Stretching of the mechanical-geometric model and two common nonlinear elastic solids

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.