Generalized thermoelasticity of microstructures: Lord-Shulman theory with modified strain gradient theory

Abstract

In the present work, the general form of coupled thermoelasticity for microstructures is derived by mixing the Lord-Shulman thermoelasticity theory with the modified strain gradient theory of microstructures. The assumptions of both Lord-Shulman and modified strain gradient theories are fully considered and the final forms of constitutive equations and also heat conduction equation are derived in the same manner as the Lord-Shulman theory method by consideration of extra energy terms included in modified strain gradient theory. To show the ability of the developed model, in a special case, one-dimensional microlayer, is considered and the governing generalized thermoelasticity equations based on Lord-Shulman and modified strain gradient theories are derived for the microlayer. A consistent Chebyshev collocation method is developed and used for solving the obtained equations. The effects of micromechanical parameters named length scale parameters were investigated by some figures. These results show that the length scale parameters have an important role in the distribution of displacement, stress, and temperature.