F‐bar‐based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking

摘要: This paper proposes a new technique which allows the use of simplex finite elements (linear triangles in 2D and linear tetrahedra 3D) large strain analysis nearly incompressible solids. The extends F-bar method proposed by de Souza Neto et al. (Int. J. Solids Struct. 1996; 33:3277-3296) is conceptually very simple: It relies on enforcement (near-)incompressibility over patch (rather than point-wise conventional displacement-based elements). Within framework method, this achieved assuming, for each element mesh, modified (F-bar) deformation gradient whose volumetric component defined as volume change ratio pre-defined elements. resulting constraint relaxation effectively overcomes locking successful under near-incompressibility. As original procedure, present methodology preserves structure equations well strain-driven format standard algorithms numerical integration path-dependent constitutive can be used regardless model adopted. are implemented within an implicit quasi-static environment. In context, closed form expression exact tangent stiffness derived. full Newton-Raphson scheme equilibrium iterations. performance assessed means comprehensive set benchmarking two- three-dimensional examples.