Finite element analysis of fracture mechanics in micromorphic theory

In this work, the kinematics and basic laws of micromorphic theory are briefly introduced. Then, constitutive equations for micromorphic thermo-visco-elastoplastic solids are rigorously derived. Finite element equations for the displacement, micromotion and temperature fields are formulated based on the principle of virtual work. As examples, three-dimensional, dynamic, finite strain, mixed mode fracture mechanics problems have been solved by a general purpose in-house developed code. Numerical results, including temperature, L2 norms of stresses, plastic strains and micromotions, are presented and the physical meanings are discussed. This paper provides theoretical fundamentals to study the thermo-visco-elastic-plastic behaviors of micromorphic solids and constructs a numerical framework to study fracture mechanics of edge-crack problems.