For the numerical simulation of time-dependent problems, recent works suggest the use of a time marching scheme based on a tensorial decomposition of the time axis. This time-separated representation is straightforwardly introduced in the framework of the Proper Generalized Decomposition (PGD). The time coordinate is transformed into a multi-dimensional time through new separated coordinates, the micro and the macro times. From a physical viewpoint, the time evolution of all the quantities involved in the problem can be followed along two time scales, the fast one (micro-scale) and the slow one (macro-scale). In this paper, the method is applied to compute the quasi-static response of an elasto-plastic structure under cyclic loadings. The study shows the existence of a physically consistent temporal decomposition in computational cyclic plasticity. Such micro-macro characterization may be particularly appealing in high-cycle loading analyses, such as aging and fatigue, addressed in a future work in progress.

翻译：针对时间相关问题数值模拟，近期研究提出了一种基于时间轴张量分解的时间推进格式。这种时间分离表示可自然引入本征广义分解（PGD）框架。通过引入新的分离坐标——微观时间与宏观时间，时间坐标被转化为多维时间。从物理角度而言，问题中所有物理量的时间演化均可沿快时间尺度（微观尺度）与慢时间尺度（宏观尺度）两个时间尺度进行追踪。本文将该方法应用于循环荷载作用下弹塑性结构准静态响应计算。研究表明，在计算循环塑性力学中存在物理一致的时间分解方式。这种微观-宏观表征方法对于高周加载分析（如未来工作中将涉及的时效与疲劳问题）具有特殊吸引力。