An FE-DMN method for the multiscale analysis of thermomechanical composites

TL;DR

This paper introduces an extended FE-DMN method for multiscale thermomechanical analysis of composites, integrating deep material networks as surrogate models at Gauss points for efficient, high-fidelity simulations of coupled inelastic and non-isothermal behaviors.

Contribution

The paper develops a novel extension of the FE-DMN framework to fully coupled thermomechanical two-scale simulations, incorporating two-way coupling and efficient implementation as a user-material subroutine.

Findings

DMNs accurately predict effective stress and temperature changes.

The approach efficiently captures microscopic inelastic and thermal effects.

Validation confirms high accuracy of the surrogate model.

Abstract

We extend the FE-DMN method to fully coupled thermomechanical two-scale simulations of composite materials. In particular, every Gauss point of the macroscopic finite element model is equipped with a deep material network (DMN). Such a DMN serves as a high-fidelity surrogate model for full-field solutions on the microscopic scale of inelastic, non-isothermal constituents. Building on the homogenization framework of Chatzigeorgiou et al. [Int. J. Plast, vol. 81, pp. 18--39, 2016], we extend the framework of DMNs to thermomechanical composites by incorporating the two-way thermomechanical coupling, i.e., the coupling from the macroscopic onto the microscopic scale and vice versa, into the framework. We provide details on the efficient implementation of our approach as a user-material subroutine (UMAT). We validate our approach on the microscopic scale and show that DMNs predict the effective stress, the effective dissipation and the change of the macroscopic absolute temperature with high accuracy. After validation, we demonstrate the capabilities of our approach on a concurrent thermomechanical two-scale simulation on the macroscopic component scale.