Skip to main content
SpringerLink
Log in
Book cover

Models and Theories in Social Systems pp 133–147Cite as

Micropolar Thermoelasticity with Voids Using Fractional Order Strain

  • Chapter
  • First Online:

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 179))

Abstract

The chapter is dealing with the study of the thermoelasticity of the micropolar materials with voids that uses the fractional order strain, in order to determine some equations of this linear thermoelasticity theory, as well as of a reciprocity relation for the mentioned bodies. Finding the form of the constitutive equations and using them for analyzing the reciprocity, toghether with obtaining the equation of thermal conductivity under the terms of our theory is the main purpose, realizing a parallel between classical theory and this specific case, leading to a better understanding of the behaviour of these materials.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Agrawal, O.P.: Generalized variational problems and Euler - Lagrange equations. Comput. Math. Appl. 59(5), 1852–1864 (2010). https://doi.org/10.1016/j.camwa.2009.08.029

    Article  MathSciNet  Google Scholar 

  • Aouadi, M.: A theory of thermoelastic materials with voids. Z. Angew. Math. Phys. 61, 357–379 (2010). https://doi.org/10.1007/s00033-009-0016-0

    Article  MathSciNet  Google Scholar 

  • Băleanu, D., Diethelm, K., Scalas, E., Trujillo, J.J.: Fractional Calculus: Models and Numerical Methods. Series on Complexity, Nonlinearity and Chaos, vol. 5, 2nd edn. World Scientific, Singapore (2012). https://doi.org/10.1142/10044

  • Caputo, M.: Linear models of dissipation whose Q is almost frequency independent-II. Geophys. J. R. Astron. Soc. 13(5), 529–539 (1967). https://doi.org/10.1111/j.1365-246X.1967.tb02303.x

    Article  Google Scholar 

  • Cattaneo, C.: Sulla conduzione del calore. Atti. Sem. Mat. Fis. Univ. Modena 3, 83–101 (1948)

    MathSciNet  MATH  Google Scholar 

  • Chirilă, A.: Generalized micropolar thermoelasticity with fractional order strain. Bull. Transilv. Univ. Braşov, Ser. III: Math. Inf. Phys. 10(59)(1), 83–90 (2017)

    Google Scholar 

  • Ciarletta, M., Scalia, A.: Some results in linear theory of thermomicrostretch elastic solids. Meccanica 39, 191–206 (2004)

    Article  MathSciNet  Google Scholar 

  • Codarcea-Munteanu, L., Marin, M: Thermoelasticity with fractional order strain for dipolar materials with voids. Bull. Transilv. Univ. Braşov, Ser. III: Math. Inf. Phys. (2017) (accepted)

    Google Scholar 

  • Cowin, S.C., Nunziato, J.W.: Linear elastic materials with voids. J. Elast. 13, 125–147 (1983)

    Article  Google Scholar 

  • El-Karamany, A.S., Ezzat, M.A.: On fractional thermoelasticity. Math. Mech. Solids 16(3), 334–346 (2011). https://doi.org/10.1177/1081286510397228

    Article  MathSciNet  Google Scholar 

  • Eringen, A.C.: Microcontinuum Field Theories I. Foundations and Solids. Springer, New York (1999)

    Book  Google Scholar 

  • Goodman, M.A., Cowin, S.C.: A continuum theory for granular materials. Arch. Ration. Mech. Anal. 44, 249–266 (1972)

    Article  MathSciNet  Google Scholar 

  • Hetnarski, R.B.: Thermal Stresses IV. Elsevier, Amsterdam (1996)

    Google Scholar 

  • Hetnarski, R.B., Ignaczak, J.: Generalized thermoelasticity. J. Therm. Stress. 22, 451–476 (1999)

    Article  MathSciNet  Google Scholar 

  • Ieşan, D.: Generalized mechanics of solids. Univ. Al. I. Cuza, Centrul de multiplicare, Iaşi (1980)

    Google Scholar 

  • Ieşan, D.: A theory of thermoelastic materials with voids. Acta Mech. 60(1–2), 67–89 (1986)

    Article  Google Scholar 

  • Iovane, G., Passarella, F.: Some theorems in thermoelasticity for micropolar porous media. Rev. Roum. Sci. Tech. Mech. Appl. 46(1–6), 9–18 (2002)

    MathSciNet  Google Scholar 

  • Lianngenga, R.: Theory of micropolar thermoelastic materials with voids. IJPAMS 9(1), 1–8 (2016)

    Google Scholar 

  • Lianngenga, R., Lalawmpuia: Micropolar elasticity containing voids. IJISET 2(12), 838–844 (2015)

    Google Scholar 

  • Malinowska, A.B., Odzijewicz, T., Torres, D.F.M.: Advanced Methods in the Fractional Calculus of Variations. Springer Briefs in Applied Sciences and Technology. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-14756-7

    Book  Google Scholar 

  • Marin, M.: The lagrange identity method in thermoelasticity of bodies with microstructure. Int. J. Eng. Sci. 32(8), 1229–1240 (1994)

    Article  MathSciNet  Google Scholar 

  • Marin, M.: On weak solutions in elasticity of dipolar bodies with voids. J. Comput. Appl. Math. 82(1–2), 291–297 (1997). https://doi.org/10.1016/s0377-0427(97)00047-2

    Article  MathSciNet  Google Scholar 

  • Marin, M.: A temporally evolutionary equation in elasticity of micropolar bodies with voids. UPB Sci. Bull. Ser. A Appl. Math. Phys. 60(3–4), 67–78 (1998)

    Google Scholar 

  • Marin, M.: Harmonic vibrations in thermoelasticity of microstretch materials. J. Vib. Acoust. 132(4), 044501,6 (2010a)

    Article  Google Scholar 

  • Marin, M.: Some estimates on vibrations in thermoelasticity of dipolar bodies. J. Vib. Control 16(1), 33–47 (2010b)

    Article  MathSciNet  Google Scholar 

  • Marin, M.: An approach of a heat-flux dependent theory for micropolar porous media. Meccanica 51, 1127–1133 (2016). https://doi.org/10.1007/s11012-015-0265-2

    Article  MathSciNet  Google Scholar 

  • Marin, M., Codarcea, L., Chirilă, A.: Qualitative results on mixed problem of micropolar bodies with microtemperatures. Appl. Appl. Math. (2017) (accepted)

    Google Scholar 

  • Markov, K.Z.: On the dilatation theory of elasticity. ZAMM Z. Angew. Math. Mech. 61(8), 349–358 (1981)

    Article  Google Scholar 

  • Nunziato, J.W., Cowin, S.C.: A nonlinear theory of elastic materials with voids. Arch. Ration. Mech. Anal. 72, 175–201 (1979)

    Article  MathSciNet  Google Scholar 

  • Podlubny, I.: Fractional Differential Equation: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and some of Their Applications. Academic Press, New York (1998)

    MATH  Google Scholar 

  • Postvenko, Y.Z.: Thermoelasticity that uses fractional heat conduction equation. J. Math. Sci. 162(2), 296–305 (2009)

    Article  MathSciNet  Google Scholar 

  • Sheoran, S.S., Kundu, P.: Fractional order generalized thermoelasticity theories: a review. Int. J. Adv. Appl. Math. Mech. 3(4), 76–81 (2016)

    MathSciNet  MATH  Google Scholar 

  • Sherief, H.H., El-Sayed, A.M.A., Abd El-Latief, A.M.: Fractional order theory of thermoelasticity. Int. J. Solids Struct. 47, 269–275 (2010)

    Article  Google Scholar 

  • Youssef, H.M.: Theory of generalized thermoelasticity with fractional order strain. J. Vib. Control 22(18), 3840–3857 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Transilvania University of Braşov, Bd. Eroilor 29, 500036, Braşov, Romania

    Lavinia Codarcea-Munteanu & Marin Marin

Authors
  1. Lavinia Codarcea-Munteanu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marin Marin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lavinia Codarcea-Munteanu .

Editor information

Editors and Affiliations

  1. Faculty of Mathematics and Computer Science, Ovidius University of Constanţa, Constanţa, Romania

    Cristina Flaut

  2. Department of Mathematics and Physics, Faculty of Military Technology, University of Defence, Brno, Czech Republic

    Šárka Hošková-Mayerová

  3. Faculty of History and Political Science, Ovidius University of Constanţa, Constanţa, Romania

    Daniel Flaut

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Codarcea-Munteanu, L., Marin, M. (2019). Micropolar Thermoelasticity with Voids Using Fractional Order Strain. In: Flaut, C., Hošková-Mayerová, Š., Flaut, D. (eds) Models and Theories in Social Systems. Studies in Systems, Decision and Control, vol 179. Springer, Cham. https://doi.org/10.1007/978-3-030-00084-4_7

Download citation

Publish with us

Policies and ethics

Search

Navigation