Cross Scale Simulation of Fiber-Reinforced Composites with Uncertainty in Machine Learning

Abstract

Cross scale simulation aims to develop computational models that can capture the behavior of a system at multiple scales, from microscopic to macroscopic level. To explore the constitutive relationship of materials, a widely used conceptual and numerical tool called Representative Volume Element (RVE) is introduced to solicit information from their subscales in finite element analysis. It characterizes the behavior at one quadrature point of a physical device by homogenizing the local behavior over finer scales. By replicating the RVE throughout the analysis domain, a homogeneous finite element model can be synthesized, simplifying the analysis of a heterogeneous material in the presence of uncertainty, such as variations in loading, material properties of micro-constituents, and modeling physical behavior. Moreover, the generation of many similar data at subscale introduced by homogenization in RVE is usually tackled by statistical methods. In this work, we explore the mechanical behavior of a hybrid composite material, consisting of glass and carbon fibers embedded in an epoxy resin for use as a battery enclosure, using a novel energy density informed neural network architecture. We model the material properties of fiber tows and resin as random variables and use input strain tensors from a macro-scale three-point bend test simulation. History of stress tensors and strain energy density are extracted as outputs for supervise learning. In the neural network architecture, Physical constraints are implemented by introducing a novel energy density layer for the prediction of stress along the direction of tows. A long-short-term-memory (LSTM) neural network training on the same dataset is also conducted for comparison. Elimination of spurious discontinuities is obtained by PCA (Principal Components Analysis) in the stress-strain curve when predicting stresses in directions transverse to the tows, YY and ZZ directions. We develop a user-defined subroutine in LS-Dyna and conduct a mesoscale simulation to verify its accuracy.