On the thermomechanical approach to the formulation of plastic constitutive equations

The non-associated flow rule causes inconvenience in the analysis of boundary value problems. However, it has been widely adopted for plastic constitutive equations of frictional materials. In addition, the pertinence of the non-associated flow rule for frictional materials has been insisted by the thermomechanical consideration. It is important to examine the pertinence and/or the validity of the thermomechanical approach to the formulation of plastic constitutive equations, whilst various works on this approach have been reported up to the present. In this article it is verified that both the associated and the non-associated flow rules are derived independent of the frictional property of materials from the dissipation functions which are more general than the ones postulated in the past studies. Thus, it is concluded that which of the flow rules is pertinent cannot be judged by the thermomechanical approach; thus this approach would be helpless in the formulation of plastic constitutive equations in the isothermal process. In addition it is indicated that the adoption of the non-associated flow rule is caused by the deficiency of the conventional constitutive equations providing that the interior of yield surface is the purely elastic domain.