for finite strain inelasticity and derive conditions for constructing a convex, zero-valued, and non-negative dual potential. To embed these principles in a neural network, we detail the architecture's design, ensuring a priori compliance with thermodynamics. To evaluate the proposed architecture, we study its performance and limitations discovering visco-elastic material behavior, though the method is not limited to visco-elasticity. In this context, we investigate different aspects in the strategy of discovering inelastic materials. Our results indicate that the novel architecture robustly discovers interpretable models and parameters, while autonomously revealing the degree of inelasticity. The iCANN framework, implemented in JAX, is publicly accessible at https://doi.org/10.5281/zenodo.14894687.

cs.LG↗

arXiv2024

Automated Model Discovery for Tensional Homeostasis: Constitutive Machine Learning in Growth and Remodeling

Soft biological tissues exhibit a tendency to maintain a preferred state of tensile stress, known as tensional homeostasis, which is restored even after external mechanical stimuli. This macroscopic behavior can be described using the theory of kinematic growth, where the deformation gradient is multiplicatively decomposed into an elastic part and a part related to growth and remodeling. Recently, the concept of homeostatic surfaces was introduced to define the state of homeostasis and the evolution equations for inelastic deformations. However, identifying the optimal model and material parameters to accurately capture the macroscopic behavior of inelastic materials can only be accomplished with significant expertise, is often time-consuming, and prone to error, regardless of the specific inelastic phenomenon. To address this challenge, built-in physics machine learning algorithms offer significant potential. In this work, we extend our inelastic Constitutive Artificial Neural Networks (iCANNs) by incorporating kinematic growth and homeostatic surfaces to discover the scalar model equations, namely the Helmholtz free energy and the pseudo potential. The latter describes the state of homeostasis in a smeared sense. We evaluate the ability of the proposed network to learn from experimentally obtained tissue equivalent data at the material point level, assess its predictive accuracy beyond the training regime, and discuss its current limitations when applied at the structural level. Our source code, data, examples, and an implementation of the corresponding material subroutine are made accessible to the public at https://doi.org/10.5281/zenodo.13946282.

cs.LG↗

arXiv2024

An anisotropic, brittle damage model for finite strains with a generic damage tensor regularization

This paper establishes a universal framework for the nonlocal modeling of anisotropic damage at finite strains. By the combination of two recent works, the new framework allows for the flexible incorporation of different established hyperelastic finite strain material formulations into anisotropic damage whilst ensuring mesh-independent results by employing a generic set of micromorphic gradient-extensions. First, the anisotropic damage model, generally satisfying the damage growth criterion, is investigated for the specific choice of a Neo-Hookean material on a single element. Next, the model is applied with different gradient-extensions in structural simulations of an asymmetrically notched specimen to identify an efficient choice in the form of a volumetric-deviatoric regularization. Thereafter, the universal framework, which is without loss of generality here specified for a Neo-Hookean material with a volumetric-deviatoric gradient-extension, successfully serves for the complex simulation of a pressure loaded rotor blade. After acceptance of the manuscript, we make the codes of the material subroutines accessible to the public at https://doi.org/10.5281/zenodo.11171630.

cs.CE↗

arXiv2023

Mechanical Comparison of Arrangement Strategies for Topological Interlocking Assemblies

Topological Interlocking assemblies are arrangements of blocks kinematically constrained by a fixed frame, such that all rigid body motions of each block are constrained only by its permanent contact with other blocks and the frame. In the literature several blocks are introduced that can be arranged into different interlocking assemblies. In this study we investigate the influence of arrangement on the overall structural behaviour of the resulting interlocking assemblies. This is performed using the Versatile Block, as it can be arranged in three different doubly periodic ways given by wallpaper symmetries. Our focus lies on the load transfer mechanisms from the assembly onto the frame. For fast a priori evaluation of the assemblies we introduce a combinatorial model called Interlocking Flows. To investigate our assemblies from a mechanical point of view we conduct several finite element studies. These reveal a strong influence of arrangement on the structural behaviour, for instance, an impact on both the point and amount of maximum deflection. The results of the finite element analysis are in very good agreement with the predictions of the Interlocking Flow model. Our source code, data and examples are available under https://doi.org/10.5281/zenodo.10246034.

cs.CE↗

arXiv2023

A comparative study of micromorphic gradient-extensions for anisotropic damage at finite strains

Modern inelastic material model formulations rely on the use of tensor-valued internal variables. When inelastic phenomena include softening, simulations of the former are prone to localization. Thus, an accurate regularization of the tensor-valued internal variables is essential to obtain physically correct results. Here, we focus on the regularization of anisotropic damage at finite strains. Thus, a flexible anisotropic damage model with isotropic, kinematic, and distortional hardening is equipped with three gradient-extensions using a full and two reduced regularizations of the damage tensor. Theoretical and numerical comparisons of the three gradient-extensions yield excellent agreement between the full and the reduced regularization based on a volumetric-deviatoric regularization using only two nonlocal degrees of freedom.

cs.CE↗