Superposition of non-ordinary state-based peridynamics and finite element method for material failure simulations, including crack propagation and strain localization is developed. By this approach, a peridynamic model capable of effectively treating strong and weak discontinuities is superimposed in the critical regions over an underlying finite element mesh placed over the entire problem domain. A rigorous variational framework of coupling local finite element and nonlocal peridynamics approximations that is free of blending parameters is developed. Several numerical examples involving mixed-model fracture, three-dimensional adaptive crack propagation and strain localization induced ductile failure demonstrate the rational and efficiency of the proposed superposition-based coupling approach.

中文翻译：

---

用于材料失效模拟的非普通状态近场动力学和有限元方法的叠加

用于材料失效模拟的非普通状态近场动力学和有限元方法的叠加，包括裂纹扩展和应变局部化。通过这种方法，能够有效处理强不连续性和弱不连续性的近场动力学模型叠加在关键区域中，覆盖在整个问题域上的底层有限元网格上。开发了耦合局部有限元和非局部近场动力学近似的严格变分框架，该框架没有混合参数。几个涉及混合模型断裂、三维自适应裂纹扩展和应变局部化引起的延性破坏的数值例子证明了所提出的基于叠加的耦合方法的合理性和有效性。