The derivation and implementation of an asynchronous direct time integration scheme for domain-decomposed finite element models is presented. To maximize clarity in the description of the proposed asynchronous integration, the scheme is restricted to the linear-elastic stress wave propagation case. The proposed method allows the integration of individual subdomains with independent time steps. There is no requirement for an integer time steps ratio of the interacting domains while maintaining zero interface energy. The subdomains are connected by the condition of the continuity of the acceleration field at the interface. In addition, the a posteriori technique is applied to satisfy the continuity of the displacement and velocity fields. Another important contribution of this paper lies in the description of the implementation — we offer the reader a general description of the implementation of the case of any number of subdomains with any number of constraints between them, while the basics of the algorithm are explained on a single domain pair. The functionality of the asynchronous integrator is verified by solving selected problems and comparing with analytical solutions and experimental measurements obtained using a Split Hopkinson pressure bar setup.

介绍了域分解有限元模型的异步直接时间积分方案的推导和实现。为了最大限度地清晰描述所提出的异步集成，该方案仅限于线性弹性应力波传播情况。所提出的方法允许将各个子域与独立的时间步集成。在保持零界面能量的同时，不需要相互作用域的整数时间步长比。子域由界面处加速度场的连续性条件连接。此外，应用后验技术来满足位移场和速度场的连续性。本文的另一个重要贡献在于对实现的描述——我们为读者提供了对任意数量的子域以及它们之间具有任意数量的约束的情况的实现的一般描述，同时算法的基础知识在单域对。通过解决选定问题并与使用 Split Hopkinson 压力杆设置获得的分析解决方案和实验测量结果进行比较，验证了异步积分器的功能。