For elastodynamic problems, significant effort has been exerted by numerical researchers to eliminate the reflection of outgoing elastic waves at the boundary of the computational domain. Eliminating these reflection is very important for correctly analyzing the dynamic response of various structures. In this paper, the enriched degree of freedom method is first proposed to absorb outgoing elastic waves; degrees of freedom are added to the nodes in the absorbing domain by using a user-defined function. Next, the gradually increasing mass matrix is derived to further dampen the elastic waves based on the theory of the perfectly matched layer. Then, a novel damping method is proposed based on the enriched degree of freedom method, and it is appropriately coupled with the XFEM and the modified Newmark algorithm to solve elastodynamic problems with infinite boundaries. Finally, the numerical results show that the proposed method is feasible and applicable for absorbing the outgoing elastic waves. Importantly, the proposed method is independent of the frequency; it can be used to simulate the field-scale model and the laboratory-scale model, and it is effective in solving problems with multiple cracks.

对于弹性动力学问题，数值研究人员已经付出了巨大的努力来消除在计算域边界处的出射弹性波的反射。消除这些反射对于正确分析各种结构的动态响应非常重要。本文首次提出了富集自由度法来吸收出射弹性波；通过使用用户定义的函数将自由度添加到吸收域中的节点。接下来，基于完美匹配层的理论，推导出逐渐增加的质量矩阵以进一步抑制弹性波。然后，提出了一种新的基于丰富自由度方法的阻尼方法，并与 XFEM 和修改后的 Newmark 算法适当结合，解决无限边界的弹性动力学问题。最后，数值结果表明，该方法对于吸收出射弹性波是可行和适用的。重要的是，所提出的方法与频率无关。可用于模拟现场尺度模型和实验室尺度模型，有效解决多裂缝问题。