On the thermomechanical behaviour of the viscoelastic Cosserat continuum

Abstract

The theory of the thermomechanical behaviour of a nonlinear and linear viscoelastic Cosserat continuum is developed in a small deformation field by making use of the fundamental concepts of continuum mechanics and irreversible thermodynamics. The formulation rests on Meixner's theory wherein the Clausius-Duhem inequality is replaced by the so-called fundamental inequality. The constitutive equations satisfy the axiom of equipresence and the axiom of material frame-indifference. The temperature gradient which also depends on the gradients of deformation and rotation is included. Under nonisothermal conditions it is found that thirteen relaxation functions are needed to describe the linear thermomechanical behaviour of a centro-symmetric isotropic viscoelastic Cosserat continuum. Finally, the explicit form of the linear thermomechanical constitutive equations of a centro-symmetric isotropic viscoelastic Cosserat materials are compared with those previously obtained on other basis byPeng andValanis [4].