The nonlinear response of Cattaneo-type thermal loading of a laser pulse on a medium using the generalized thermoelastic model

• Main Authors: Farshad Shakeriaski, Maryam Ghodrat
• Format: Article
• Language: English
• Published: Elsevier 2020-04-01
• Series: Theoretical and Applied Mechanics Letters
• Subjects: Thermal wave propagation; Nonlinear generalized thermoelasticity; Cattaneo’s heat conduction; Laser pulse heating
• Online Access: http://www.sciencedirect.com/science/article/pii/S2095034920300465

ABSTRACT: The nonlinear thermoelastic responses of an elastic medium exposed to laser generated short-pulse heating are investigated in this article. The thermal wave propagation of generalized thermoelastic medium under the impact of thermal loading with energy dissipation is the focus of this research. To model the thermal boundary condition (in the form of thermal conduction), generalized Cattaneo model (GCM) is employed. In the reference configuration, a nonlinear coupled Lord-Shulman-type generalized thermoelasticity formulation using finite strain theory (FST) is developed and the temperature dependency of the thermal conductivity is considered to derive the equations. In order to solve the time-dependent and nonlinear equations, Newmark’s numerical time integration technique and an updated finite element algorithm is applied and to ensure achieving accurate continuity of the results, the Hermitian elements are used instead of Lagrangian’s. The numerical responses for different factors such as input heat flux and nonlinear terms are expressed graphically and their impacts on the system’s reaction are discussed in detail. The results of the study are presented for Green–Lindsay model and the findings are compared with Lord-Shulman model especially with regards to heat wave propagation. It is shown that the nature of the laser’s thermal shock and its geometry are particularly determinative in the final stage of deformation. The research also concluded that employing FST leads to achieving more accuracy in terms of elastic deformations; however, the thermally nonlinear analysis does not change the results markedly. For this reason, the nonlinear theory of deformation is required in laser related reviews, while it is reasonable to ignore the temperature changes compared to the reference temperature in deriving governing equations.