A pseudo-strain energy density function for mechanical behavior modeling of visco-hyperelastic materials

In this paper, a constitutive phenomenological framework is proposed for the mechanical behavior of the visco-hyperelastic materials. This phenomenological framework is based on the concept of developing the schemas of the classical linear theory to the nonlinear regime. For this purpose, at first, the structure of the constitutive law of a viscoelastic material is constructed in the linear behavior case. In this construction, it can be observed that the stress can be decomposed into the sum of the elastic part and viscous part with a time function. In generalization of the rebuilt framework of the linear theory to a nonlinear regime to model the mechanical behavior of visco-hyperelastic materials, a pseudo-strain energy density function including elastic and viscous parts is assumed. The hyperelastic behaviors of the developed nonlinear model is organized via a Hookean-type constitutive equation in terms of the power law and exponential strain measures which have a high flexibility for capturing the mechanical behaviors with different trends from the S-shaped to J-shaped forms. The time part of the developed framework is proposed such that it can model the long-term memory fading principle. For this purpose, the new weight functions are used such that they can capture the rate behavior and recognize the relaxation curves with different starting points from stretch and rate of stretch. Finally, in order to do the comprehensive evaluation of the performance of the proposed model, the high strain rate tensile and compression tests, separately and simultaneously; and also, the relaxation tests at different levels from strain and strain rate beside the moderate rate tensile tests are examined to calibrate the model for different mechanical behaviors. It is observed that there is a good accordance between the test data and predictions of the model for the mechanical behavior of visco-hyperelastic materials.