A Consistent Numerical Method for the Solution of Nonlinear Elasticity Problems at Finite Strains

1971 ◽  
Vol 20 (3) ◽  
pp. 462-481 ◽  
Author(s):  
S. Nemat-Nasser ◽  
H. D. Shatoff
Keyword(s):  
Numerical Method ◽  
Nonlinear Elasticity ◽  
Finite Strains ◽  
Elasticity Problems

scholarly journals NUMERICAL SOLUTION OF NONLINEAR ELASTICITY PROBLEMS WITH LAVRENTIEV PHENOMENON

2007 ◽  
Vol 17 (10) ◽  
pp. 1619-1640 ◽  
Author(s):  
YU BAI ◽  
ZHIPING LI
Keyword(s):  
Numerical Solution ◽  
Nonlinear Elasticity ◽  
Upper Bound ◽  
Perturbation Parameter ◽  
Numerical Results ◽  
Convergence Theory ◽  
Lavrentiev Phenomenon ◽  
Convergence Theorems ◽  
Elasticity Problems ◽  
Singular Minimizers

A convergence theory is established for a truncation method in solving polyconvex elasticity problems involving the Lavrentiev phenomenon. Numerical results on a recent example by Foss et al., which has a polyconvex integrand and admits continuous singular minimizers, not only verify our convergence theorems but also provide a sharper estimate on the upper bound of a perturbation parameter for the existence of the Lavrentiev phenomenon in the example.

AN EFFICIENT NUMERICAL METHOD FOR CAVITATION IN NONLINEAR ELASTICITY

2011 ◽  
Vol 21 (08) ◽  
pp. 1733-1760 ◽  
Author(s):  
XIANMIN XU ◽  
DUVAN HENAO
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Method ◽  
Nonlinear Elasticity ◽  
Elastic Energy ◽  
Finite Element Approximation ◽  
Void Coalescence ◽  
Element Approximation ◽  
Nonconforming Finite Element ◽  
First Time

This paper is concerned with the numerical computation of cavitation in nonlinear elasticity. The Crouzeix–Raviart nonconforming finite element method is shown to prevent the degeneration of the mesh provoked by the conventional finite element approximation of this problem. Upon the addition of a suitable stabilizing term to the elastic energy, the method is used to solve cavitation problems in both radially symmetric and non-radially symmetric settings. While the radially symmetric examples serve to illustrate the efficiency of the method, and for validation purposes, the experiments with non-centered and multiple cavities (carried out for the first time) yield novel observations of situations potentially leading to void coalescence.

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