Stochastic and differentiable constitutive modeling of dissipative materials

Abstract: 

Constitutive models are central to accurate mechanical predictions across industries and have traditionally been developed through phenomenological approaches to capture material complexities such as nonlinearity, time dependence, and path dependence. The Generalized Standard Materials (GSM) framework has been instrumental in this process by ensuring thermodynamic consistency. However, most models have historically relied on deterministic assumptions, and implementing them numerically poses challenges, particularly due to the need for consistent tangent operators to achieve computational efficiency in structural analysis. Today, with emerging connections to convex optimization and neural network architectures, new opportunities arise to advance these models using developments in machine learning and mathematical optimization.

In this talk, we present novel formulations for dissipative materials by incorporating insights from optimization, finance, and machine learning. First, we extend the GSM framework to a stochastic setting, deriving thermodynamically consistent effective behaviors—average, optimistic, and pessimistic—under uncertainty through risk measures. Second, we discuss machine-learning-compatible implementations of these models, using implicit and automatic differentiation (AD) to streamline the traditionally challenging computation of tangent operators and enable automated sensitivity analyses. This approach not only facilitates model calibration but also supports the integration of complex behaviors, such as multi-surface plasticity, into efficient, data-driven applications.

Le mardi 3 décembre 2024 à 11h00 / Amphithéâtre François Canac, LMA

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