大变形固体力学中高效的应变空间超降阶法
Efficient strain-space hyperreduction in large-deformation solid mechanics
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中文总结 AI 辅助
研究大变形固体力学问题，通过满足特定边界条件在应变空间推广经验求积法等技术，将其应变空间版本与标准位移空间公式比较，在两个超弹性示例问题上，应变空间方法在运行时间和精度权衡上更优，E3C和EMSL有显著加速和高精度。
中文摘要 AI 辅助
应变空间模型降阶（MOR）技术在计算均匀化问题的运行时间和精度权衡方面表现出色。本文将该技术推广到大变形固体力学问题。通过离线计算边界一致场的提升来满足任意值、参数化的狄利克雷边界条件，从而在应变空间中提出经验求积法（ECM）的一个版本，并推广经验校正聚类求积法（E3C）和经验材料采样与线性化（EMSL）。将EMSL、ECM和E3C的应变空间版本与能量守恒加权和采样（ECSW）的标准位移空间公式进行比较。在两个具有参数化材料行为和变形的超弹性示例问题上，应变空间方法在运行时间和精度的权衡上优于位移空间方法。特别是E3C和EMSL分别实现了10000倍和100000倍的加速，同时保持了高精度。当在线和离线运行时间预算非常有限时，EMSL是首选方法，而当稍微多一点运行时间可以接受时，E3C产生了极高的精度。
英文摘要
Strain-space model order reduction (MOR) techniques have recently been shown to achieve exceptional performance in terms of the tradeoff between runtime and accuracy achieved in computational homogenisation problems. In this article, we generalise such techniques to problems in large-deformation solid mechanics beyond the context of computational homogenisation. Arbitrary-valued, parameterised Dirichlet boundary conditions are satisfied by construction using a lifting with boundary-consistent fields computed offline. This allows us to pose a version of the Empirical Cubature Method (ECM) [24,25] in strain space and generalise the Empirically Corrected Cluster Cubature (E3C) [46,48,49] as well as Empirical Material Sampling and Linearisation (EMSL) [17] beyond computational homogenisation problems. The strain-space versions of EMSL, ECM, and E3C are compared against each other and a standard displacement-space formulation of Energy Conserving Weighting and Sampling (ECSW) [15]. On two hyperelastic example problems with parameterised material behaviour and deformation, the strain-space methods outperform the displacement-space alternative in the tradeoff between runtime and accuracy. E3C and EMSL in particular facilitate 10,000 and 100,000-fold speedups, respectively, while retaining high levels of accuracy. EMSL is shown to be the method of choice when online and offline runtime budgets are very limited, while E3C yields exceptional levels of accuracy when slightly more runtime is acceptable.
