Abstract
A new representation theorem for the deformation gradient rate in the presence of cracks and kinematic constraints is presented. This representation theorem uses an extension of the concept of transformation strains to finite deformations. Based on the representation theorem the overall concentration factor was decomposed into contributions from the opening and sliding of cracks and from material nonhomogeneities. Also, inelastic deformations at the microscale were related to those at the macroscale through elastic concentration factors, where it was found that some of the elastic deformation at the microscale may contribute to the macroscale inelastic deformations.
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