The role of dissipation regarding the concept of purely mechanical theories in plasticity

Abstract

The concept of a purely mechanical theory is revisited within the framework of continuum thermodynamics. It is based on three assumptions: (i) the additive split of the specific free energy into a mechanical contribution not depending on the temperature and a contribution that depends on the temperature only, (ii) a homogeneous and stationary temperature field, and (iii) a negligible heat supply. The consequences of these three assumptions on the dissipation inequality in form of the Clausius–Duhem inequality are discussed. It is shown, that these three assumption yield a vanishing dissipation. This result is valid for the classical Cauchy–Boltzmann continuum as well as for extended continua. Many plasticity theories consider the first two assumptions tacitly, however the role of the heat supply is not discussed. Here, the consequences of a vanishing dissipation with respect to a local crystal plasticity theory are discussed, exemplarily. The paper does not favor a purely mechanical theory but highlights the implications of such an approach.