On Effective Young’s Modulus and Poisson’s Ratio of the Auxetic Thermoelastic Material
Maruszewski Bogdan, Drzewiecki Andrzej, Starosta Roman
Poznan University of Technology, Institute of Applied Mechanics
Jana Pawła II 24, 60-965 Poznan
E-mail: bogdan.maruszewski@put.poznan.pl, andrzej.drzewiecki@put.poznan.pl, roman.starosta@put.poznan.pl
Received:
Received: 11 November 2016; revised: 06 December 2016; accepted: 07 December 2016; published online: 30 December 2016
DOI: 10.12921/cmst.2016.0000050
Abstract:
The paper deals with an influence of the excitation frequency and the dimensions of a free supported thermoelastic plate on the effective Poisson’s ratio and the effective Young’s modulus. Both of these parameters are not, in such a situation, the elastic material constants. The considered thermoelastic problem has been modelled within the extended thermodynamical model. Therefore, the above effective elastic coefficients are also dependent on the thermal relaxation time. The numerical analysis of those coefficients vs. excitation frequency both for normal and auxetic plates have been presented.
Key words:
auxetics, effective elastic coefficients, thermoelastic damping
References:
[1] W. Nowacki, Thermoelasticity, Pergamon, Oxford 1962.
[2] W. Nowacki, Dynamic problems of thermoelasticity, Noord-
hoff, Leyden 1975.
[3] B.A. Boley, J.H. Weiner, Theory of thermal stresses, Wiley,
New York – London 1960.
[4] N. Noda, R.B. Hetnarski, Y. Tanigawa, Thermal stresses,
Taylor & Francis, New York – London 2003.
[5] B.T. Maruszewski, A. Drzewiecki, R. Starosta, Thermoelas-
tic damping and thermal relaxation time in auxetics, Applied
Mechanics and Materials, 432, 215-220 (2013).
[6] B.T. Maruszewski, A. Drzewiecki, R. Starosta, L. Restuccia,
Thermoelastic damping in an auxetic rectangular plate with
thermal relaxation: forced vibrations, Journal of Mechanics
of Materials and Structures., 8,(8-10), 403-413 (2013).
[7] J.B. Alblas, A note on the theory of thermoelastic damping,
Journal of Thermal Stresses, 4, (3-4), 333-355 (1981).
[8] C. Zener, Internal friction in solids, Physical Review, 52, (3),
230-235 (1937).
[9] J.B. Alblas, On the general theory of thermoelastic friction,
Applied Scientific Research A,10, (1), 349-362 (1961).
[10] B. Maruszewski, Nonlinear thermoelastic damping in circular
plate, Zeitschrift für Angewandte Mathematik und Mechanik,
72, (4), T75-T78 (1992).
[11] J. Ignaczak, M. Ostoja-Starzewski, Thermoelasticity with
finite wave speeds, Oxford University Press, New York 2010.
[12] M. Chester, Second sound in solids, Physical Rev, 131, (5),
2013 (1963).
[13] B. Maruszewski, Evolution equations of thermodiffusion in
paramagnets, International Journal of Engineering Science,
26, (11), 1217-1230 (1988).
[14] D. Jou, J. Casas-Vazquez, G. Lebon, Extended irreversible
thermodynamics, Reports on Progress in Physics, 51, (8),
1105 (1988).
[15] R. Lakes, Foam structures with a negative Poisson’s ratio,
Science, 235(4792), 1038-1040 (1987).
[16] K.W. Wojciechowski, Two-dimensional isotropic system
with negative Poisson’s ratio, Physics Letters A, 137,(1-2),
60-64 (1989).
[17] V.V. Novikov, K.W. Wojciechowski, Negative Poisson co-
efficient of fractal structures, Physics of the Solid State, 41,
1970-1975 (1999).
[18] A.A. Pozniak, H. Kamiński, P.K ̨edziora, B. Maruszewski,
T. Str ̨ek, K.W. Wojciechowski, Anomalous deformation of
constrained auxetic square, Reviews on Advanced Materials
Science, 23,(2), 169-174 (2010).
[19] P. Kolat, B. Maruszewski, K.W. Wojciechowski, Solitary
waves in auxetic plates, Journal of Non-Crystalline Solids,
356, 2001-2009 (2010).
[20] P. Kolat, B. Maruszewski, K.V. Tretiakov, K.W. Woj-
ciechowski, Solitary waves in auxetic rods, Physica Status
Solidi (b), 248, (1), 148-157 (2011).
[21] L.D. Landau, E.M. Lifshitz, Theory of elasticity, Pergamon
Press 1970.
[22] A. Alderson, K.L. Alderson, K.E. Evans, J.N. Grima, M.R.
Wiliams, P.J. Davies, Modelling the deformation mechanisms,
structure-property relationships and applications of auxetic
nanomaterials, Physica Status Solidi (b), 242, (3) , 499-508
(2005).
The paper deals with an influence of the excitation frequency and the dimensions of a free supported thermoelastic plate on the effective Poisson’s ratio and the effective Young’s modulus. Both of these parameters are not, in such a situation, the elastic material constants. The considered thermoelastic problem has been modelled within the extended thermodynamical model. Therefore, the above effective elastic coefficients are also dependent on the thermal relaxation time. The numerical analysis of those coefficients vs. excitation frequency both for normal and auxetic plates have been presented.
Key words:
auxetics, effective elastic coefficients, thermoelastic damping
References:
[1] W. Nowacki, Thermoelasticity, Pergamon, Oxford 1962.
[2] W. Nowacki, Dynamic problems of thermoelasticity, Noord-
hoff, Leyden 1975.
[3] B.A. Boley, J.H. Weiner, Theory of thermal stresses, Wiley,
New York – London 1960.
[4] N. Noda, R.B. Hetnarski, Y. Tanigawa, Thermal stresses,
Taylor & Francis, New York – London 2003.
[5] B.T. Maruszewski, A. Drzewiecki, R. Starosta, Thermoelas-
tic damping and thermal relaxation time in auxetics, Applied
Mechanics and Materials, 432, 215-220 (2013).
[6] B.T. Maruszewski, A. Drzewiecki, R. Starosta, L. Restuccia,
Thermoelastic damping in an auxetic rectangular plate with
thermal relaxation: forced vibrations, Journal of Mechanics
of Materials and Structures., 8,(8-10), 403-413 (2013).
[7] J.B. Alblas, A note on the theory of thermoelastic damping,
Journal of Thermal Stresses, 4, (3-4), 333-355 (1981).
[8] C. Zener, Internal friction in solids, Physical Review, 52, (3),
230-235 (1937).
[9] J.B. Alblas, On the general theory of thermoelastic friction,
Applied Scientific Research A,10, (1), 349-362 (1961).
[10] B. Maruszewski, Nonlinear thermoelastic damping in circular
plate, Zeitschrift für Angewandte Mathematik und Mechanik,
72, (4), T75-T78 (1992).
[11] J. Ignaczak, M. Ostoja-Starzewski, Thermoelasticity with
finite wave speeds, Oxford University Press, New York 2010.
[12] M. Chester, Second sound in solids, Physical Rev, 131, (5),
2013 (1963).
[13] B. Maruszewski, Evolution equations of thermodiffusion in
paramagnets, International Journal of Engineering Science,
26, (11), 1217-1230 (1988).
[14] D. Jou, J. Casas-Vazquez, G. Lebon, Extended irreversible
thermodynamics, Reports on Progress in Physics, 51, (8),
1105 (1988).
[15] R. Lakes, Foam structures with a negative Poisson’s ratio,
Science, 235(4792), 1038-1040 (1987).
[16] K.W. Wojciechowski, Two-dimensional isotropic system
with negative Poisson’s ratio, Physics Letters A, 137,(1-2),
60-64 (1989).
[17] V.V. Novikov, K.W. Wojciechowski, Negative Poisson co-
efficient of fractal structures, Physics of the Solid State, 41,
1970-1975 (1999).
[18] A.A. Pozniak, H. Kamiński, P.K ̨edziora, B. Maruszewski,
T. Str ̨ek, K.W. Wojciechowski, Anomalous deformation of
constrained auxetic square, Reviews on Advanced Materials
Science, 23,(2), 169-174 (2010).
[19] P. Kolat, B. Maruszewski, K.W. Wojciechowski, Solitary
waves in auxetic plates, Journal of Non-Crystalline Solids,
356, 2001-2009 (2010).
[20] P. Kolat, B. Maruszewski, K.V. Tretiakov, K.W. Woj-
ciechowski, Solitary waves in auxetic rods, Physica Status
Solidi (b), 248, (1), 148-157 (2011).
[21] L.D. Landau, E.M. Lifshitz, Theory of elasticity, Pergamon
Press 1970.
[22] A. Alderson, K.L. Alderson, K.E. Evans, J.N. Grima, M.R.
Wiliams, P.J. Davies, Modelling the deformation mechanisms,
structure-property relationships and applications of auxetic
nanomaterials, Physica Status Solidi (b), 242, (3) , 499-508
(2005).
