The Finite Cell Method for Elasto-Plastic Problems

In this paper we discuss the application of finite cell method to the problems of elasto-plasticity. The Finite cell method is the high order finite element method applied to an extended domain. This domain can be discretized using simple meshes used only for integration purposes. In several papers, the method has been verified for regular and singular problems of elasticity. The finite cell method enjoys fast convergence in terms of the degrees of freedom; however, the computation cost of the method depends very much on the integration scheme. In the current paper, the standard Gauss quadrature is used but the weights in this scheme are modified slightly if the Voronoi polygon supporting an integration point is occupied only partially by the physical domain. In a further attempt, the position of the integration point for the weak discontinuity problems is changed to the centroid of the physical part of the Voronoi polygon. These two modifications have improved the convergence behavior of the method. Converging to acceptable results, even for singular problems, when the mesh does not conform to the boundaries, and the shape functions are standard high order polynomials, is the key advantage of the finite cell method. Any effort to enrich the approximation space is not necessary. This paper shows that the method can reach accurate results for elasto-plastic problems too.