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 behavior. 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 forecast, 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.

在计算塑性的框架内，最新进展表明，弹塑性结构在循环载荷下的准静态响应可能表现出时间多尺度行为。特别是，可以使用弱侵入性多时间适当广义分解（MT-PGD）根据时间微观尺度和宏观尺度模式来计算系统响应。在这项工作中，利用时间响应的这种微观-宏观表征来构建弹塑性本构关系的数据驱动模型。这可以被视为预测器-校正器方案，其中预测由宏观时间演化驱动，并且通过空间中的稀疏采样来执行校正。一旦非线性项被预测，多次 PGD 算法就可以快速计算总应变。该算法在计算时间方面显示出相当大的收益，为在非常大的时间间隔内定义的历史相关问题的数值模拟开辟了新的视角。