A thermodynamic theory of damage in elastic inorganic and organic solids

This contribution presents the foundations of a thermodynamic theory of damage in elastic solids, developed in collaboration with the late J. Kestin and with E. Honein and T. Honein. The theory is rooted in the so-called conservative or conventional thermodynamics of irreversible processes, where the concept of a local thermodynamic state plays a prominent role. An elastic body prone to damage is regarded as a thermodynamic system characterized by a set of extensive variables that can be defined in both equilibrium and nonequilibrium states and assigned approximately the same values in both the physical space and the abstract state space (i.e., the Gibbsian phase space of constrained equilibria). The extensive variables introduced include internal parameters which describe the damaged state of the body and whose conjugate intensive variables, or affinities, constitute a generalization of Eshelby’s concept of a “force on an elastic singularity”. The local state approximation is applied by assigning to the entropy and temperature in physical space local values which can be calculated in the Gibbsian phase space by the well-established methods of equilibrium thermodynamics. This leads to an explicit expression for the entropy production. The rate equations for the damage are then postulated in such a way as to conform to the second part of the second law of thermodynamics. The resulting theory captures many features of real inorganic material behavior in which no mass loss is sustained. By contrast, damage of organic materials, such as compact bone subject to osteoporosis, is accompanied by bone mass loss. This feature can be accommodated in the theory proposed by a suitable adjustment of the expression of the Gibbs free energy.