arXiv subjects

Gaëtan Cortes

Publications and source records attributed to Gaëtan Cortes.

3 recordsLinked to original sources

arXiv2026

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

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.

cond-mat.soft↗

arXiv2025

Data-Driven Dynamic Friction Models based on Recurrent Neural Networks

In this concise contribution, it is demonstrated that Recurrent Neural Networks (RNNs) based on Gated Recurrent Unit (GRU) architecture, possess the capability to learn the complex dynamics of rate-and-state friction (RSF) laws from synthetic data. The data employed for training the network is generated through the application of traditional RSF equations coupled with either the aging law or the slip law for state evolution. A novel aspect of this approach is the formulation of a loss function that explicitly accounts for the direct effect by means of automatic differentiation. It is found that the GRU-based RNNs effectively learns to predict changes in the friction coefficient resulting from velocity jumps (with and without noise in the target data), thereby showcasing the potential of machine learning models in capturing and simulating the physics of frictional processes. Current limitations and challenges are discussed.

physics.geo-ph↗

arXiv2024

Phase-space iterative solvers

We introduce an iterative method to solve problems in small-strain non-linear elasticity, termed ``Phase-Space Iterations'' (PSIs). The method is inspired by recent work in data-driven computational mechanics, which reformulated the classic boundary value problem of continuum mechanics using the concept of ''phase space'' associated with a mesh. The latter is an abstract metric space, whose coordinates are indexed by strains and stress components, where each possible state of the discretized body corresponds to a point. Two subsets are then defined: an affine space termed ``physically-admissible set'' made up by those points that satisfy equilibrium and a ``materially-admissible set'' containing points that satisfy the constitutive law. Solving the boundary-value problem amounts to finding the intersection between these two subdomains. In the linear-elastic setting, this can be achieved through the solution of a set of linear equations; when material non-linearity enters the picture, such is not the case anymore and iterative solution approaches are necessary. Our iterative method consists on projecting points alternatively from one set to the other, until convergence. To evaluate the performance of the method, we draw inspiration from the ''method of alternative projections'' and the ''method of projections onto convex sets'', both of which have a robust mathematical foundation in terms of conditions for the existence of solutions and guarantees convergence. This foundation is leveraged to analyze the simplest case and to establish a geometric convergence rate. We also present a realistic case to illustrate PSIs' strengths when compared to the classic Newton-Raphson method, the usual tool of choice in non-linear continuum mechanics. Finally, its aptitude to deal with constitutive laws based on neural network is also showcased.

math.NA↗