The finite cell method for the J2 flow theory of plasticity

The finite cell method (FCM) is an extension of a high-order finite element approximation space with the aim of simple meshing. In this paper, the FCM is implemented for J2 flow theory with nonlinear isotropic hardening for small displacements and small strains. The Newton–Raphson iteration scheme, combined with a radial return algorithm, is applied to find approximate solutions for the underlying physically nonlinear problem. A modified quadtree integration scheme is presented for the first time to capture the geometry accurately and overcome the high calculation cost of the standard quadtree integration scheme. Numerical examples in two and three dimensions demonstrate the efficiency of the FCM and the proposed integration scheme at solving materially nonlinear problems.

► The FCM is an extension of the p  -FEM with the aim of simple meshing. ► In this paper, the FCM is implemented for J2J2 flow theory. ► A modified quadtree integration scheme is presented. ► Numerical examples in 2D and 3D demonstrate the efficiency of the FCM.