Constitutive relations for cracked metal matrix composites

A method is given for the prediction of the overall stress-strain response of elastoplastic solids containing a doubly periodic rectangular array of cracks. The behavior of the undamaged inelastic material is represented by constitutive laws for metal matrix composites based on a micromechanics analysis. The effect of cracking is incorporated by adopting a second order expansion of the displacement vector, in conjunction with the equations of equilibrium and displacement and traction continuity conditions. Due to the nonlinearity and path dependence of deformation, the stresses need to be represented by a higher order expansion than the second. The method is implemented to predict the overall stress-strain response of a cracked isotropic inelastic material, as well as cracked unidirectional and laminated metal matrix composites.