Size dependent generalized thermoelasticity: Green-Lindsay theory with modified strain gradient theory

Abstract

The present work is a development of the Green-Lindsay (GL) thermoelasticity theory for micro continuum bodies. The micro continuum modified strain gradient theory is used here based on the Green-Lindsay theory of the micro continuum media. In fact, the present work is a combination of Green-Lindsay thermoelasticity theory with modified strain gradient continuum theory. All assumptions of GL and modified strain gradient theory are satisfied and the final general forms of constitutive relations and also heat conduction equation are extracted. As an application of the derived formulation, a one-dimensional microlayer is considered and the newly derived equations are applied to it. Finally, the governing equations of coupled generalized thermoelasticity of the microlayer are solved using the Chebyshev collocation method. Effects of microscale parameters appearing in modified strain gradient theory on the dynamic thermo-elastic response of microlayer are investigated.