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Volume changes associated with the deformation of rubber-like solids

1976; Elsevier BV; Volume: 24; Issue: 6 Linguagem: Inglês

10.1016/0022-5096(76)90007-7

1873-4782

Ray W. Ogden,

Rheology and Fluid Dynamics Studies

Volume changes accompanying the deformation of rubber-like solids are analysed on the basis of isotropic elasticity theory. In particular, a simple, but general, result relating the volume and the stretch in simple tension is obtained. This is achieved by the introduction of certain modified principal stretches which allow the dependence of the strain energy on the isochoric and the dilatational parts of the deformation to be considered separately. The fact that volume changes in rubber-like solids are typically of order 0.01 % is used to linearize the stress-deformation relations in the dilatation. This enables the dilatation to be given explicitly as a function of the stretch in simple tension. Specific results are obtained for certain classes of constitutive law and good agreement with the experimental data for simple tension is demonstrated. Results for equi-biaxial tension and pure shear are also given in anticipation of further experimental data becoming available. The need for volume-change data for a wide variety of types of strains is emphasized.