Linearization and implementation of venu model in small strain theory for polyamide 6.6

Abstract

The so-called VENU model is a visco-hyperelastic constitutive model, designed for amorphous rubbery polymers, which is based on an original approach initially developed by N. Billon (J. Appl. Polym. Sci. 125:4390-4401, 2012) and extended by A. Maurel-Pantel et al. (Int. J. Plast. 67:102126, 2015) to three-dimensional thermomechanical framework. In the aforementioned references, the constitutive equations and thermodynamical framework are presented within large deformation theory. However, in fatigue tests of polymeric composites significant temperature gradients are noticed despite the fact that the measured strains are within the small strain theory. In addition, well established techniques and tools of micromechanics for polymeric composites are applicable in small deformation regions. These observations render important the reduction of the VENU model in the case of linear strains. Here, a method is proposed for the reduction of the VENU model to small strain theory. A proper numerical scheme is also provided, based on the so-called return-mapping algorithm. The model capabilities are illustrated by comparing numerical calculations with available experimental data for polyamide 66.