reaction and creep: Qualitative observations Homogenization of composite materials undergoing stress assisted diffusion

Preliminary qualitative results are given for an ongoing effort to obtain global constitutive equations for stress assisted diffusion, reaction and creep by homogenizing the solution to a local boundary value problem of continuum thermodynamics. Both the local and global constitutive equations are specified by the free energy (the thermodynamic potential) and the dissipation potential for the generalized fluxes. The effects of stress assisted diffusion and reaction in the local boundary value problem are accounted for by using chemical eigenstrains in the kinematic equation. Even though the local diffusion, reaction and creep are purely dissipative, the corresponding global phenomena store free energy in the eigenstress fields which arise due to the incompatibility of the eigenstrains. A severe shortcoming of homogenization with reaction and diffusion is that neither the concentration of a chemical species within the representative volume element nor the volume averaged species concentration are uniquely related to the species concentration on the boundary of the representative volume element.

Homogenization of composite materials undergoing stress assisted diffusion, reaction and creep: Qualitative observations Conference Paper