An excellent agreement between this theory and the experimental data from simple tension, pure shear and equibiaxial tension tests is demonstrated. Principal axes techniques are used where appropriate. A strain-energy function which is a linear combination of strain invariants defined by ϕ( α) = ( a 1 α+ a 2 α+ a 3 α–3)/ α is proposed and the principal stretches a 1, a 2 and a 3 are used as independent variables subject to the incompressibility constraint a 1 a 2 a 3 = 1. The purpose of this paper is, while making full use of the inherent simplicity of isotropic elasticity, to construct a strain-energy function which: (i) provides an adequate representation of the mechanical response of rubberlike solids, and (ii) is simple enough to be amenable to mathematical analysis. Furthermore, recently proposed special forms of the strain-energy function are rather complicated functions of two invariants. However, the usual practice of writing the strain energy as a function of two independent strain invariants has, in general, the effect of complicating the associated mathematical analysis (this is particularly evident in relation to the calculation of instantaneous moduli of elasticity) and, consequently, the basic elegance and simplicity of isotropic elasticity is sacrificed. The existence of a strain-energy function has usually been postulated, and the simplifications appropriate to the assumptions of isotropy and incompressibility have been exploited. Many attempts have been made to reproduce theoretically the stress–strain curves obtained from experiments on the isothermal deformation of highly elastic ‘rubberlike' materials.
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March 2023
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