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Large strain analysis of rubber-like materials based on a perturbed Lagrangian variational principle

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Abstract

A mixed finite element method is presented for the large strain analysis of rubber-like materials, which are considered to be nearly incompressible. Two types of constitutive relations are included: generalized Rivlin and Ogden's models. The finite element equations are derived on the basis of a perturbed Lagrangian variational principle from which both the displacement and pressure fields are independently approximated by appropriate shape functions. A physically meaningful pressure parameter is introduced in the expression of complementary energy. In the paper, a special effort is made to split the deformation energy into two distinct parts: isochoric and hydrostatic parts. By doing this, a quadratic convergence rate of nonlinear iterative solution is achieved, particularly for problems deformed in the large strain range. The finite element equations are specialized for a two-dimensional 9-node Lagrange element with three-term pressure parameters. Five examples are given to demonstrate the application of the proposed numerical algorithm.

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Authors and Affiliations

  1. Department of Civil Engineering, University of Akron, 44325-3905, Akron, OH, USA

    T. Y. P. Chang, A. F. Saleeb & G. Li

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  1. T. Y. P. Chang
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  2. A. F. Saleeb
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  3. G. Li
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Additional information

Communicated by S. N. Atluri, December 17, 1990

Research work supported by National Science Foundation under the grant number EET-8714628

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Chang, T.Y.P., Saleeb, A.F. & Li, G. Large strain analysis of rubber-like materials based on a perturbed Lagrangian variational principle. Computational Mechanics 8, 221–233 (1991). https://doi.org/10.1007/BF00577376

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