Representation of solutions of strain gradient dual-phase-lag thermoelasticity and effects of scale-length parameter in half-space

This work concerns the strain gradient theory of thermoelasticity with dual-phase-lag model. We obtain the Galerkin-type representation solution of the field equations. The strain gradient scale-length parameter plays an essential role in the material response. Therefore, we analyze the microstructural effect through the scale-length parameter on an isotropic thermoelastic half-space. We formulate the problem with a suitable boundary condition. The solution of the different field variables such as temperature, displacement, stresses, and double stresses is obtained in the Laplace transform domain. Then, we apply a numerical method for Laplace inversion to find the solution for different fields in the physical domain. The results are displayed in graphical form to show the microstructural effect through the scale-length parameter.