CREEP AND STRESS-RELAXATION OF AN INCOMPRESSIBLE VISCOELASTIC MATERIAL OF THE RATE TYPE

In this work, a constitutive equation for an isotropic, nonlinear viscoelastic material of the rate type is introduced to study the nonlinear viscoelastic responses of rubber-like materials. This constitutive equation not only predicts creep, recovery, and stress relaxation processes which are of significant interest to engineering applications but also depicts these processes through a simple mathematical structure. The constitutive theory of the rate type generalizes the standard linear solid of classical linear viscoelasticity and contains the viscoelasticity of the differential type as its special case. It has been found that the stress relaxation process is characterized by a universal solution regardless of the response functions of the material. For the creep process, the only difference existing between the viscoelastic materials of the rate type and the differential type is the creeping speed. Closed form solutions are obtained for creep of a viscoelastic Mooney-Rivlin material in simple shear and a viscoelastic neo-Hookean material in simple extension.