Finite gradient elasticity and plasticity: a constitutive thermodynamical framework

In Bertram (Continuum Mech Thermodyn. doi: 10.1007/s00161-014-0387-0 , 2015 ), a mechanical framework for finite gradient elasticity and plasticity has been given. In the present paper, this is extended to thermodynamics. The mechanical theory is only briefly repeated here. A format for a rather general constitutive theory including all thermodynamic fields is given in a Euclidian invariant setting. The plasticity theory is rate-independent and unconstrained. The Clausius–Duhem inequality is exploited to find necessary and sufficient conditions for thermodynamic consistency. The residual dissipation inequality restricts the flow and hardening rules in combination with the yield criterion.