Title of article :
F-bar-based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids. Part I: formulation and benchmarking
Author/Authors :
E. A. de Souza Neto، نويسنده , , F. M. Andrade Pires، نويسنده , , D. R. J. Owen، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2005
Abstract :
This paper proposes a new technique which allows the use of simplex finite elements (linear triangles
in 2D and linear tetrahedra in 3D) in the large strain analysis of nearly incompressible solids.
The new technique extends the F-bar method proposed by de Souza Neto et al. (Int. J. Solids
and Struct. 1996; 33:3277–3296) and is conceptually very simple: It relies on the enforcement of
(near-)incompressibility over a patch of simplex elements (rather than the point-wise enforcement of
conventional displacement-based finite elements). Within the framework of the F-bar method, this is
achieved by assuming, for each element of a mesh, a modified (F-bar) deformation gradient whose
volumetric component is defined as the volume change ratio of a pre-defined patch of elements.
The resulting constraint relaxation effectively overcomes volumetric locking and allows the successful
use of simplex elements under finite strain near-incompressibility. As the original F-bar procedure,
the present methodology preserves the displacement-based structure of the finite element equations as
well as the strain-driven format of standard algorithms for numerical integration of path-dependent
constitutive equations and can be used regardless of the constitutive model adopted. The new elements
are implemented within an implicit quasi-static environment. In this context, a closed form expression
for the exact tangent stiffness of the new elements is derived. This allows the use of the full Newton–
Raphson scheme for equilibrium iterations. The performance of the proposed elements is assessed
by means of a comprehensive set of benchmarking two- and three-dimensional numerical examples
Keywords :
volumetric locking , Incompressibility , Finite strains
Journal title :
International Journal for Numerical Methods in Engineering
Journal title :
International Journal for Numerical Methods in Engineering