A nonlinear mixture theory for the dynamic response of a laminated composite under large deformations

A nonlinear mixture theory of solids is derived to model the dynamic response of a laminated medium under large deformations. The composite is made of constituents which obey a nonlinearly elastic constitutive law. The microstructure effects are taken into account in this mixture model in which every constituent has its own motion but is allowed to interact with the other. The model is developed by applying an asymptotic expansion, which by a proper truncation can be cast into nonlinear binary mixture equations. Linearization of the equations for the case of infinitesimal deformations yields the linear mixture model developed previously. The model is applied to a laminated slab under time dependent loading and results are given for both positive and negative loadings and contrasted with the corresponding linear responses.