A viscoelastic constitutive model and numerical aspects

In the present work a finite-strain constitutive law for isotropic viscoelastic solids is formulated. The formulation originates front the generalized Maxwell model, and the total stress is described in a sum of the stresses of an elastic mode and several relaxation modes. Exploiting a novel analytical result that the hypoelastic rate constitutive equation based on the logarithmic stress rate is consistent with elasticity, see e.g. Mao et al. (1997b, 7999), a hypoelasticity-based evolution equation of stress (described in the logarithmic corotational coordinate system) for the relaxation modes is established. The nonlinear material behavior is included in the model by describing the dependencies of the relaxation times, the shear and volumetric moduli on deformation. The stress is integrated in the logarithmic corotational fram, and further "pushed forward", with the rotation tensor specified by the logarithmic spin, into the current configuration, and a finite-strain constitutive law for the Cauchy stress is derived. The constitutive model is also coded and three numerical examples involving large deformation and rotation are presented. The first two examples numerically reveal the elasticity-consistency of the selected hypoelastic equation and support the conclusion in Xiao et al. (1999). The third numerical example proves that the developed viscoelastic material law is suitable for the characterization of the viscoelastic behavior of polymers at finite strain.