# Inverse Design of Metainterfaces for Static Friction Control: Beyond the Hertzian Limit

arXiv: https://arxiv.org/abs/2605.11012 · HTML: https://mlsanity.com/paper/2605.11012/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 36 references that are in the map.
- First posted on arXiv 10 May 2026.

## Builds on (most cited first, 4 of 4)

- [JAX-FEM: A differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science](https://mlsanity.com/paper/2212.00964/) (2022)
- [Tailoring Frictional Properties of Surfaces Using Diffusion Models](https://mlsanity.com/paper/2401.05206/) (2024)
- [Frictional contact of soft polymeric shells](https://mlsanity.com/paper/2401.14926/) (2024)
- [Friction on Demand: A Generative Framework for the Inverse Design of Metainterfaces](https://mlsanity.com/paper/2511.03735/) (2025)

## Abstract (arXiv)

Programming the static friction of mechanical interfaces is critical for soft robotics, haptics, and precision gripping. Static friction is governed by the real contact area, and standard rough surfaces exhibit a linear area-load scaling inherent to classical Archard and Greenwood-Williamson models, severely restricting their functional range. Here, we propose a framework for the inverse design of tribological metainterfaces engineered for programmable contact behaviors. By utilizing general axisymmetric asperities, we unlock nonlinear macroscopic responses unattainable by standard Hertzian contacts. To solve the inverse problem, we embed a fully differentiable contact mechanics engine within a neural network and a quadratic optimizer. We leverage regularized physical gradients to automatically discover non-standard topographies that reproduce complex target friction laws, with only a few asperities in unit cells. The predicted designs are strictly validated against high-fidelity Boundary Element Method (BEM) simulations. This framework bridges data-driven optimization and rigorous physics, offering a scale-invariant pathway for discovering functional tribological surfaces.