Implicit implementation of the stabilized non-ordinary state-based peridynamic model

This paper presents a stabilized non-ordinary state-based peridynamic model, in which the numerical instability problems induced by the zero-energy mode are overcome. The implicit discretization formulation of this model is proposed. In order to depict the progressively damaging process in coarse discretization conditions, a bilinear damage model based on the influence function is developed. An implicit implementation of the stabilized non-ordinary state-based peridynamic model is presented, in which an iterative procedure based on the secant stiffness method is used to solve the nonlinear problem. This method does not need to introduce a damping term in solving static problems, and relatively large load steps are desirable. Five numerical examples are analyzed to demonstrate the effectiveness of the present method for quantitatively simulating the quasi-static crack propagation problems.