Time-discontinuous state-based peridynamics for elasto-plastic dynamic fracture problems

Abstract

A time-discontinuous state-based peridynamic method (SBPD-TD) is developed in this paper to model the transient problems of wave and crack propagation in solids. In this method, the non-local deformation gradient is derived in a consistent way using the least square method, so that the classical elasto-plastic constitutive relationship can be directly adopted in the SBPD based on the correspondence material modeling. Then the displacement field and the velocity field are interpolated independently in the temporal domain respectively, in which the jump terms representing the discontinuities of variables are introduced between the adjacent time steps. After that, an integral weak form in the temporal domain of the spatially discrete governing equations is constructed and the basic formula of SBPD-TD is derived. The above-mentioned characteristics ensure that the SBPD-TD can accurately capture the sharp gradient characteristics in the propagation of elastic and plastic stress waves and effectively control the spurious numerical oscillations. Several representative numerical examples show that the SBPD-TD provides more accurate and satisfactory results when compared with the conventional SBPD, and has broad applications to predict the contact impact fracture behaviors of various materials.