MATHEMATICAL ANALYSIS OF SUCCESSIVE LINEAR APPROXIMATION FOR MOONEY-RIVLIN MATERIAL MODEL IN FINITE ELASTICITY

R. Cipolatti; I-Shih Liu; M. A. Rincon

doi:10.11948/2012027

2012 Volume 2 Issue 4

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R. Cipolatti, I-Shih Liu, M. A. Rincon. MATHEMATICAL ANALYSIS OF SUCCESSIVE LINEAR APPROXIMATION FOR MOONEY-RIVLIN MATERIAL MODEL IN FINITE ELASTICITY[J]. Journal of Applied Analysis & Computation, 2012, 2(4): 363-379. doi: 10.11948/2012027

Citation:

R. Cipolatti, I-Shih Liu, M. A. Rincon. MATHEMATICAL ANALYSIS OF SUCCESSIVE LINEAR APPROXIMATION FOR MOONEY-RIVLIN MATERIAL MODEL IN FINITE ELASTICITY[J]. Journal of Applied Analysis & Computation, 2012, 2(4): 363-379. doi: 10.11948/2012027

MATHEMATICAL ANALYSIS OF SUCCESSIVE LINEAR APPROXIMATION FOR MOONEY-RIVLIN MATERIAL MODEL IN FINITE ELASTICITY

1 Instituto de Matemática, Universidade Federal do Rio de Janeiro, CP. 68530, 21945-970, Rio de Janeiro, Brasil;
2 Dep. Ciência da Computação, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Brasil

Abstract

Abstract

For calculating large deformations of solid bodies, we have proposed a method of successive linear approximation, by considering the relative Lagrangian formulation. In this article we briefly describe this method, which is applied for nearly incompressible Mooney-Rivlin materials. We prove the existence and uniqueness of weak solutions for associated boundary value problems that arise in each step of the method. In our analysis we consider also a non-standard case, where the coefficients present in the constitutive function of Mooney-Rivlin materials do not satisfy the usual E-inequalities.
- Linearized constitutive equations /
- Mooney-Rivlin material /
- relative lagrangian formulation /
- existence and uniqueness
MSC: 74B15;74B20;74G20;74G30;74S30

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References

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