Crack kinking in isotropic and orthotropic micropolar peridynamic solids

Abstract

A micropolar peridynamic model is presented for characterizing crack propagation in isotropic and orthotropic brittle materials. The analytical formulation of the two-dimensional model is based on the definition of a micropotential energy function that accounts for the four independent elastic constants that define orthotropy and that in the limit can be reduced to isotropy. A distinctive feature of the model is that the bonds’ elastic parameters are continuous functions of orientation with respect to principal material axes. By defining three deformation parameters that quantify bond stretch, bond shear deformation and particles relative rotation, the first continuum bond-based peridynamic model is obtained for two-dimensional Cauchy orthotropic materials characterized by four independent material moduli that is suitable for describing fracture as well as homogeneous and non-homogeneous deformations.The accuracy of the computational model as applied to crack-tip analyses is assessed by comparing the displacement and stress fields within the boundary layer that develops in the immediate vicinity of a crack with the analytical asymptotic results for an orthotropic continuum. The extension of such cracks when they are subjected to mixed-mode loading is simulated under the assumption of illustrative crack extension criteria, and the predictions are compared to those of the maximum hoop stress intensity factor criterion (HSIF-criterion) and the maximum energy release rate criterion (G-criterion).