Computation of Homogenized Constitutive Tensor of Elastic Solids Containing Evolving Cracks

The determination of the equivalent (homogenized) constitutive tensor is one of the most important steps in multiscale models as well as in the classical homogenization theory. In this article, a procedure for determining the homogenized instantaneous (tangent) constitutive tensor of elastic materials containing growing cracks is proposed. The primary purpose of this procedure is its use in two-way coupled multiscale finite element algorithms that can model crack formation and propagation at the local microstructure. The procedure is basically developed by relating the local displacement field to the global strain tensor at each location and using first-order homogenization techniques. The finite element formulation is developed and some example problems are presented in order to verify and demonstrate the model capabilities.