Strain‐Space Hyperreduction Using Empirically Corrected Cluster Cubature With Linear and Quadratic Approximation Spaces

ABSTRACT Strain‐space reduced cubature techniques such as the Empirically Corrected Cluster Cubature (E3C) considerably reduce the integration effort incurred in computational homogenisation problems. In this work, we apply E3C in tandem with projection‐based model reduction techniques utilising both linear and quadratic approximation spaces. For simulations on an example porous hyperelastic representative volume element (RVE), E3C leads to considerably improved performance, whether with linear or quadratic approximation spaces, over alternative hyperreduction approaches explored in our previous work. As expected, a quadratic ansatz allows for the construction of smaller approximation spaces than a linear one, with equal accuracy. However, in the example explored here, this does not translate into an improved tradeoff between accuracy and runtime.