Discovering Thermodynamically Admissible Dissipation Potentials via Grammar-Based Symbolic Regression

2026-05-29

AI Summary

This work addresses the challenge that existing data-driven approaches struggle to simultaneously ensure thermodynamic admissibility and interpretability in constitutive modeling of inelastic materials. Building upon the generalized standard materials framework, the authors propose a convexity-preserving, grammar-guided symbolic regression method to directly identify dissipation potentials from data that inherently satisfy thermodynamic constraints. By constructively enforcing convexity and non-negativity of the dissipation potential, the approach rigorously guarantees non-negative mechanical dissipation and provides a unified formulation for rate-dependent and viscoplastic behaviors featuring a genuine elastic domain. Validated on both noisy synthetic data and experimental shear tests of real elastomers, the method successfully captures the amplitude-dependent softening of dynamic moduli and significantly outperforms a calibrated linear Zener model.

Abstract

Constitutive laws for inelastic materials must satisfy strict thermodynamic admissibility requirements, yet current data-driven approaches sacrifice interpretability, even when formal guarantees are provided by physics-encoded architectures. We propose a symbolic regression framework for the data-driven discovery of dissipation potentials governing the evolution of internal variables within the Generalized Standard Materials (GSM) formalism. Starting from the Clausius--Duhem inequality, we enforce the thermodynamic requirements, convexity and non-negativity, that the dual dissipation potential must satisfy to guarantee non-negative mechanical dissipation. These requirements are formulated in the general subdifferential setting, encompassing rate-dependent (viscoelastic) and viscoplastic dissipative mechanisms, including potentials with genuine elastic domains, within a unified framework. Candidate potentials are generated by a composition-extended convexity-preserving grammar that guarantees thermodynamic admissibility \emph{by construction}. The framework is validated on synthetic datasets spanning Newtonian, power-law, and Bingham viscoplastic ground truths under process and measurement noise, and on experimental oscillatory shear measurements of a synthetic elastomer across multiple strain amplitudes and frequencies, where the discovered potentials reproduce the amplitude-dependent softening of the dynamic moduli and outperform a calibrated linear Zener baseline.

Problem

• dissipation potential
• thermodynamic admissibility
• symbolic regression
• constitutive laws
• Generalized Standard Materials

Innovation

• symbolic regression
• dissipation potential
• thermodynamic admissibility
• convexity-preserving grammar
• Generalized Standard Materials