AI summaryⓘ
The authors extended a special technique called strain-space model order reduction (MOR), which helps speed up complex calculations in materials science, to more general problems involving large shape changes in solid materials. They developed ways to handle complex boundary conditions automatically and improved existing methods for faster and more accurate simulations. When tested on example problems, their new strain-space methods performed better and much faster than previous approaches working in displacement space. Specifically, two methods called E3C and EMSL achieved huge speed improvements while keeping accuracy, with EMSL better for limited computing time and E3C better when more time is allowed.
strain-spacemodel order reductioncomputational homogenisationEmpirical Cubature Method (ECM)Empirically Corrected Cluster Cubature (E3C)Empirical Material Sampling and Linearisation (EMSL)Energy Conserving Weighting and Sampling (ECSW)large-deformation solid mechanicsparameterised boundary conditionshyperelasticity
Authors
Erik Faust, Lisa Scheunemann
Abstract
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.