On the constitutive relations of materials with evolving microstructure due to microcracking

This paper discusses the practical implementation of a thermodynamically based procedure for the derivation of the e€ective nonlinear constitutive relations for composites with evolving microstructure. Examples of the procedure for the case of an elastic periodic composite with several growing cracks are presented. These examples are intended to show how the use of this procedure di€ers from the traditional global-local analysis approach and how well suited it is for use with general purpose structural analysis packages