Effective hyperelastic material parameters from microstructures constructed using the planar Boolean model

Abstract We construct two-dimensional, two-phase random heterogeneous microstructures by stochastic simulation using the planar Boolean model, which is a collection of overlapping grains. The structures obtained are discretized finite elements. A Neo-Hooke law assumed for phases microstructure, and tension tests simulated ensembles microstructure samples. determine effective material parameters, i.e., Lamé moduli $$\lambda ^*$$ ? ? $$\mu ? , on macroscale fitting macroscopic model to microscopic stress data, averaging over many parameters considered as functions microscale geometric including grain shape. also consider size Representative Volume Element (RVE) given precision an ensemble size. use structured unstructured meshes provide comparison with FE $$^2$$ 2 method.