A viscoelastic constitutive model of rubber under small oscillatory load superimposed on large static deformation

A viscoelastic constitutive equation of rubber that is under small oscillat ory load superimposed on large static deformation is proposed. The model is derived through linearization of Simo's nonlinear viscoelastic constitutiv e model and reference configuration transformation. Most importantly, in th is model, static deformation correction factor is introduced to consider th e influence of pre-strain on the relaxation function. Natural statically pr edeformed state is served as reference configuration. The proposed constitu tive equation is extended to a generalized viscoelastic constitutive equati on that includes widely used Morman's model as a special case using objecti ve stress increment. The proposed constitutive model is tested for dynamic behavior of rubber specimens with different carbon black content. It is con cluded from the test that the assumption that the effects of static deforma tion can be separated from time effects, which is the basis of Morman's mod el, is only applicable to unfilled rubber. The viscoelastic constitutive eq uation for filled rubber must include, therefore, the influence of the stat ic deformation on the time effects. The suggested constitutive equation wit h static deformation correction factor shows good agreement with test value s.