A thermomechanical modeling and simulation of viscoplastic large deformation behavior for polymeric materials (1st report, non-coaxiality of constitutive equation originated in strain rate dependence)

Polymeric materials have various characteristics of deformation, e.g., strain rate dependence (viscoplasticity) at room temperature, strain localization just after initial yielding and propagation of a localized region with strain hardening. Viscoplasticity has been usually represented by a constitutive equation of plasticity with a hardening law including a plastic strain rate. However, such a modeling is not thermodynamically consistent with the hardening law dependent on strain rate. In this paper, a strain rate tensor is introduced into free energy and a thermodynamic force conjugate to this rate is newly defined. On the basis of the principle of increase of entropy and one of maximal entropy production rate, a non-coaxial constitutive equation of viscoplasticity is derived as a flow rule in which a dissipation function plays the role of plastic potential. It is shown that a strain rate dependent constitutive equation must be always non-coaxial in a thermodynamically consistent theory.