Abstract A dual peridynamics (PD) for brittle fracture is implemented in the commercial software Abaqus by means of UEL/VUEL and UMAT/VUMAT subroutines, thereby, the peridynamic finite element method (PDFEM) will come into being. To this end, the concept of the peridynamic node and element is defined, subsequently, the peridynamic element internal force vector and mass matrix for the explicit PDFEM and the peridynamic element stiffness matrix for the implicit PDFEM are derived and constructed for the explicit and the implicit finite element implementation of the dual peridynamics in Abaqus, respectively. Additionally, a dual-based coupling approach is developed to couple the PDFEM and FEM to optimize the computational efficiency and accuracy of the pure PDFEM. Several numerical examples involving the static and dynamic crack propagation are investigated and the satisfactory results show the availability of the PDFEM and the hybrid model between PDFEM and FEM. Moreover, the finite element implementation of peridynamics in Abaqus may pave the way to an increased application of peridynamics to the practical engineering problems.

中文翻译：

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用于脆性断裂的双近场动力学的 Abaqus 实现

摘要 在商业软件Abaqus中通过UEL/VUEL和UMAT/VUMAT子程序实现了脆性断裂的对偶近场动力学(PD)，从而产生了近场动力学有限元法(PDFEM)。为此，定义了近场动力学节点和单元的概念，随后推导并构造了显式 PDFEM 的近场动力学单元内力矢量和质量矩阵以及隐式 PDFEM 的近场动力学单元刚度矩阵。分别在 Abaqus 中对双近场动力学的有限元实现。此外，还开发了一种双基耦合方法来耦合 PDFEM 和 FEM，以优化纯 PDFEM 的计算效率和准确性。研究了几个涉及静态和动态裂纹扩展的数值例子，令人满意的结果表明 PDFEM 以及 PDFEM 和 FEM 之间的混合模型的可用性。此外，近场动力学在 Abaqus 中的有限元实现可能为近场动力学在实际工程问题中的更多应用铺平道路。