Multi-time-step coupling of peridynamics and classical continuum mechanics for dynamic brittle fracture

Abstract

Peridynamics (PD), as a nonlocal theory, is well-suited for solving problems with discontinuities, such as cracks. However, the nonlocal effect of peridynamics makes it computationally expensive for dynamic fracture problems in large-scale engineering applications. As an alternative, this study proposes a multi-time-step (MTS) coupling model of PD and classical continuum mechanics (CCM) based on the Arlequin framework. Peridynamics is applied to the fracture domain of the structure, while continuum mechanics is applied to the rest of the structure. The MTS method enables the peridynamic model to be solved at a small time step and the continuum mechanical model is solved at a larger time step. Consequently, higher computational efficiency is achieved for the fracture domain of the structure while ensuring computational accuracy, and this coupling method can be easily applied to large-scale engineering fracture problems.

Figures (17)

• Figure 1: (a)the peridynamic problem, (b)the classical continuum problem.
• Figure 2: Decomposition of two subdomains.
• Figure 3: Time steps for the two subdomains with time step ratio $m$, where $t_j=t_0+j\triangle t^{PD},\ j=0,\cdots,m$.
• Figure 4: The geometry and domain decomposition, where the overlapping domain $\Omega^O=\Omega^P\cap\Omega^C$.
• Figure 5: The variation of the weight function $\alpha(\bm{x})$ between subdomains.