On the compressible quasilinear viscoelastic simple uniaxial deformation

We study the compressible simple uniaxial deformation within the quasilinear viscoelasticity theory. We impose a longitudinal stretch (in both extension and compression), and we investigate the role of compressibility in such a deformation by computing the lateral deformation and the uniaxial stress for an isotropic homogeneous material sample under lateral-free traction conditions. Several tests are examined, and conclusions are drawn based on a set of three strain energy densities that describe compressible hyperelastic behaviours by varying the set of involved parameters. The dissipated energy is also computed for a typical one-cycle experimental test. Furthermore, we examine recent experiments on visco-elastomeric syntactic foams in light of our results, comparing them with the simplified model using the rate-independent nonlinear Poisson functions.