Nonlocal anisotropic model for deformation and fracture using peridynamic operator method

Abstract

This paper proposes a nonlocal anisotropic model for deformation and fracture based on peridynamic operator method. The classic anisotropic theory is reformulated from its local form into nonlocal form by using peridynamic operator method. The final solution formulation is developed by employing variational principles and Lagrange's equations. In the case of the circular interaction domain, this model can be regarded as a novel anisotropic ordinary state-based peridynamic model. Moreover, we present for the first time the energetic failure criterion for the weak anisotropic fracture. Unlike the existing anisotropic peridynamic models that consider only two fracture toughness constants for orthogonal orientation, the fracture toughness in this criterion is an orientation-dependent function. Additionally, we develop an implicit static solution procedure to investigate corresponding crack propagation problems. Several numerical examples demonstrate the effectiveness and ability of the proposed model in handling the deformation and fracture behaviours of anisotropic materials.