Multiscale finite element analysis of uncertain-but-bounded heterogeneous materials at finite deformation

A new computationally interval homogenization modelling for heterogeneous materials with uncertain-but-bounded parameters is presented in a deformation controlled setting, and the homogenization analysis in the context of elasticity at finite deformation is then addressed by an integrative approach of finite element method with the optimization algorithms where the interval uncertainty in the microstructure of the material is fully considered. Different deformation-controlled boundary conditions are imposed on the representative volume element, and the interval effective quantities involving the tangent tensor and the first Piola–Kirchhoff stress tensor as well as the strain energy together with the effective moduli are obtained. The influences of different uncertain cases on the interval effective quantities are also analyzed. For the purpose of verification, the results from particle swarm optimization (PSO) algorithm are compared with those obtained from genetic algorithm (GA) and Monte-carlo simulation. The feasibility and validity of the proposed modelling method are evidenced by the well-agreed consequences among the above algorithms.