Abstract
The variety of hyperelastic materials and the design of new modifications and technical applications requires the development of a description of nonlinear deformation properties. The most commonly used constitutive relations of the Mooney-Rivlin and Yeoh models are based on polynomial decompositions. Mechanical-geometric modeling (hereinafter - MGM) is a new way of constructing constitutive relations and strain energy densities within the nonlinear theory of elasticity. In this paper, a comparison of the deformation behavior of MGM with the traditional Mooney-Rivlin and Yeoh models was carried out. Comparative analysis is accompanied by diagrams for uniaxial and biaxial stretching. The effectiveness of the new model was proved.
Highlights
A huge variety of various materials that undergoes the large deformations is used in modern manufacturing and engineering
Given that the classic Mooney-Rivlin and Yeoh models characterize incompressible solids, an additional incompressibility condition was added for mechanical-geometric modeling (MGM) I3 1, where I3 O12O22O32 is the third invariant of the Cauchy-Green strain measure
The specific strain energy density "a priori" has properties that allow it to be used in nonlinear elastic theory
Summary
A huge variety of various materials that undergoes the large deformations is used in modern manufacturing and engineering. The Ogden potential has recently been used increasingly, in particular to describe the properties of biological tissues Another approach, based on statistical physics and some assumptions about the structure of the material, leads to the Gent strain energy density Here I1 is the first invariant of the Cauchy-Green strain measure G : I1 O12 O22 O32 and P, Jm are material constants of the model, or Arruda-Boyce strain energy density D is a factor varying from 0 (i.e. fully incompressible material) up to 1, and J I3 , I3 O12O22O32 is the third invariant of the Cauchy-Green strain measure G This further complicates the mathematical setting of problems of the nonlinear theory of elasticity. An extensive overview of the contemporary strain energy densities of nonlinear solids is given in [10]
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