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Abstract:
In this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

Keywords:
hyperelasticity, rubberlike materials, polyconvexity, material parameters

Abstract:
In the paper a general approach to modelling of anisotropic linear viscoelastic material properties is presented. Rychlewski's (1983) spectral decomposition theorem is used and one dimensional relaxation functions of linear viscoelasticity model is adopted to eigenvalues of stiffness tensor and named Kelvin relaxation functions. Proposed model was implemented in the FEM system Abaqus on the example of transversely isotropic and isotropic material. On the basis of experimental data available in literature, models were calibrated and verified. Constitutive relations were used in the complex boundary value problem modelling standard rutting test used in road sector to assess the resistance of asphalt mixtures to rutting.

Keywords:
constitutive modeling, viscoelasticity, finite element method, anisotropic materials, asphalt concretes