Efficient cut-cell quadrature based on moment fitting for materially nonlinear analysis

Abstract Cut-cell quadrature based on the moment fitting scheme generates an accurate numerical integration rule for each cut element with the same small number of point evaluations as a standard Gauss quadrature rule. It therefore significantly increases the efficiency of unfitted finite element schemes such as the finite cell method that have often relied on cut-cell integration with prohibitively many quadrature points. Moment fitting, however, does not directly apply to inhomogeneous integrands as they result from nonlinear material behavior. In this article, we describe a novel modification of moment fitting approach that opens the door for its application in materially nonlinear analysis. The basic idea is the decomposition of each cut cell into material subdomains, each of which can be assigned a physically valid location where constitutive integration and the update of local history variables can be performed. We formulate a moment fitting scheme for each material subdomain using the same quadrature points, such that the resulting weights from all material subdomains can be added and the total number of point evaluations remains the same as in standard Gauss quadrature. We discuss numerical details of the modified scheme, including its ramifications for consistent linearization, and demonstrate its optimal performance in the context of the finite cell method and elastoplasticity.