Successive linear approximation for finite elasticity

A method of successive Lagrangian formulation of linear approximation for solving boundary value problems of large deformation in finite elasticity is proposed. Instead of solving the nonlinear problem, by assuming time steps small enough and the reference configuration updated at every step, we can...

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Bibliographic Details
Published inComputational & applied mathematics Vol. 29; no. 3; pp. 465 - 478
Main Authors Liu, I-Shih, Cipolatti, Rolci A, Rincon, Mauro A
Format Journal Article
LanguageEnglish
Published Sociedade Brasileira de Matemática Aplicada e Computacional 2010
Subjects
MATHEMATICS, APPLIED
boundary value problem
large deformation
successive Lagrangian formulation
numerical computation
nonlinear elastic materials
incremental method
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ISSN1807-0302
2238-3603
DOI10.1590/S1807-03022010000300008

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Summary:A method of successive Lagrangian formulation of linear approximation for solving boundary value problems of large deformation in finite elasticity is proposed. Instead of solving the nonlinear problem, by assuming time steps small enough and the reference configuration updated at every step, we can linearize the constitutive equation and reduce it to linear boundary value problems to be solved successively with incremental boundary data. Moreover, nearly incompressible elastic body is considered as an approximation to account for the condition of incompressibility. For the proposed method, numerical computations of pure shear of a square block for Mooney-Rivlin material are considered and the results are compared with the exact solutions. Mathematical subject classification: Primary: 65C20; Secondary: 74B20.
ISSN:1807-0302
2238-3603
DOI:10.1590/S1807-03022010000300008