Fractional Thermoelasticity Model of a 2D Problem of Mode-I Crack in a Fibre-Reinforced Thermal Environment

Document Type : Research Paper


1 Department of Mathematics, Faculty of Science, King Abdulaziz University P.O. Box 80203, Jeddah 21589, Saudi Arabia

2 Department of Mathematics, Faculty of Science, Kafrelsheikh University Kafrelsheikh 33516, Egypt

3 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt


A model of fractional-order of thermoelasticity is applied to study a 2D problem of mode-I crack in a fibre-reinforced thermal environment. The crack is under prescribed distributions of heat and pressure. The normal mode analysis is applied to deduce exact formulae for displacements, stresses, and temperature. Variations of field quantities with the axial direction are illustrated graphically. The results regarding the presence and absence of fiber reinforcement and fractional parameters are compared. Some particular cases are also investigated via the generalized thermoelastic theory. The presented results can be applied to design different fibre-reinforced isotropic thermoelastic elements subjected to the thermal load in order to meet special technical requirements.


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