The finite cell method for the J2 flow theory of plasticity

Authors:
Alireza Abedian;Jamshid Parvizian;Alexander DüSter;Ernst Rank
Affiliations:
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran;Department of Industrial Engineering, Isfahan University of Technology, Isfahan, Iran;Numerische Strukturanalyse mit Anwendungen in der Schiffstechnik (M-10), Technische Universität Hamburg-Harburg, Hamburg, Germany;Lehrstuhl für Computation in Engineering, Fakultät für Bauingenieur- und Vermessungswesen, Technische Universität München, München, Germany
Venue:
Finite Elements in Analysis and Design
Year:
2013

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Abstract

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 J"2 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.