Continuous defects: dislocations and disclinations in finite elasto-plasticity with initial dislocations heterogeneities
Within the constitutive framework of second order plasticity, following [4, 5] , under the assumptions that the plastic distortion is not compatible, and the plastic connection is not compatible with the plastic distortion and has metric property, we define the lattice defects in crystalline elastoplastic materials. The curl of plastic distortion, which defines the Burgers vector, is a measure of the dislocations. The disclination is characterized in terms of the second order tensor, which
... tensor, which enters the expression of the plastic connection and generates the Frank vector. The free energy density is postulated to be dependent on the elastic deformation and the measures of the defects. The non-local, diffusion-type evolution equations for plastic distortion and the damage tensor are derived to be compatible with the dissipation inequality, while the micro stress momenta, associated with the plastic and disclination mechanisms, are derived from the free energy function. We restrict the evolution equations for defects to small elastic and plastic distortions, considered to be wedge disclinations and edge dislocations. The finite element method is applied to numerically study the evolution of the defects, when the initial dislocation heterogeneities are considered.