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：本文提出了一种用于模拟循环加载下弹塑性固体的多时间尺度公式。我们利用适当广义分解（PGD）将位移分解为多个时间尺度，将空间与循环内依赖性从循环间变化中分离出来。与标准增量方法在每个时间步求解（非线性和计算密集型）力学平衡方程不同，所提出的PGD方法允许仅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由简单的标量代数方程描述。数值模拟展示了复杂的循环响应，包括一个二维问题以及对单桩基础的应用，结果表明，通过数值方法可获得具有有限时空自由度的PGD解，仅需少量模态即可精确捕捉参考响应。