Machine learning based modeling of path-dependent materials for finite element analysis

Abstract

Geological materials typically demonstrate a nonlinear and path-dependent behavior. Recently, data-driven techniques have emerged as a promising alternative to the traditional constitutive models or expensive micro-scale simulations, which can expedite simulations of complex geological systems. In particular, Recurrent Neural Networks (RNNs) are capable of capturing the history-dependent material behavior. However, one of the major limitations of RNNs is the dependence of the output stress on size of the strain increments. Since strain increments typically vary largely during simulations within nonlinear Finite Element (FE) solvers and are not known a priori, this limitation hinders the application of RNN constitutive models to FE modeling, leading to large errors and/or lack of convergence. In this work, we propose new model architectures and a random walk-based training data generation method to address this shortcoming. The proposed methodology is applied to J2 and Drucker–Prager plasticity models and tested in FE simulations of a range of boundary value problems with monotonic and cyclic linear and sinusoidal loading. Numerical results are presented to demonstrate the robustness of the proposed approach within the Newton’s method with varying strain increments and for unseen loading scenarios, as well as its consistency for decreasing/increasing rates of applied external loading.