By using nonlocal discrete force functions, peridynamics (PD) can effectively deal with the problems involving discontinuities and singularities. As a continuum-based particle method, the material point method (MPM) and its advanced version, generalized interpolation material point method (GIMP), use local and nonlocal spatial discretization, respectively, to effectively simulate large deformations and multi-phase (solid–fluid–gas) interactions via mapping and remapping between material points and associated background nodes. However, nonlocal constitutive modeling has rarely been employed in the MPM or GIMP for simulating failure evolution. To combine the strengths of both PD and MPM/GIMP for better simulating the failure evolution under transient loading, an attempt is made to eliminate the limitation in the original PD due to the volume integration so that both MPM/GIMP and PD could be smoothly combined via volume modification. One-dimensional examples are employed to demonstrate and verify the proposed volume modification peridynamics and its combination with MPM/GIMP.

通过使用非局部离散力函数，周动力学（PD）可以有效处理涉及不连续性和奇异性的问题。作为基于连续体的粒子方法，材料点方法（MPM）及其高级版本（广义插值材料点方法（GIMP））分别使用局部和非局部空间离散化，以有效地模拟大变形和多相（固相物质点与关联的背景节点之间的映射和重新映射，从而实现了流体（气体）相互作用。但是，非局部本构模型很少在MPM或GIMP中用于模拟故障演变。为了结合PD和MPM / GIMP的优势来更好地模拟瞬态载荷下的失效演化，尝试消除由于体积集成而对原始PD造成的限制，以便可以通过更改体积将MPM / GIMP和PD平滑组合。一维示例用于演示和验证建议的体积修改围动力学及其与MPM / GIMP的组合。