Mixed stabilized finite element methods in nonlinear solid mechanics Part I: Formulation

• Published in: Computer methods in applied mechanics and engineering Vol. 199; no. 37-40; pp. 2559 - 2570
• Main Authors: CERVERA, M, CHIUMENTI, M, CODINA, R
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier 01.08.2010
• Subjects: Approximation; C (programming language); Displacement; Exact sciences and technology; Finite element method; Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematical models; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Nonlinearity; Numerical analysis. Scientific computation; Physics; Sciences and techniques of general use; Solid mechanics; Structural and continuum mechanics; Solid mechanics; Nonlinear solid mechanics; High strain; Subgrid scale method; Stabilization; Irreducible operator; Displacement(deformation); Large displacement; Modeling; Mixed method; Finite element method; Algebraic sub-grid scales; Stabilization methods; Orthogonal sub-grid scales; Mixed finite element interpolations
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2010.04.006

This paper exploits the concept of stabilized finite element methods to formulate stable mixed stress/displacement and strain/displacement finite elements for the solution of nonlinear solid mechanics problems. The different assumptions and approximations used to derive the methods are exposed. The proposed procedure is very general, applicable to 2D and 3D problems. Implementation and computational aspects are also discussed, showing that a robust application of the proposed formulation is feasible. Numerical examples show that the results obtained compare favorably with those obtained with the corresponding irreducible formulation.