# High-Order Elasticity Interpolants for Microstructure Simulation

arXiv: https://arxiv.org/abs/2303.03120 · HTML: https://mlsanity.com/paper/2303.03120/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2023.

## Built on by (most cited first, 1 of 1)

- [Representing Flow Fields with Divergence-Free Kernels for Reconstruction](https://mlsanity.com/paper/2504.01913/) (2025)

## Abstract (arXiv)

We propose a novel formulation of elastic materials based on high-order interpolants, which fits accurately complex elastic behaviors, but remains conservative. The proposed high-order interpolants can be regarded as a high-dimensional extension of radial basis functions, and they allow the interpolation of derivatives of elastic energy, in particular stress and stiffness. Given the proposed parameterization of elasticity models, we devise an algorithm to find optimal model parameters based on training data. We have tested our methodology for the homogenization of 2D microstructures, and we show that it succeeds to match complex behaviors with high accuracy.