A viscoelastic constitutive equation of rubber that is under small oscillatory load superimposed on large static deformation is proposed. The suggested constitutive model is verified through comparison between dynamic tests and calculation with the model.
Linearized Simo's Viscoelastic Model(LSVM) is derived through linearization of Simo's model and reference configuration transformation. Static deformation correction factor is introduced to the proposed model in order to consider the influence of pre-strain on the dynamic behavior of rubber, The-correction factor enables the model to describe the non-separable nature of filled rubber. Two specific forms of static deformation correction factor are suggested. One uses normalized strain energy and the other uses generalized octahedral shear strain as static deformation measure.
LSVM is extended to a generalized viscoelastic constitutive equation that includes widely used Morman's model as a special case using objective stress increment. The generalized model has following characteristics. First, it satisfies principle of frame indifference. Second, it approaches to elastic material behavior under very slow and fast deformation.
The proposed model is implemented in a finite element code that enables us to calculate the behavior of rubber structure. Compression test and complex stress state test are analyzed by the developed code in the verification process of the suggested model. Large deformability and incompressibility of rubber are treated by updated Lagrangian formulation with pressure-displacement mixed method. A finite element formulation that predicts the dynamic behavior of rubber components is derived using static analysis results, increment relation equations of each variables and the proposed viscoelastic model.
Dynamic tests are conducted to verify the proposed constitutive model and to estimate the nonlinear nature of rubber behavior. The dynamic tests are composed of tension test, compression test and complex stress state test. Three different kinds of rubber specimen with different carbon black content are used to appreciate the effects of filler.
In the tension test, it is observed that dynamic Young's modulus increases after initial decrease with progression of static deformation for filled rubber. The effects of static deformation are not affected by imposed deformation frequency. The dependence of complex modulus on the static strain is in proportion to the amount of carbon black. It is concluded from the test the assumption that the effects of static deformation can be separated from time effects, which is the basis of Morman's model, is only applicable to unfilled rubber and the viscoelastic constitutive equation for filled rubber must include the influence of the static deformation on the time effects. The constitutive equation with static deformation correction factor shows good agreement with test results.
Compression test and complex stress state test are used for verification of the suggested model under complex deformation and stress. In compression test, the proposed model has better performance than the existing model in anticipating the dynamic stiffness variation by static deformation. A dynamic stiffness peak is observed in the complex stress state test. The proposed model successfully predicts the peak that can not be described by existing model. As a conclusion of experiments, it is estimated that the proposed model effectively describes the behavior of rubber under complex deformation and stress.
