A Time-Discontinuous Peridynamic Method For Transient Problems Involving Crack Propagation

A time-discontinuous peridynamic method (TDPD) for modeling transient problems of wave and crack propagation in solids is presented in this article. The main features of the TDPD are that the displacement field and the velocity field are independently interpolated in the temporal domain by using cubic and linear functions, respectively. Jump terms representing discontinuities of the variables are introduced between the adjacent time steps. The weak form and a new time integration scheme are derived by combining the peridynamic governing equations with the time-discontinuous method. The displacement field is continuous while discontinuous jumps are introduced into the velocity field. Those characteristics enable the TDPD to accurately capture the sharp gradient in stress and effectively control the spurious numerical oscillation. The effectiveness of the TDPD is first demonstrated through two representative numerical examples of wave propagation. Three additional examples are presented to show the advantages of the TDPD in the simulation of dynamic crack propagation problems. It is shown that TDPD provides more accurate and satisfactory results when compared with the traditional time integration scheme.