Hyperelasticity

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Hyperelasticity studies how materials such as elastomers and soft tissues respond to large deformations, often describing stress through a strain-energy function. Researchers use finite element methods alongside learned constitutive laws, including physics-constrained neural networks, to identify material behavior from experiments and simulate complex geometries. Neural operators and graph-based surrogates can speed up stress prediction and multiscale homogenization, while differentiable solvers help fit models directly to measured deformation data. A central challenge is balancing accuracy and computational speed with physical guarantees such as stability and polyconvexity, especially for loading conditions or geometries not seen during training.

Latest papers

18 papers1 paper in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

Polyconvex neural-network surrogates with learned paired directional features for anisotropic hyperelastic homogenization
Oct 8, 2026S. Ares de Parga, A. Cornejo, J. A. Hernández +1Neural Surrogate Modeling Hyperelasticity
Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Barcelona, Spain · Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA · Universitat Politècnica de Catalunya, Department of Civil and Environmental Engineering (DECA), Barcelona, Spain +1
Data-Driven Discovery of Composition-Dependent Constitutive Models for Hyperelasticity and Viscoelasticity of Digital Materials
Sep 3, 2026Josué García-Ávila, Beijun Shen, Manuel K. Rausch +2Hyperelasticity Materials Science
Department of Mechanical Engineering, Columbia University, New York City, USA · Department of Mechanical Engineering Columbia University New York City, NY 10027, USA · Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, Austin, USA +3
Generalizing Soft Tissue Deformation and Force Prediction Across Material Stiffness and Geometry
Aug 21, 2026Madina Kojanazarova, Sidaty El Hadramy, Philippe C. CattinDeformable Object Simulation Neural Surrogate Modeling
University of Basel, Department of Biomedical Engineering, Allschwil, Switzerland
Benchmarking data-driven material models on the classic Treloar dataset
Aug 14, 2026Hagen Holthusen, Moritz Flaschel, Denisa Martonová +1Hyperelasticity Physics-Informed ML
Institute of Applied Mechanics, Egerlandstraße 5, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany · Department of Mechanical Engineering, Stanford University, 440 Escondido Mall, California 94305, United States.
Interval and fuzzy physics-augmented neural networks (iPANN and fPANN) for uncertainty quantification and propagation in constitutive modeling
Jul 22, 2026Somesh Pratap Singh, Govinda Anantha Padmanabha, Jingye Tan +4Uncertainty Quantification Hyperelasticity
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, 14853, NY, USA · Ecole Polytechnique Federale de Lausanne (EPFL), 1015, Lausanne, Switzerland · Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, 90007, CA, USA +2
Implementation of Hyperelastic Physics-Augmented Neural Networks in the Explicit Finite Element Codes Simcenter Radioss and OpenRadioss with Applications to Impact Events
Jun 29, 2026Lukas Maurer, Sascha Eisenträger, Marian Bulla +1Neural Surrogate Modeling Efficient Neural Network Inference
Institute of Materials, Technologies and Mechanics Otto von Guericke University Magdeburg Magdeburg, D-39106 · Siemens Digital Industries Am Kabellager 9 Köln, D-51063
Spectrally Safe Neural Operator Warm-Starts for Large-Scale Newton Solvers
Jun 20, 2026Jaemin Oh, Youngkyu Lee, Jerome Darbon +1Spectral Regularization PDE Solving
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field data
Jun 12, 2026Benjamin Alheit, Siddhant Kumar, Mathias PeirlinckHyperelasticity Materials Science
Department of BioMechanical Engineering, Faculty of Mechanical Engineering, Delft University of Technology · Department of Material Science Engineering, Faculty of Mechanical Engineering, Delft University of Technology
PINNOCHIO: Physics-Informed Neural Network for Coupled Hyperelastic Interface-Volume Simulation in Orthognathic Surgery
Jun 1, 2026Jungwook Lee, Daeseung Kim, Kevin Gu +6Neural Surrogate Modeling Hyperelasticity
Department of Biomedical Engineering and Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute, Troy, NY 12180, USA · Department of Oral and Maxillofacial Surgery, Houston Methodist Research Institute, Houston, TX 77030, USA · Department of Neurosurgery, Baylor College of Medicine, Houston, TX 77030, USA
Machine Learning Surrogate Modeling for Homogenization of Hyperelastic Materials with Boolean Microstructures
May 31, 2026Matthias Brändel, Oliver RheinbachNeural Surrogate Modeling Hyperelasticity
Technische Universität Bergakademie Freiberg, Institut für Numerische Mathematik und Optimierung, Fakultät für Mathematik und Informatik, 09596 Freiberg, Germany.
FreeForm: Reduced-Order Deformable Simulation from Particle-Based Skinning Eigenmodes
May 28, 2026Donglai Xiang, Vismay Modi, Rishit Dagli +5Hyperelasticity Reduced-Order Modeling
NVIDIA · 1NVIDIA · University of Toronto
WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains
May 23, 2026Bokai Zhu, Qinghui Zhang, Timon RabczukNeural PDE Solvers PDE Solving
School of Science, Harbin Institute of Technology, Shenzhen, P. R. China. · School of Science, Harbin Institute of Technology, Shenzhen, Guangdong. · Institute of Structural Mechanics, Bauhaus-Universität Weimar, Weimar, 99423, Germany.
Automatic-Differentiation-Enabled Finite Element Model Updating: Learning Constitutive Neural Networks from Structural Deformation Data
May 22, 2026Matthias Knipper, Chenyi Ji, Malte Brand +1Automatic Differentiation Hyperelasticity
Computational Mechanics in Medicine, Applied Medical Engineering, RWTH Aachen University Pauwelsstraße 20, 52074 Aachen, Germany · Institute for Continuum and Material Mechanics, Hamburg University of Technology, Eißendorfer Straße 42, 21073 Hamburg, Germany
DiffPhD: A Unified Differentiable Solver for Projective Heterogeneous Materials in Elastodynamics with Contact-Rich GPU-Acceleration
May 14, 2026Shih-Yu Lai, Sung-Han Tien, Jui-I Huang +9Robotics Simulation Hyperelasticity
National Taiwan University · MoonShine Animation Studio · National University of Singapore +3
Physics-Informed Reduced-Order Operator Learning for Hyperelasticity in Continuum Micromechanics
May 8, 2026Hamidreza Eivazi, Henning WesselsStructural Mechanics Hyperelasticity
Division Data-Driven Modeling of Mechanical Systems, Institute of Applied Mechanics, Technische Universität Braunschweig, Pockelsstr. 3, 38106 Braunschweig, Germany
Hyperelastic constitutive model discovery with differentiable finite elements and structure-preserving neural networks
Mar 27, 2026Francesco RegazzoniStructure-Preserving Neural Networks Hyperelasticity
MOX, Department of Mathematics, Politecnico di Milano, Milan, Italy
A Hybrid Conditional Diffusion-DeepONet Framework for High-Fidelity Stress Prediction in Hyperelastic Materials
Mar 18, 2026Purna Vindhya Kota, Meer Mehran Rashid, Somdatta Goswami +1Neural Surrogate Modeling Hyperelasticity
Department of Civil and Systems Engineering, Johns Hopkins University, 3400 N. Charles Street, Baltimore, 21218, MD, USA
Physics-Informed Graph Neural Networks to Reconstruct Local Fields Considering Finite Strain Hyperelasticity
Jul 5, 2025Manuel Ricardo Guevara Garban, Yves Chemisky, Étienne Prulière +1Physics-Informed GNNs Structural Mechanics
Univ. Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295, Talence 33400 France · Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800, Talence 33400 France · Arts et Metiers Institute of Technology, CNRS, Bordeaux INP, I2M, UMR 5295, Talence 33400 France

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Polyconvex neural-network surrogates with learned paired directional features for anisotropic hyperelastic homogenization

S. Ares de Parga, A. Cornejo, J. A. Hernández, R. Rossi

Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Barcelona, Spain · Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA · Universitat Politècnica de Catalunya, Department of Civil and Environmental Engineering (DECA), Barcelona, Spain+1

Neural Surrogate Modeling Hyperelasticity

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Approximating the effective anisotropic hyperelastic response of a representative volume element (RVE) requires constitutive expressiveness, mechanical consistency, and computational efficiency. This work develops a polyconvex physics-augmented neural network (PANN) construction based on paired directional features whose orientations, stretch powers, and determinant exponents adapt to the RVE response. The features are composed with convex, componentwise nondecreasing cores, realized as an input-convex neural network (ICNN) or an input-convex Kolmogorov-Arnold network (ICKAN). The complete energies satisfy objectivity, an exactly stress-free reference, two-dimensional polyconvexity, and prescribed growth conditions by construction, and nonnegative energy is certified separately for the selected models. On a multicavity and a single-cavity periodic cell, these energies are compared with an Unconstrained energy, trained identically without the curvature and growth constraints, and with three hyperreduced projection-based reduced-order models (HPROMs), which serve as physics-based references. On the first cell, learning the features lowers the stress error sevenfold, and six features suffice on both. The constrained energies remain below one percent in stress error and in the displacement error of a tensile-coupon FE

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application with a full-order reference, whereas the Unconstrained energy and the HPROMs are more accurate inside the data. Beyond the data, however, the Unconstrained energy loses rank-one convexity, and under confined compression it stops below half of the 500 MPa that the constrained energies reach. These results quantify what the guarantees cost in accuracy and what they secure beyond the data.