Ordered rate constitutive theories for thermoviscoelastic solids without memory incorporating internal and Cosserat rotations

The work in this paper is based on a non-classical continuum theory in the Lagrangian description for thermoviscoelastic solids without memory in which the conservation and balance laws are derived by incorporating internal rotations ((i)Theta) arising from the Jacobian of deformation (J), as well as Cosserat rotations ((e)Theta) at a material point. Such non-classical solids have additional energy storage due to rotations and additional dissipation due to rotation rates compared to classical continuum theories. Rotations (i)Theta are completely defined by J, whereas displacements u and Cosserat rotations (e)Theta are degrees of freedom at each material point. When (i)Theta and (e)Theta are resisted by the deforming matter, conjugate moments arise, which together with ((i)Theta, (e)Theta) and ((i)(Theta) over dot, (e)(Theta) over dot) result in additional work and rate of work. This paper utilizes thermodynamic framework for non-classical solids derived based on internal as well as Cosserat rotations and presents a thermodynamically consistent derivation of the constitutive theories that incorporate the aforementioned deformation physics. The constitutive theories are derived using the conditions resulting from the entropy inequality in conjunction with the representation theorem.