A size-dependent generalized thermoelastic diffusion theory and its application

To capture the transient responses for the thermally and chemically shocked structure at micro or nanoscale, the present work is devoted to establish a size-dependent generalized thermoelastic diffusion theory within the thermodynamic framework. The uniqueness theorem and reciprocity theorem are, respectively, obtained. The corresponding generalized variational principle is developed using the semi-inverse method. In numerical implementation, a semi-infinite medium subjected to thermal and chemical shock at one end is considered and solved by the Laplace transformation. Numerical results are obtained and illustrated graphically. It can be concluded that the nonlocal scale parameter has a significant affect on the displacement and stress, which is excessively important in determining the material's failure in complex environment. In addition, the numerical results show that the temperature, chemical potential, stress, and concentration are greatly influenced by the fractional order parameter.