A machine learning based multi-scale finite element framework for nonlinear composite materials

Abstract Multiscale modeling of inelastic behavior of composite materials is challenging due to high computational costs associated with high-fidelity simulations and transferring information across scales. Recently, data-driven techniques have emerged as a promising approach to expedite multiscale simulations of heterogeneous materials. In particular, Recurrent Neural Networks (RNNs) have been proven advantageous in capturing path-dependent material behavior (e.g. plasticity). However, application of RNNs within nonlinear finite element (FE) solvers remains challenging due to dependence of model outputs (stresses) on the strain increment size. Since during iterations of the nonlinear FE solvers irregular input strain increments are required which are not known in advance, implementation of RNN-based constitutive models in nonlinear FE solvers can lead to lack of convergence and large errors. Moreover, widespread application of RNN-based surrogate models in multiscale FE simulations requires integration of the trained surrogate model within existing widely used FE software packages. In this work, we develop a Gated Recurrent Unit (GRU) based 3D multiscale framework for elasto-plastic composite materials and make it accessible in a public repository. For this purpose, we develop an effective algorithm to generate training data from high-fidelity simulations of Representative Volume Elements (RVEs). Subsequently, we develop a FORTRAN algorithm which incorporates trained GRU models as a user material (UMAT) subroutine within the finite element software ABAQUS to perform multiscale finite element simulations. A range of 3D and 2D boundary value problems under different load cases are presented to demonstrate the accuracy and robustness of the proposed methodology.