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 81:18–39, 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.
Highlights
Many common engineering materials are characterized by a thermomechanically coupled mechanical behavior, i.e., involving a coupling between temperate and deformation
In the work at hand, we extended the framework of direct deep material network (DMN) to fully coupled thermomechanical two-scale simulations
We built upon the first-order homogenization framework of thermomechanical composites established by Chatzigeorgiou et al [5], who showed that there is no fluctuation of the absolute temperature on the microscopic scale
Summary
Many common engineering materials are characterized by a thermomechanically coupled mechanical behavior, i.e., involving a coupling between temperate and deformation. Masi and co-workers [49,50] proposed so-called thermodynamics-based artificial neural networks (TANN) which ensure thermodynamic consistency a priori Their findings indicate that the predictive capabilities of TANNs outperform those of standard ANNs. Please note that the mentioned approaches only consider a one-way thermomechanical coupling, i.e., from the temperature on the effective properties, and not vice versa. We take special care in incorporating the coupling of microscopic mechanical deformation onto the macroscopic temperature and vice versa into our approach For this purpose, we exploit the homogeneity of the absolute temperature on the microscopic scale to arrive at an efficient solution scheme for solving the balance of linear momentum of a direct DMN.
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