Vijayaraghavan S, Wu L, Noels L, Bordas S P A, Natarajan S, Beex L A A
Faculty of Science, Technology and Medicine, University of Luxembourg, 6 Avenue de la Fonte, Esch-Sur-Alzette, Luxembourg.
University of Liege, Bât. B52/3 Computational & Multiscale Mechanics of Materials, Quartier Polytech 1, allée de la Découverte 9, 4000, Liège, Belgium.
Sci Rep. 2023 Aug 7;13(1):12781. doi: 10.1038/s41598-023-38104-x.
This contribution discusses surrogate models that emulate the solution field(s) in the entire simulation domain. The surrogate uses the most characteristic modes of the solution field(s), in combination with neural networks to emulate the coefficients of each mode. This type of surrogate is well known to rapidly emulate flow simulations, but rather new for simulations of elastoplastic solids. The surrogate avoids the iterative process of constructing and solving the linearized governing equations of rate-independent elastoplasticity, as necessary for direct numerical simulations or (hyper-)reduced-order-models. Instead, the new plastic variables are computed only once per increment, resulting in substantial time savings. The surrogate uses a recurrent neural network to treat the path dependency of rate-independent elastoplasticity within the neural network itself. Because only a few of these surrogates have been developed for elastoplastic simulations, their potential and limitations are not yet well studied. The aim of this contribution is to shed more light on their numerical capabilities in the context of elastoplasticity. Although more widely applicable, the investigation focuses on a representative volume element, because these surrogates have the ability to both emulate the macroscale stress-deformation relation (which drives the multiscale simulation), as well as to recover all microstructural quantities within each representative volume element.
本文讨论了在整个模拟域中模拟解场的替代模型。该替代模型使用解场的最具代表性的模态，并结合神经网络来模拟每个模态的系数。这种类型的替代模型在快速模拟流动方面是众所周知的，但在弹塑性固体模拟中却是相当新的。该替代模型避免了直接数值模拟或（超）降阶模型中构建和求解与速率无关的弹塑性线性化控制方程的迭代过程。相反，新的塑性变量在每个增量中只计算一次，从而节省了大量时间。该替代模型使用循环神经网络在神经网络内部处理与速率无关的弹塑性的路径依赖性。由于仅针对弹塑性模拟开发了少数此类替代模型，其潜力和局限性尚未得到充分研究。本文的目的是在弹塑性背景下更深入地了解它们的数值能力。尽管适用性更广，但研究集中在一个代表性体积单元上，因为这些替代模型既能模拟宏观尺度的应力 - 变形关系（驱动多尺度模拟），又能恢复每个代表性体积单元内的所有微观结构量。
