Homogenization methods and macro-strength of composites

A multi-phase periodic composite subjected to inhomogeneous shrinkage or temperature deformation and prescribed mechanical loads is considered. The asymptotic homogenisation is applied for calculation of homogenized macrostresses. A non-local approximate macro-strength condition, defined on homogenised stress-field, is derived from the micro-strength conditions and their convergence to the approximate macro-strength condition, as the structure period tends to zero, is proved.