An implicit boundary finite element method with extension to frictional sliding boundary conditions and elasto-plastic analyses

• Published in: Computer methods in applied mechanics and engineering Vol. 358; p. 112620
• Main Authors: Lu, Kaizhou, Coombs, William M., Augarde, Charles E., Hu, Zhendong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.01.2020; Elsevier BV
• Subjects: Boundary conditions; Dirichlet boundary conditions; Dirichlet problem; Elasto-plasticity; Fictitious domain; Finite element method; Frictional boundary; Immersed boundary; Implicit boundary method; Interpolation; Step functions; Stiffness matrix; Weighting functions; Elasto-plasticity; Frictional boundary; Implicit boundary method; Fictitious domain; Immersed boundary; Dirichlet boundary conditions
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2019.112620

Implicit boundary methods, which enrich the interpolation structure with implicit weight functions, are straightforward methods for the enforcement of Dirichlet boundary conditions. In this article, we follow the implicit boundary method that uses approximate step functions (the step boundary method) developed by Kumar et al. and provide modifications that have several advantages. Roller boundary conditions have wide practical applications in engineering, however, the step boundary method for roller boundary conditions with inclinations has yet to be fully formulated through to the final linear system of equations. Thus we provide a complete derivation that leads to simplified stiffness matrices compared to the original approach, which can be implemented directly in fictitious domain finite element analysis. The approach is then extended, we believe for the first time, to the nonlinear cases of frictional boundary conditions and elasto-plastic material behaviour. The proposed formulation and procedures are validated on a number of example problems that test different aspects of the method. •Simplified stiffness matrices compared to the original approach.•A complete derivation to include mixed Dirichlet/Neumann boundaries at any inclination.•Extension to include frictional sliding boundary conditions.•Extension to elasto-plastic analyses.•Combined framework for frictional boundaries and elasto-plasticity.