In this paper both of the elastic-viscoelastic correspondence principle and time stepping method, which can convert viscoelasticity to elasticity, are employed to the boundary element method (BEM) to solve the contact problems between multiple rigid punches and anisotropic viscoelastic foundation. The one based upon the correspondence principle has the restriction on time-invariant boundaries, and hence can only be applied to the cases of complete indentation whose contact region as well as contact status are time-independent. The other based upon the time stepping method is processed step-by-step in time domain, and its boundary conditions may vary in each time step, and hence can be applied to both complete and incomplete indentations. Both methods are valid for the frictionless or frictional contact surface, the punches can be in equilibrium status or in quasi-static sliding condition, and the number of punches and the punch profiles are arbitrary. Benefited by the elastic system used for BEM, both methods hold the feature that no meshes are required on the rigid punches and holes/cracks. Through the iteration procedure and numerical examples presented in this study, we see that the one based upon time-stepping method is much more general and efficient than the other one.

本文将弹性-粘弹性的对应原理和可以将粘弹性转换为弹性的时间步长方法应用于边界元方法（BEM），以解决多个刚性冲头与各向异性粘弹性基础之间的接触问题。基于对应原理的一个具有时不变边界的限制，因此只能应用于接触区域和接触状态与时间无关的完全压痕的情况。基于时间步长方法的另一个在时域中逐步进行处理，其边界条件可能在每个时间步中有所变化，因此可以应用于完整和不完整的压痕。两种方法均适用于无摩擦或摩擦接触表面，冲头可以处于平衡状态或准静态滑动状态，并且冲头的数量和冲头轮廓是任意的。得益于用于BEM的弹性系统，这两种方法都具有以下特点：刚性冲头和孔/裂纹不需要网格。通过本研究中介绍的迭代过程和数值示例，我们看到一种基于时间步长方法的方法比另一种方法更为通用和有效。