Within the framework of computational plasticity, recent advances show that the quasi-static response of an elasto-plastic structure under cyclic loadings may exhibit a time multiscale behaviour. In particular, the system response can be computed in terms of time microscale and macroscale modes using a weakly intrusive multi-time Proper Generalized Decomposition (MT-PGD). In this work, such micro-macro characterization of the time response is exploited to build a data-driven model of the elasto-plastic constitutive relation. This can be viewed as a predictor-corrector scheme where the prediction is driven by the macrotime evolution and the correction is performed via a sparse sampling in space. Once the nonlinear term is forecasted, the multi-time PGD algorithm allows the fast computation of the total strain. The algorithm shows considerable gains in terms of computational time, opening new perspectives in the numerical simulation of history-dependent problems defined in very large time intervals.

翻译：在计算塑性力学框架下，最新研究表明，循环加载下弹塑性结构的准静态响应可能表现出时间多尺度行为。具体而言，可采用弱侵入式多时间本征正交分解（MT-PGD）方法，根据时间微尺度与宏尺度模态计算系统响应。本研究利用这种时间响应的微-宏表征特性，构建弹塑性本构关系的数据驱动模型。该模型可视为预测-校正方案：预测由宏观时间演化驱动，校正通过空间稀疏采样实现。一旦非线性项被预测，多时间PGD算法即可快速计算总应变。该算法在计算时间方面展现出显著优势，为极长时间区间内历史依赖问题的数值模拟开辟了新前景。