Nonlinear homogenized properties of defected composite materials

•The nonlinear homogenized response of defected periodic composites is analyzed.•The influence of crack self-contact, instability and bifurcation is considered.•Novel crack boundary terms lead to a not self-adjoint variational problem.•Special classes of crack boundary data are individuated.•Self-contact nonlinearities and fracture greatly influence the macroscopic response.

The macroscopic response of elastic composite materials with periodic defected microstructures under large deformations is analyzed. The effects of microscopic instability and bifurcation are studied by using an updated Lagrangian formulation and frictionless self-contact between crack faces is accounted. Two special classes of homogenization problems are examined: effective contact and self-adjoint data. Numerical applications are developed by means of an FE approach with reference to a cellular material with diagonal microcracks and to a laminated microstructure with interface debonding. The strong role of crack self-contact nonlinearities and the influence of microscopic defects on the homogenized composite properties are pointed out.