Response of fractional ordered micropolar thermoviscoelastic half-space with diffusion due to ramp type mechanical load

Abstract

• Interactions caused by mechanical shock in micropolar diffusive medium are studied. • Problem has been modeled in context of generalized fractional thermoelasticity. • Laplace and Fourier transforms are used to solve the problem. • Effects of fractional parameter, micropolarity and diffusion are noticed. The current manuscript is devoted to scrutinize the effects of fractional parameter, micropolarity and diffusion on the interactions caused by a ramp type mechanical shock in a generalized thermo-viscoelastic solid half-space. The medium is assumed to be unstrained and unstressed initially and has uniform temperature. The problem has been modeled by employing the fractional generalization of the Lord–Shulman theory to carry the investigation. The governing equations in xz -plane are handled with an analytical–numerical technique based on Laplace–Fourier transforms. Expressions for displacement, stresses, temperature and mass concentration in the physical domain are obtained using a numerical inversion technique. The problem is illustrated by computing the numerical values of the field variables for a magnesium crystal like material. Comparisons of the physical quantities are shown in figures to study the effects of fractional parameter, micropolarity, diffusion and ramp parameter. Some particular cases of interest have also been inferred from the present problem.