Modeling of nonlinearhyper-viscoelasticand stress softening behaviors of acrylonitrile butadiene rubber/polyvinyl chloride nanocomposites reinforced by nanoclay and graphene

This research work is devoted to the development of multiple material models as constitutive equations for the description of the complex mechanical behavior of a series of nanocomposites based on the acrylonitrile butadiene rubber (NBR)/polyvinyl chloride (PVC) reinforced by nanoclay graphene. The preparation method and the mechanical with other properties of these nanocomposites were already investigated and reported in our previous work. The developed model consists of the Marlow hyperelastic integral equation, strain hardening power-law equation for the nonlinear viscoelastic behavior as well as Ogden and Roxburgh equation to simulate the stress softening behavior. Stress relaxation tests were first carried out to show the nonlinear viscoelastic behavior of the samples. Simple tensile and volumetric tests were performed for Marlow model. The parameters of the nonlinear viscoelastic and stress softening equations in the model were determined by solving an inverse problem using a novel numerical algorithm, which was based on the combination of an optimization loop using Down Hill simplex method and finite element simulation of a dumbbell test specimen under load. To achieve this task, quasi-static tests under cyclic loading with different final extensions and three extensional rates were also performed. Then, their corresponding finite element models were developed and the associated inverse problems were solved. Comparing the force-displacement data obtained via simulation using the mentioned model with their corresponding experimental data confirms of the model correctness and its applicability. Moreover, the mechanical behaviors of both neat and reinforced polymer blend (NBR/PVC) with nanofillers are shown to be supportive of the computed parameters.