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Large deformations of a new class of incompressible elastic bodies

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Abstract

The consequences of the constraint of incompressibility is studied for a new class of constitutive relation for elastic bodies, for which the left Cauchy–Green tensor is a function of the Cauchy stress tensor. The requirement of incompressibility is imposed directly in the constitutive relation, and it is not necessary to assume a priori that the stress tensor should be divided into two parts, a constraint stress and a constitutively specified part, as in the classical theory of nonlinear elasticity.

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Authors and Affiliations

  1. Departamento de Ingeniería Mecánica, Universidad de Chile, Beauchef 851, Santiago Centro, Santiago, Chile

    R. Bustamante

  2. Departamento de Matemáticas, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaiso, Chile

    O. Orellana

  3. Escuela de Ingeniería Civil, Universidad de Valparaíso, General Cruz 222, Valparaiso, Chile

    R. Meneses

  4. Department of Mechanical Engineering, University of Texas A&M, College Station, TX, USA

    K. R. Rajagopal

Authors
  1. R. Bustamante
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  2. O. Orellana
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  3. R. Meneses
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  4. K. R. Rajagopal
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Correspondence to R. Bustamante.

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Bustamante, R., Orellana, O., Meneses, R. et al. Large deformations of a new class of incompressible elastic bodies. Z. Angew. Math. Phys. 67, 47 (2016). https://doi.org/10.1007/s00033-016-0638-y

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  • DOI: https://doi.org/10.1007/s00033-016-0638-y

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