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Thermal-stress analysis of a damaged solid sphere using hyperbolic two-temperature generalized thermoelasticity
Hamdy M Youssef1,2, Alaa A El-Bary3, Eman A N Al-Lehaibi4
1Mathematics Department, Faculty of Education, Alexandria University, Alexandria, Egypt. youssefanne2005@gmail.com.
Scientific Reports
|January 28, 2021
Summary
This study examines how rotation affects a thermoelastic sphere using hyperbolic two-temperature theory. Rotation and mechanical damage significantly impact deformation and stress, but minimally affect temperature rise.
Area of Science:
- Solid mechanics
- Continuum mechanics
- Thermodynamics
Background:
- Generalized thermoelasticity theories address limitations of classical models.
- The hyperbolic two-temperature theory accounts for distinct thermal relaxation times.
- Mechanical damage models are crucial for understanding material failure under stress.
Purpose of the Study:
- To investigate the influence of rotation on a thermoelastic solid sphere.
- To analyze the effects of mechanical damage within a hyperbolic two-temperature framework.
- To model a rotating thermoelastic sphere under thermal shock conditions.
Main Methods:
- Development of a mathematical model for a homogeneous, isotropic, rotating thermoelastic sphere.
- Application of hyperbolic two-temperature generalized thermoelasticity theory.
- Numerical analysis and graphical representation of results for various parameters.
Main Results:
- The two-temperature parameter significantly affects all studied functions.
- Rotation and mechanical damage have a substantial impact on displacement, stress, and strain energy.
- Conductive and dynamical temperature rise are minimally influenced by damage and rotation.
Conclusions:
- Rotation and mechanical damage are critical factors in thermoelastic behavior of spheres.
- The hyperbolic two-temperature model provides insights into wave propagation with finite speeds.
- This research contributes to understanding complex thermo-mechanical responses in rotating structures.
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