A theory of coupled strain-gradient plasticity with species transport at small deformations

This work presents a mechanical isotropic rate-independent theory for plastically deformed materials coupled with species transport. The mass and virtual power balances are natural ingredients used in this work to obtain appropriate local balance laws for species transport, macroscopic, and microscopic forces. The second law of thermodynamics is another key tool used to obtain thermodynamically consistent constitutive relations for the species flux and microscopic stresses. The free energy is approximated as a quadratic form and used to obtain the energetic microscopic stresses as linear combinations of their respective energy conjugates and the species densities. Rate-independent Mises flow rule is deduced in terms of accumulated plastic strain and species density. Furthermore, variational formulation for the coupled theory is obtained as a variational inequality.

Automated summary

This work presents a mechanical isotropic rate-independent theory that couples plastically deformed materials with species transport. Natural ingredients such as mass and virtual power balances are used to obtain local balance laws, while the second law of thermodynamics is applied to derive thermodynamically consistent constitutive relations. The theory also includes a variational inequality formulation for the coupled system.