A neural network-based material cell for elastoplasticity and its performance in FE analyses of boundary value problems

Abstract

This research focuses on evaluating the capacity and performance of a network-based material cell as a constitutive model for boundary-value problems. The proposed material cell aims to replicate constitutive relationships learned from datasets generated by random loading paths following a stochastic Gaussian process. The material cell demonstrates its effectiveness across three progressively complex constitutive models by incorporating physical extensions and symmetry constraint as prior knowledge. To address the challenge of magnitude gaps between strain increments in training sets and finite element simulations, an adaptive linear transformation is introduced to mitigate prediction errors. The material cell successfully reproduces constitutive relationships in finite element simulations, and its performance is comprehensively evaluated by comparing two different material cells: the sequentially trained gated recurrent unit (GRU)-based material cell and the one-to-one trained deep network-based material cell. The GRU-based material cell can be trained without explicit calibration of the internal variables. This enables us to directly derive the constitutive model using stress–strain data without consideration of the physics of internal variables.