A stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations
By Michele Chiumenti, Quino Valverde, Carlos Agelet de Saracibar, Miguel Cervera. 2002
139 citations recorded by the source corpus.
In this paper a stabilized finite element method to deal with incompressibility in solid mechanics is presented. A mixed formulation involving pressure and displacement fields is used and a continuous linear interpolation is considered for both fields. To overcome the Babuska–Brezzi condition, a stabilization technique based on the orthogonal sub-scale method is introduced. The main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements, which are easy to generate for real industrial applications. Results are compared with standard Galerkin and Q1P0 mixed formulations for nearly incompressible problems in the context of linear elasticity.
Subfields: Computational Mechanics, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/240beb29bd915ac4c427a88b9579b2720c248407
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In Computational Mechanics
- Miguel Cervera
- Michele Chiumenti
- Eugenio Oñate
- Carlos Agelet de Saracibar
- Robert Taylor
- J. Rojek
- O. C. Zienkiewicz
- Ramon Codina
In Mechanics of Materials
- Miguel Cervera
- Michele Chiumenti
- Carlos Agelet de Saracibar
- Eugenio Oñate
- Ramon Codina
- J. Rojek
- O. C. Zienkiewicz
- Robert Taylor
Citations in the corpus
- Finite calculus formulation for incompressible solids using linear triangles and tetrahedra (2004, methodology): “A similar intepretation of the FIC procedure as an equation modification method is presented in Reference [29].”
- Mixed stabilized finite element methods in nonlinear solid mechanics: Part II: Strain localization (2010, methodology): “In previous works, the authors have applied stabilized mixed displacementpressure methods ([16], [17], [18], [19], [20], [21] and [1]) to the solution of J2 elasto-plastic and damage problems with simplicial elements.”
- Softening, localization and stabilization: capture of discontinuous solutions in J2 plasticity (2004, methodology): “In the cases of elastic incompressibility or smooth widespread, non-localizing, plastic responses, they are able to preclude the pressure oscillations that arise if the standard Galerkin method is used (see References [25, 26]).”