ORIGINAL PAPER
Anti-plane deformation in Green-Naghdi(Type III) thermoelastic medium
 
More details
Hide details
1
Mathematics, Chandigarh University, India
 
2
Mechanical, University of Zielona Gora, Poland
 
3
Civil Engineering, Chandigarh University, India
 
These authors had equal contribution to this work
 
 
Submission date: 2025-02-04
 
 
Final revision date: 2025-03-18
 
 
Acceptance date: 2025-05-22
 
 
Online publication date: 2025-09-02
 
 
Publication date: 2025-09-02
 
 
Corresponding author
Praveen Ailawalia   

Mathematics, Chandigarh University, 17 c, 133001, AMBALA CANTT, India
 
 
International Journal of Applied Mechanics and Engineering 2025;30(3):1-10
 
KEYWORDS
TOPICS
ABSTRACT
Anti-plane problems in elastic, viscoelastic, functionally graded material, and thermoelastic medium have been discussed by researchers in the past. The anti-plane problem in the context of Green-Naghdi(Type III) thermoelasticity has been unexplored. In the present work, a crack in a strip of Green Nagdhi(Type III) thermoelastic medium is discussed under anti-plane shear conditions. The lower boundary of the strip is fixed and it is displaced along the upper boundary. The crack surface is assumed to be traction-free. The expressions of displacement, temperature, and shear stress are obtained. The values of these expressions are then obtained using MATLAB software and the values are then plotted against horizontal distance. The effect of the width of the strip on the components is shown through graphical results. It is found that the width of the strip affects all the physical quantities. The shearing stress along the width of the strip is less oscillatory as compared to the shearing stress along the length of the strip.
REFERENCES (45)
1.
Biot M.A. (1967): Thermoelasticity and irreversible thermodynamics.– Journal of Applied Physics, vol.27, No.3, pp.240-253.
 
2.
Lord H.W. and Shulman Y. (1967): A generalized dynamical theory of thermoelasticity.– Journal of the Mechanics and Physics of Solids, vol.15, No.5, pp.299-309.
 
3.
Green A.E. and Lindsay K.A. (1972): Thermoelasticity.– Journal of Elasticity, vol.2, No.1, pp.1-7.
 
4.
Green A.E. and Naghdi P.M. (1991): A re-examination of the basic postulates of thermomechanics.– Proceedings of Royal Society London. Series A: Mathematical and Physical Sciences, vol.432, No.1885, pp.171-194.
 
5.
Green A.E. and Naghdi P.M. (1992): On undamped heat waves in an elastic solid.– Journal of Thermal Stresses, vol.15, No.2, pp.253-264.
 
6.
Green A.E. and Naghdi P.M. (1993): Thermoelasticity without energy dissipation.– Journal of Elasticity, vol.31, No.3, pp.189-208.
 
7.
Quintanilla R. (2001): Structural stability and continuous dependence of solutions of thermoelasticity of type III.– Discrete and Continuous Dynamical Systems-B, vol.1, No.4, Id 463.
 
8.
Quintanilla R. (2007): On the impossibility of localization in linear thermoelasticity.– Proceedings of Royal Society. A: Mathematical, Physical and Engineering Sciences, vol.463, No.2088, pp.3311-3322.
 
9.
Bargmann S., Favata A. and Podio-Guidugli P. (2014): A revised exposition of the Green Naghdi theory of heat propagation.– Journal of Elasticity, vol.114, No.2, pp.143-154.
 
10.
Aouadi M., Lazzari B. and Nibbi R. (2014): A theory of thermoelasticity with diffusion under Green Naghdi models.– ZAMM, vol.94, No.10, pp.837-852.
 
11.
Kumar R., Sharma N. and Lata P. (2016): Thermomechanical interactions due to hall current in transversely isotropic thermoelastic with and without energy dissipation with two temperatures and rotation.– Journal of Solid Mechanics, vol.8, No.4, pp.840-858.
 
12.
Othman M.I. and Eraki E.E. (2017): Generalized magneto-thermoelastic half-space with diffusion under initial stress using three-phase-lag model.– Mechanics Based Design of Structures and Machines, vol.45, No.2, pp.145-159.
 
13.
Ezzat M.A., El-Karamany A.S. and El-Bary A.A. (2018): Two-temperature theory in Green-Naghdi thermoelasticity with fractional phase-lag heat transfer.– Microsystem Technologies, vol.24, No.2, pp.951-961.
 
14.
Aouadi M., Ciarletta M. and Tibullo V. (2019): Analytical aspects in strain gradient theory for chiral Cosserat thermoelastic materials within three Green-Naghdi models.– Journal of Thermal Stresses, vol.42, No.6, pp.681-697.
 
15.
Conti M., Pata V. and Quintanilla R. (2020): Thermoelasticity of Moore Gibson Thompson type with history dependence in the temperature.– Asymptotic Analysis, vol.120,No.1-2, pp.1-21.
 
16.
Abouelregal A. (2020): On Green and Naghdi thermoelasticity model without energy dissipation with higher order time differential and phase-lags.– Journal of Applied Computational Mechanics, vol.6, No.3, pp.445-456.
 
17.
Sarkar N. and Atwa S.Y. (2019): Two-temperature problem of a fiber reinforced thermoelastic medium with a Mode-I crack under Green Naghdi theory.– Microsystem Technologies, vol.25, pp.1357-1367.
 
18.
Atwa S.Y. (2014): Generalized magneto-thermoelasticity with two temperature and initial stress under Green-Naghdi theory.– Applied Mathematical Modelling, vol.38, pp.5217-5230.
 
19.
Abbas I.A. (2015): A GN model for thermoelastic interaction in a microscale beam subjected to a moving heat source.– Acta Mechanica, vol.226, pp.2527-2536.
 
20.
Ailawalia P., Sharma A., Marin M. and Öchsner A. (2024): Analysis of an initially stressed functionally graded thermoelastic medium (type III) without energy dissipation.– Continuum Mechanics and Thermodynamics, vol.36, pp.1553-1564.
 
21.
Pany C., Parthan S. and Mukhopadhyay M. (2003): Wave propagation in orthogonally supported periodic curved panels.– Journal of Engineering Mechanics (ASME), vol.129, No.3, pp.342-349.
 
22.
Abbas I.A and Othman M.I.A. (2012): Plane waves in generalized thermo-microstretch elastic solid with thermal relaxation using finite element method.– International Journal of Thermophysics, vol.33, pp.2407-2423.
 
23.
Abbas I.A. (2015): Generalized thermoelastic interaction in functional graded material with fractional order three-phase lag heat transfer.– Journal of Central South University, vol.22, pp.1606-1613.
 
24.
Marin M., Ochsner A., Bhatti M.M. (2020): Some results in Moore-Gibson-Thompson thermoelasticity of dipolar bodies.– ZAMM, vol.100, No.12, Art No.e202000090.
 
25.
Abbas I.A., Saeed T. and Alhothuali M. (2020): Hyperbolic two-temperature photo-thermal interaction in a semiconductor medium with a cylindrical cavity.– Silicon, vol.13, pp.1871-1878.
 
26.
Alzahrani F.S. and Abbas I.A. (2020): Photo-thermal interactions in a semiconducting media with a spherical cavity under hyperbolic two-temperature model.– Mathematics, vol.8, No.4, Article ID 585.
 
27.
Lotfy Kh., Sharma S., Halouani B., Ahmed A., El-Bary A.A., Tantawi R.S. and Elidy E.S. (2025): Stochastic process of magneto-photo-thermoelastic waves in semiconductor materials with the change in electrical conductivity.– Journal of Elasticity, vol.157, No.11, DOI:10.1007/s10659-024-10104-6.
 
28.
Rice J.R. (1968): Mathematical Analysis in the Mechanics of Fracture.– in Fracture An Advanced Treatise, vol.2, Pergamon Press, Oxford, pp.191-311.
 
29.
Paulino G.H., Saif M.T.A. and Mukherjee S. (1993): A finite elastic body with a curved crack loaded in anti-plane shear.– International Journal of Solids and Structures, vol.30, pp.1015-1037.
 
30.
Erdogan F. (1985): The crack problem for bonded non-homogeneous materials under antiplane shear loading.– ASME Journal of Applied Mechanics, vol.52, pp.823-828.
 
31.
Ang W.T., Clements D.L. and Cooke T. (1999): A hyper singular boundary integral equation for antiplane crack problems for a class of inhomogeneous anisotropic elastic materials.– Engineering. Analysis and Boundary Elements, vol.23, pp.567-572.
 
32.
Atkinson C. and Chen C.Y. (1996): The influence of layer thickness on the stress intensity factor of a crack lying in an elastic(viscoelastic) layer embedded in a different elastic(viscoelastic) medium(mode III analysis).– International Journal of Engineering Science, vol.34, pp.639-658.
 
33.
Pettinger A. and Abeyaratne R. (2000): On the nucleation and propagation of thermoelastic phase transformations in anti-plane shear. Part 1. Couple-stress theory.– Computational Mechanics, vol.26, pp.13-24.
 
34.
Pettinger A and Abeyaratne R. (2000): On the nucleation and propagation of thermoelastic phase transformations in anti-plane shear: Part 2. Problems.– Computational Mechanics, vol.26, pp.25-38.
 
35.
Zhou X. and Shui G. (2020): Propagation of transient elastic waves in multilayered composite structure subjected to dynamic anti-plane loading with thermal effects.– Computers and Structures, vol.241, Article Id 112098.
 
36.
Zhou X. and Shui G. (2024): Thermal effect on the transient behavior of a piezomagnetic half-space subjected to dynamic anti-plane load.– Mathematics and Mechanics of Solids, vol.29, No.10, pp.2048-2080.
 
37.
Li C. and Weng G.J. (2002): Antiplane crack problem in functionally graded piezoelectric materials.– ASME Journal of Applied Mechanics, vol.69, No.4, pp.481-488.
 
38.
Paulino G.H. and Jin Z. (2001): Viscoelastic functionally graded materials subjected to anti plane shear fracture.– ASME Journal of Applied Mechanics, vol.68, No.2, pp.284-293.
 
39.
Zelentsov V.B., Lapina P.A., Mitrin B. and Kudish I.I. (2022): An antiplane deformation of a functionally graded half-space.– Continuum Mechanics and Thermodynamics, vol.34, pp.909-920.
 
40.
Xian-Fang Li and Tian-You Fan. (2007): Dynamic analysis of a crack in a functionally graded material sandwiched between two elastic layers under anti-plane loading.– Computers and Structures, vol.79, No.2, pp.211-219.
 
41.
Lee J.M. and Ma C.C. (2010): Analytical solutions for an antiplane problem of two dissimilar functionally graded magnetoelectroelastic half-planes.– Acta Mechanica, vol.212, pp.21-38.
 
42.
Sladek J., Sladek V. and Zhang C.Z. (2003): Dynamic response of a crack in a functionally graded material under an anti-plane shear impact load, key engineering.– Materials, vol.251-252, pp.123-136.
 
43.
Mojtaba A. and Rasul B. (2013): Dynamic behavior of several cracks in functionally graded strip subjected to anti-plane time-harmonic concentrated loads.– Acta Mechanica Solida Sinica, vol.26, No.6, pp.691-705.
 
44.
Cinelli G. and Pilkey W.D. (1971): Normal mode solutions of linear dynamic field theories using Green's extended identity.– International Journal of Engineering Science, vol.9, No.11, pp.1123-1141.
 
45.
Dhaliwal R.S and Singh A. (1980): Dynamic Coupled Thermoelasticity.– Hindustan Publications Corporation, New Delhi, India, p.747.
 
eISSN:2353-9003
ISSN:1734-4492
Journals System - logo
Scroll to top