A generalization of thermodynamic orthogonality to random media

Basic relations of Ziegler's theory of thermodynamic orthogonality are generalized to random media. Two basic cases of interpreting randomness in nonconservative material response are considered, and, accordingly, the mean, the average, and the effective dissipation functions are identified. It is found that when a homogeneity condition is fulfilled, these functions satisfy very simple equalities. When a quasi-homogeneity condition is satisfied, these function lead to very concise forms of effective Legendre transformations. An interpretation of the extremum principles corresponding to the derived relations is given.