Pre-trained transformer model as a surrogate in multiscale computational homogenization framework for elastoplastic composite materials subjected to generic loading paths

Abstract

A composite material typically exhibits complex behavior at the engineer scale, arising from the interactions between its underlying constituent phases, as well as the competitions between micro-processes. It is generally a daunting task to develop an engineering model to adequately capture the essential micro mechanisms that propagate onto the macro scale. To this end, the multiscale computational homogenization (FE2) method enables a consistent coupling across length scales, to give results that compare well with direct numerical simulations having the full micro-structural details, without the need for any constitutive assumptions nor calibrations at the macro scale. Despite its predictive capabilities, the typical computational homogenization method is still computationally too expensive for most practical problems, as the coupling between micro and macro scales are solved simultaneously during its numerical implementation. In this presentation, focusing on the elastoplastic behavior of fiber-reinforced composite, we address this bottleneck with an offline development of a microscopic surrogate model for a given micro-structure, to be incorporated into a standard nonlinear FE framework, for rapid online implementations at the macro scale. For the offline training phase, we adopt the transformer-based architecture within a pre-training and fine-tuning framework. The proposed pre-trained transformer model is capable of parallelizing computations to effectively capture global dependencies within the strain-stress data sequences. To reduce the data generation cost, a constructed source representative volume element (RVE) having a single central heterogeneity with an identical volume fraction with the target RVE is utilized, to rapidly generate a huge source dataset for a pre-training process. The performance of the surrogate model is first demonstrated by comparing its predictions under random loading paths against the reference homogenized RVE responses. Next, the surrogate model is incorporated into a macro FE framework, and its predictive capabilities illustrated via the generic loading of two specimens with different microstructures, each having a different loading–unloading path. Finally, a chunking method is discussed as a potential remedy for managing very long load sequences.