Substitution approach for decoupled two-scale analysis of materially nonlinear composite plates

A new substitution approach is proposed for decoupled two-scale analysis of a materially nonlinear composite plate with in-plane periodic meso-structures within the framework of computational homogenization. The macroscopic nonlinear mechanical behavior of the plate is characterized by numerical plate tests on an in-plane unit structure (IPUS), which enables us to obtain the relationship between macroscopic resultant stresses and generalized strains. Then, we postulate that the original composite plate can be substituted by an equivalent laminated plate that exhibits approximately the same macroscopic response. The material parameters of each lamina of this substitute, which is referred to as mesoscopic substitution model (meso-SM), are identified using an optimization method so that it could be equivalent to the original IPUS. After the parameter identification, the corresponding macroscopic substitution model (macro-SM) can be analyzed with appropriate analysis software that supports laminated plate elements. Representative numerical examples are presented to validate the appropriateness of the proposed approach by performing comparative calculations with the results obtained from the original composite plates.