Constitutive model and finite element formulation for isothermal yield behavior of polymeric materials

Previous research has shown that the yield-like behavior of polymers at finite strain for different temperatures would be well explained by a hyperelastic model. This study is concerned with the modeling and numerical simulation of the isothermal viscoelastic yield phenomenon given an appropriate definition of yield for polymeric materials. Silling's non-convex internal energy density function for the investigation of mechanical response of elastic crystals in phase transformation is incorporated into the viscohyperelastic constitutive equation designed to model polymeric yield behaviors. This model is a generalized K-BKZ stress relaxation model. A generalized B-bar finite element method based on a variational principle of the Hu-Washizu type is employed to solve the numerical difficulty due to an internal material constraint, incompressibility, in polymers. The Irons patch test and LBB condition are addressed for numerical convergence of the derived mixed finite element. Three representative examples (simple shear, uniaxial tension with recompression and azimuthal shear problems) are carefully studied. The corresponding numerical results indicate that the emergence of shear bands, dissipation of energy in hysteresis loops, loss of symmetry and yield in a cyclical loading can be simulated by our constitutive theory. We may interpret polymeric yield behavior as a result of phase transformation. A possible approach to facilitating a solution searching process is briefly discussed.