A viscoplastic constitutive model for polymeric materials at finite deformations

The rate-form constitutive equations of Maxwell viscoelastic element and elastic-plastic material at finite deformations are respectively developed by using the approach proposed by Shen [Int. J. Solids and Structures, volume 43 (2006), pp. 5613-5627.]. The constitutive model for polymers consists of a Maxwell element in parallel with an elastic-plastic element. The two elements are subjected to a same deformation and their stresses added together are the total stress. Thus, a constitutive model for polymers at finite deformation is presented. The rate-form constitutive equation for polymers satisfies the principle of objectivity though it need not make the choice of the objective rate of stress. As an application of the model, the simple shear is worked out. It is expected that the proposed constitutive model is suitable for describing the dynamic behavior of polymers and polymer composites at finite deformations