# Data-Driven Discovery of Composition-Dependent Constitutive Models for Hyperelasticity and Viscoelasticity of Digital Materials

arXiv: https://arxiv.org/abs/2609.04541 · HTML: https://mlsanity.com/paper/2609.04541/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 59 references that are in the map.
- First posted on arXiv 3 Sep 2026.

## Builds on (most cited first, 14 of 14)

- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Polyconvex anisotropic hyperelasticity with neural networks](https://mlsanity.com/paper/2106.14623/) (2021)
- [A new family of Constitutive Artificial Neural Networks towards automated model discovery](https://mlsanity.com/paper/2210.02202/) (2022)
- [Neural networks meet hyperelasticity: A guide to enforcing physics](https://mlsanity.com/paper/2302.02403/) (2023)
- [A review on data-driven constitutive laws for solids](https://mlsanity.com/paper/2405.03658/) (2024)
- [Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equations](https://mlsanity.com/paper/2110.03774/) (2021)
- [Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations](https://mlsanity.com/paper/2302.03598/) (2023)
- [Viscoelastic Constitutive Artificial Neural Networks (vCANNs) - a framework for data-driven anisotropic nonlinear finite viscoelasticity](https://mlsanity.com/paper/2303.12164/) (2023)
- [Finite electro-elasticity with physics-augmented neural networks](https://mlsanity.com/paper/2206.05139/) (2022)
- [Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material models](https://mlsanity.com/paper/2602.17750/) (2026)
- [Polyconvex Physics-Augmented Neural Network Constitutive Models in Principal Stretches](https://mlsanity.com/paper/2503.00575/) (2025)
- [A physics-augmented neural network framework for finite strain incompressible viscoelasticity](https://mlsanity.com/paper/2511.02959/) (2025)
- [Physics Augmented Machine Learning Discovery of Composition-Dependent Constitutive Laws for 3D Printed Digital Materials](https://mlsanity.com/paper/2507.02991/) (2025)

## Abstract (arXiv)

Digital materials fabricated by multi-material 3D printing are designed as controlled mixtures of stiff and compliant constituents, yielding effective responses that span more than an order of magnitude in apparent stiffness and exhibit strongly nonlinear, composition-dependent, and rate-dependent dissipative behavior. Classical finite-strain viscoelastic models represent such behavior with closed-form strain energy functions for equilibrium and non-equilibrium stresses as well as evolution of internal variables, which may limit flexibility when a single constitutive model is expected to generalize across materials and loading rates. Here, we present a data-driven multi-material constitutive modeling framework that generalizes a formulation by Bergstr"om and Boyce. The proposed framework retains the structure of the classical model, namely multiplicative kinematics, invariant-based strain-energy functions, and a scalar dissipative evolution law directed along the normalized nonequilibrium deviatoric stress. For the equilibrium branch, the data-driven discovery framework either directly predicts closed-form model parameters as functions of composition or automatically constructs a polyconvex strain-energy function using neural ordinary differential equations (NODEs). The nonequilibrium branch kinetics are learned similarly, either by directly identifying closed-form parameters across compositions or by using appropriately constrained artificial neural networks. Using multi-rate uniaxial compression data across multiple material compositions, we show that the proposed formulation captures rate-dependent stiffness and hysteresis across compositions while preserving thermodynamic consistency.