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Chavan, K. S.; Lamichhane, B. P.; Wohlmuth, B. I.

Locking-free finite element methods for linear and nonlinear elasticity in 2D and 3D. (English) Zbl 1173.74404

Comput. Methods Appl. Mech. Eng. 196, No. 41-44, 4075-4086 (2007).
Summary: The uniform convergence of finite element approximations based on a modified Hu-Washizu formulation for the nearly incompressible linear elasticity is analyzed. We show the optimal and robust convergence of the displacement-based discrete formulation in the nearly incompressible case with the choice of approximations based on quadrilateral and hexahedral elements. These choices include bases that are well known, as well as newly constructed bases. Starting from a suitable three-field problem, we extend our \(\alpha \)-dependent three-field formulation to geometrically nonlinear elasticity with Saint-Venant Kirchhoff law. Additionally, an \(\alpha \)-dependent three-field formulation for a general hyperelastic material model is proposed. A range of numerical examples using different material laws for small and large strain elasticity is presented.

Cited in 1 Review
Cited in 17 Documents

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
74B20 Nonlinear elasticity

Keywords:

Hu-Washizu formulation; mixed finite elements; low-order approximations; uniform convergence

Software:

UG
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Full Text: DOI

References:

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