Multiscale computation on feedforward neural network and recurrent neural network

Homogenization methods can be used to predict the effective macroscopic properties of materials that are heterogenous at micro- or fine-scale. Among existing methods for homogenization, computational homogenization is widely used in multiscale analyses of structures and materials. Conventional computational homogenization suffers from long computing times, which substantially limits its application in analyzing engineering problems. The neural networks can be used to construct fully decoupled approaches in nonlinear multiscale methods by mapping macroscopic loading and microscopic response. Computational homogenization methods for nonlinear material and implementation of offline multiscale computation are studied to generate data set. This article intends to model the multiscale constitution using feedforward neural network (FNN) and recurrent neural network (RNN), and appropriate set of loading paths are selected to effectively predict the materials behavior along unknown paths. Applications to two-dimensional multiscale analysis are tested and discussed in detail.