Abstract2018-05-24T12:52:58+00:00

On the modelling of incompressibility in linear and non-linear elasticity with the master-slave approach

Author (s): Muñoz, J.J.
Journal: International Journal for Numerical Methods in Engineering

Volume: 74, Issue 2
Pages: 269 – 293
Date: 2008

Abstract:
The master-slave approach is adapted to model the kinematic constraints encountered in
incompressibility. The method presented here allows to obtain discrete displacement and pressure
fields for arbitrary finite element formulations that have discontinuous pressure interpolations. The
resulting displacements satisfy exactly the incompressibility constraints in a weak sense, and are obtained solving a system of equations with the minimum (independent) degrees of freedom. In linear
analysis, the method reproduces the well known stability results for inf-sup compliant elements, and
permits to compute the pressure modes (physical or spurious) when they exist. By rewriting the
equilibrium equations of a hyperelastic material, the method is extended to non-linear elasticity, while
retaining the exact fulfilment of the incompressibility constraints in a weak sense. Problems with
analytical solution in two and three dimensions are tested and compared to other solution methods.

  
  

Bibtex:

@article {NME:NME2166,
author = {Muñoz, J. J.},
title = {On the modelling of incompressibility in linear and non-linear elasticity with the master–slave approach},
journal = {International Journal for Numerical Methods in Engineering},
volume = {74},
number = {2},
publisher = {John Wiley & Sons, Ltd.},
issn = {1097-0207},
url = {http://dx.doi.org/10.1002/nme.2166},
doi = {10.1002/nme.2166},
pages = {269--293},
keywords = {master–slave, constraints, incompressibility, inf–sup, mixed elements, hyperelasticity},
year = {2008},
}