ABSTRACT
The presence of dissipative phenomena in mechanics of materials necessitates a formulation of continuum mechanics consistent with principles of thermodynamics, leading to so-called thermomechanics or continuum thermodynamics. As elaborated by Maugin (1999), there are now four classical continuum thermodynamics theories: thermodynamics of irreversible processes (TIP); thermodynamics with internal variables (TIV); rational thermodynamics (RT); extended (rational) thermodynamics (ET). All of these are deterministic, homogeneous continuum theories without clear account of the underlying random compositions of materials-that is, they a priori postulate the existence of the RVE. Strictly speaking, some statistical treatments were carried out as a bridge from micro to macro levels for select variants of the above theories-for example, by Ziegler (1963, 1970) for TIV (see below), or by Muschik et al. (2000) for TIP (see Chapter 8)—but such studies were only concerned with providing foundations from the standpoint of statistical physics directly to the level of the RVE, without making clear what the size of the RVE actually should be. Given the widespread use of TIV in mechanics of materials (e.g., Lemaitre and Chaboche, 1990), we now set out to generalize it so as to provide a link to random microstructures.
