This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. We leverage the proper generalized decomposition (PGD) to decompose the displacements into multiple time scales, separating the spatial and intra-cyclic dependence from the inter-cyclic variation. In contrast with the standard incremental approach, which solves the (non-linear and computationally intensive) mechanical balance equations at every time step, the proposed PGD approach allows the mechanical balance equations to be solved exclusively for the small-time intra-cyclic response, while the large-time inter-cyclic response is described by simple scalar algebraic equations. Numerical simulations exhibiting complex cyclic responses, including a 2D problem and an application to a monopile foundation, demonstrate that PGD solutions with a limited number of space-time degrees of freedom may be obtained numerically, only requiring a few modes to accurately capture the reference response.

翻译：本文提出了一种多时间尺度建模方法，用于模拟循环载荷作用下的弹塑性固体。我们利用广义特征分解（PGD）将位移分解为多个时间尺度，从而将空间响应和循环内依赖性与循环间变化分离开来。与在每个时间步求解（非线性且计算密集的）力学平衡方程的标准增量方法不同，所提出的PGD方法仅需针对小时间尺度的循环内响应求解力学平衡方程，而大时间尺度的循环间响应则通过简单的标量代数方程进行描述。数值模拟展示了复杂的循环响应行为，包括一个二维问题以及单桩基础应用实例，结果表明，仅需少量时空自由度即可通过数值方法获得PGD解，并且只需少量模式即可精确捕捉参考响应。