# Learning Elastic Constitutive Material and Damping Models

arXiv: https://arxiv.org/abs/1909.01875 · HTML: https://mlsanity.com/paper/1909.01875/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2019.

## Built on by (most cited first, 10 of 10)

- [Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamics](https://mlsanity.com/paper/2304.14369/) (2023)
- [Neural Material Adaptor for Visual Grounding of Intrinsic Dynamics](https://mlsanity.com/paper/2410.08257/) (2024)
- [UniPhy: Learning a Unified Constitutive Model for Inverse Physics Simulation](https://mlsanity.com/paper/2505.16971/) (2025)
- [Neural Metamaterial Networks for Nonlinear Material Design](https://mlsanity.com/paper/2309.10600/) (2023)
- [Differentiable programming across the PDE and Machine Learning barrier](https://mlsanity.com/paper/2409.06085/) (2024)
- [Category-Level Global Camera Pose Estimation with Multi-Hypothesis Point Cloud Correspondences](https://mlsanity.com/paper/2209.14419/) (2022)
- [Aligning Perception, Reasoning, Modeling and Interaction: A Survey on Physical AI](https://mlsanity.com/paper/2510.04978/) (2025)
- [SpringTime: Learning Simulatable Models of Cloth with Spatially-varying Constitutive Properties](https://mlsanity.com/paper/2507.21288/) (2025)
- [Parameter-Efficient Conditioning for Material Generalization in Graph-Based Simulators](https://mlsanity.com/paper/2511.05456/) (2025)
- [Learning 3D Garment Animation from Trajectories of A Piece of Cloth](https://mlsanity.com/paper/2501.01393/) (2025)

## Abstract (arXiv)

Commonly used linear and nonlinear constitutive material models in deformation simulation contain many simplifications and only cover a tiny part of possible material behavior. In this work we propose a framework for learning customized models of deformable materials from example surface trajectories. The key idea is to iteratively improve a correction to a nominal model of the elastic and damping properties of the object, which allows new forward simulations with the learned correction to more accurately predict the behavior of a given soft object. Space-time optimization is employed to identify gentle control forces with which we extract necessary data for model inference and to finally encapsulate the material correction into a compact parametric form. Furthermore, a patch based position constraint is proposed to tackle the challenge of handling incomplete and noisy observations arising in real-world examples. We demonstrate the effectiveness of our method with a set of synthetic examples, as well with data captured from real world homogeneous elastic objects.