On the analysis of cross-ply laminates with micro-cracks and inelastic deformation (Q1282613)

We propose a general framework for the analysis of cross-ply laminates with micro-matrix cracks and inelastic deformation. For this purpose, admissible stress fields are constructed which satisfy equilibrium and all boundary and interface conditions. We use the principle of minimum complementary energy to derive a differential equation for the stress function from which the stress field of the composite can be derived. The inhomogeneous terms of the differential equation involve the inelastic strains which are loading-history dependent. The Green's function of the differential equation is then obtained. Using the Green's function and a constitutive equation, two-dimensional stress and strain states in the composite at any time are represented by an integral of the Green's function and the inelastic strains accumulated up to that time. This new analysis takes into consideration the microcrack-microcrack interaction, as well as the interaction between the microcracks and the inelastic deformation, and provides a point-wise variation of the stress field instead of average stress field as most of the analytic approaches yield.