Simulating crack growth and failure in a composite: A vector model for a layered composite material

A model is proposed for cracking and failure in a layered composite having an inhomogeneous microstructure. The model uses a union of vector spaces for the mechanical characteristics of the material and the volume contents of the layers. The elastic parameters for each layer are considered as random functions of an arbitrarily defined volume. The state of stress and strain are described by the components of the macrostress and macrostrain tensors with respect to a certain (structural) volume.