ArticleComputer methods in applied mechanics and engineering2022
Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equations.
Article in Computer methods in applied mechanics and engineering, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 15 papers.
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15 citing papers in PubMed.
- Monotone Peridynamic Neural Operator for Nonlinear Material Modeling with Conditionally Unique Solutions.Computer methods in applied mechanics and engineering · 2026Article
- LLM-driven design of physics-constrained constitutive models: Two agents are better than one.Machine learning for computational science and engineering · 2026Article
- Bayesian Inference Framework to Identify Skin Material PropertiesbioRxiv : the preprint server for biology · 2025Article
- Exploring hyperelastic material model discovery for human brain cortex: Multivariate analysis vs. artificial neural network approaches.Journal of the mechanical behavior of biomedical materials · 2025Article
- Generative Hyperelasticity with Physics-Informed Probabilistic Diffusion Fields.Engineering with computers · 2025Article
- A universal material model subroutine for soft matter systems.Engineering with computers · 2025Article
- Democratizing biomedical simulation through automated model discovery and a universal material subroutine.Computational mechanics · 2025Article
- The mechanical and sensory signature of plant-based and animal meat.NPJ science of food · 2024Article
- Automated data-driven discovery of material models based on symbolic regression: A case study on the human brain cortex.Acta biomaterialia · 2024Article
- Data-driven continuum damage mechanics with built-in physics.Extreme Mechanics Letters · 2024Article
- Benchmarking physics-informed frameworks for data-driven hyperelasticity.Computational mechanics · 2024Article
- Synergistic Integration of Deep Neural Networks and Finite Element Method with Applications of Nonlinear Large Deformation Biomechanics.Computer methods in applied mechanics and engineering · 2023Article
- PyTorch-FEA: Autograd-enabled finite element analysis methods with applications for biomechanical analysis of human aorta.Computer methods and programs in biomedicine · 2023Article
- Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations.Computer methods in applied mechanics and engineering · 2023Article
- Data-driven Modeling of the Mechanical Behavior of Anisotropic Soft Biological Tissue.Engineering with computers · 2022Article
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Authors and funding
3 authors.
Funding
Abstract
Data-driven methods are becoming an essential part of computational mechanics due to their advantages over traditional material modeling. Deep neural networks are able to learn complex material response without the constraints of closed-form models. However, data-driven approaches do not a priori satisfy physics-based mathematical requirements such as polyconvexity, a condition needed for the existence of minimizers for boundary value problems in elasticity. In this study, we use a recent class of neural networks, neural ordinary differential equations (N-ODEs), to develop data-driven material models that automatically satisfy polyconvexity of the strain energy. We take advantage of the properties of ordinary differential equations to create monotonic functions that approximate the derivatives of the strain energy with respect to deformation invariants. The monotonicity of the derivatives guarantees the convexity of the energy. The N-ODE material model is able to capture synthetic data generated from closed-form material models, and it outperforms conventional models when tested against experimental data on skin, a highly nonlinear and anisotropic material. We also showcase the use of the N-ODE material model in finite element simulations of reconstructive surgery. The framework is general and can be used to model a large class of materials, especially biological soft tissues. We therefore expect our methodology to further enable data-driven methods in computational mechanics.
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