Skip to main content
Erschienen in: Archive of Applied Mechanics 11/2018

28.07.2018 | Reply

A least squares approach for effective shear properties in an \({{\varvec{n}}}\)-layered sphere model

verfasst von: Rolf Mahnken, Peter Lenz, Christian Dammann

Erschienen in: Archive of Applied Mechanics | Ausgabe 11/2018

Einloggen

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This work presents the derivation of the effective shear modulus for a heterogeneous material composed of multilayered composite spheres embedded in a linear elastic matrix. It is based on the composite spheres model known from the literature. In contrast to Herve and Zaoui (Int J Eng Sci 31:1–10, 1993), the effective shear modulus is obtained by equating the results of two models: In the first model, a heterogeneous sphere is embedded in an equivalent homogeneous material, whereas in the second model, the heterogeneous sphere is replaced by an equivalent homogeneous sphere. In the context of both, a shear stress approach and a shear deformation approach, this results in an overdetermined system of equations which is solved with the least squares method. In a numerical study, our results are compared to effective moduli and bounds from the literature. Furthermore, a convincing agreement with experimental data for glass microspheres embedded in a polyester matrix is demonstrated.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
Zurück zum Zitat Bulut, O., Kadioglu, N., Ataoglu, S.: Absolute effective elastic constants of composite materials. Struct. Eng. Mech. 57(5), 897–920 (2016)CrossRef Bulut, O., Kadioglu, N., Ataoglu, S.: Absolute effective elastic constants of composite materials. Struct. Eng. Mech. 57(5), 897–920 (2016)CrossRef
2.
Zurück zum Zitat Christensen, R.M.: Mechanics of Composite Materials. Dover Publications, Mineola (1979) Christensen, R.M.: Mechanics of Composite Materials. Dover Publications, Mineola (1979)
3.
Zurück zum Zitat Christensen, R.M., Lo, K.H.: Solutions for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids 27(4), 315–330 (1979)CrossRef Christensen, R.M., Lo, K.H.: Solutions for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids 27(4), 315–330 (1979)CrossRef
4.
Zurück zum Zitat Dvorak, G.: Micromechanics of Composite Materials. Springer, Berlin (2013)CrossRef Dvorak, G.: Micromechanics of Composite Materials. Springer, Berlin (2013)CrossRef
5.
Zurück zum Zitat Gusev, A.: Effective coefficient of thermal expansion of n-layered composite sphere model: exact solution and its finite element validation. Int. J. Eng. Sci. 84, 54–61 (2014)MathSciNetCrossRef Gusev, A.: Effective coefficient of thermal expansion of n-layered composite sphere model: exact solution and its finite element validation. Int. J. Eng. Sci. 84, 54–61 (2014)MathSciNetCrossRef
6.
Zurück zum Zitat Hashin,Z.: The elastic moduli of heterogeneous materials. Division of Engineering and Applied Physics, Harvard University, Contract Nonr 1866(2), TR 9, (1960) Hashin,Z.: The elastic moduli of heterogeneous materials. Division of Engineering and Applied Physics, Harvard University, Contract Nonr 1866(2), TR 9, (1960)
8.
Zurück zum Zitat Hashin, Z., Shtrikman, S.: A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11(2), 127140 (1963)MathSciNetCrossRef Hashin, Z., Shtrikman, S.: A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11(2), 127140 (1963)MathSciNetCrossRef
9.
Zurück zum Zitat Herve, E., Zaoui, A.: n-layered inclusion-based micromechanical modelling. Int. J. Eng. Sci. 31, 1–10 (1993)CrossRef Herve, E., Zaoui, A.: n-layered inclusion-based micromechanical modelling. Int. J. Eng. Sci. 31, 1–10 (1993)CrossRef
10.
Zurück zum Zitat Kerner, E.H.: The elastic and thermo-elastic properties of composite media. Proc. Phys. Soc. Lond. Sect. B 69(8), 808 (1956)CrossRef Kerner, E.H.: The elastic and thermo-elastic properties of composite media. Proc. Phys. Soc. Lond. Sect. B 69(8), 808 (1956)CrossRef
11.
Zurück zum Zitat Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity, 4th edn. Dover Publications, Mineola (1944)MATH Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity, 4th edn. Dover Publications, Mineola (1944)MATH
12.
Zurück zum Zitat Mahnken, R., Dammann, C.: A three-scale framework for fibre-reinforced-polymer curing Part I: microscopic modeling and mesoscopic effective properties. Int. J. Solids Struct. 100, 341–355 (2016)CrossRef Mahnken, R., Dammann, C.: A three-scale framework for fibre-reinforced-polymer curing Part I: microscopic modeling and mesoscopic effective properties. Int. J. Solids Struct. 100, 341–355 (2016)CrossRef
13.
Zurück zum Zitat Mahnken, R., Dammann, C.: A three-scale framework for fibre-reinforced-polymer curing Part II: mesoscopic modeling and macroscopic effective properties. Int. J. Solids Struct. 100, 356–375 (2016)CrossRef Mahnken, R., Dammann, C.: A three-scale framework for fibre-reinforced-polymer curing Part II: mesoscopic modeling and macroscopic effective properties. Int. J. Solids Struct. 100, 356–375 (2016)CrossRef
14.
Zurück zum Zitat Mahnken, R., Dammann, C., Lenz, P.: (n)- and (n+1)-layered composit sphere models for thermo-chemo-mechanical effective properties. Int. J. Multiscale Comput. Eng. 15(4), 295–322 (2017)CrossRef Mahnken, R., Dammann, C., Lenz, P.: (n)- and (n+1)-layered composit sphere models for thermo-chemo-mechanical effective properties. Int. J. Multiscale Comput. Eng. 15(4), 295–322 (2017)CrossRef
15.
Zurück zum Zitat Richard, T.G.: The mechanical behavior of a solid microsphere filled composite. J. Compos. Mater. 9(2), 108–113 (1975)CrossRef Richard, T.G.: The mechanical behavior of a solid microsphere filled composite. J. Compos. Mater. 9(2), 108–113 (1975)CrossRef
16.
Zurück zum Zitat Slaughter, W.: The Linearized Theory of Elasticity, 1st edn. Birkhäuser, Basel (2002)CrossRef Slaughter, W.: The Linearized Theory of Elasticity, 1st edn. Birkhäuser, Basel (2002)CrossRef
Metadaten
Titel
A least squares approach for effective shear properties in an -layered sphere model
verfasst von
Rolf Mahnken
Peter Lenz
Christian Dammann
Publikationsdatum
28.07.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
Archive of Applied Mechanics / Ausgabe 11/2018
Print ISSN: 0939-1533
Elektronische ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-018-1431-5

Weitere Artikel der Ausgabe 11/2018

Archive of Applied Mechanics 11/2018 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.