State space approach to study thermal shock problem in nonlocal thermoelastic medium with double porosity

Abstract

In this article, a two-dimensional problem is studied in a homogeneous isotropic thermoelastic medium with double porosity in the context of nonlocal thermoelasticity and the problem is treated in the presence of the Green–Naghdi model of type-III. Constitutive relations and field equations are derived and the state space approach is employed to solve this problem. Thermal shock is applied on the boundary of the surface. From these relations and expressions, we have calculated stress components, displacement components, and temperature for different values of distance and time numerically and plotted graphically to demonstrate and compare theoretical results. The influences of void parameters, locality, and nonlocality on the various physical quantities are also analyzed. Some particular and special cases are also deduced from this study and compared with the existing results.

Keywords:

• Double porosity
• Eringen’s nonlocal thermoelasticity
• Green–Naghdi model type-III
• state space approach
• thermal shock

Disclosure statement

The authors declare that there is no conflict of interest.

Additional information

Funding

Research work of Chandra Sekhar Mahato is financially supported by NET-JRF Fellowship of University Grants Commission, New Delhi, India.