A kinematically stabilized linear tetrahedral finite element for compressible and nearly incompressible finite elasticity. (English) Zbl 1539.74472
Summary: We propose a stabilized linear tetrahedral finite element method for static, finite elasticity problems involving compressible and nearly incompressible materials. Our approach relies on a mixed formulation, in which the nodal displacement unknown filed is complemented by a nodal Jacobian determinant unknown field. This approach is simple to implement in practical applications (e.g., in commercial software), since it only requires information already available when computing the Newton-Raphson tangent matrix associated with irreducible (i.e., displacement-based) finite element formulations. By nature, the proposed method is easily extensible to nonlinear models involving visco-plastic flow. An extensive suite of numerical tests in two and three dimensions is presented, to demonstrate the performance of the method.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 74B20 | Nonlinear elasticity |
Keywords:
variational multiscale method; stabilized methods; finite deformation; nonlinear elasticity; piece-wise linear interpolation; nearly incompressible elasticitySoftware:
SymPyReferences:
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