An attempt to separate elastic strain energy density of linear elastic anisotropic materials based on strains considerations
Article
First Online:
Received:
Revised:
- 275 Downloads
- 2 Citations
Abstract
A promising new effort toward the decomposition of the elastic strain energy density of linear elastic anisotropic materials into a dilatational and a distortional part is presented. By assuming that volume changes must keep the material symmetries unchanged, a new physical perspective is presented and interesting definitions are drawn. This new perspective necessitates the introduction of a strain parameter m characteristic of the material’s anisotropy. This strain parameter besides easing the calculation of the dilatational and distortional energetic terms additionally accounts for the directional sensitivity of anisotropic materials.
Keywords
Bulk Modulus Shape Change Anisotropic Material Orthotropic Material Strain Parameter
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Mises von R.: Mechanik der festen Körper im plastisch deformablen Zustand. Math.-Phys. 1(4), 582–592 (1913)Google Scholar
- 2.Huber, M.T.: Distortion strain energy as a measure of strength of the materials (in Polish). Gzasopismo Techniczne XXII, Lwow (1904)Google Scholar
- 3.Hencky H.: Zur Theorie plastischer Deformationen und der hierdurch im Material hervorgerufenen Nachspannungen. ZAMM 4, 323–334 (1924)CrossRefGoogle Scholar
- 4.Kowalczyk K., Ostrowska-Maciejewska J.: Arch. Mech. 54(5–6), 497–523 (2002)MathSciNetMATHGoogle Scholar
- 5.Sutcliffe S.: Spectral decomposition of the elasticity tensor. J. Appl. Mech. 59, 762–773 (1992)MathSciNetMATHCrossRefGoogle Scholar
- 6.Rychlewski J.: Elastic energy decomposition and limit criteria. Adv. Mech. 7, 51–80 (1984)Google Scholar
- 7.Rychlewski J.: On Hooke’s law. PMM (English translation) 48, 303–314 (1984)MathSciNetGoogle Scholar
- 8.Rychlewski J.: Unconventional approach to linear elasticity. Arch. Mech. 59(4), 149–171 (1995)MathSciNetGoogle Scholar
- 9.Olszak W., Ostrowska-Maciejewska J.: The plastic potential in the theory of anisotropic elastic-plastic solids. Eng. Fract. Mech. 21, 625–632 (1985)CrossRefGoogle Scholar
- 10.Kowalczyk K., Ostrowska-Maciejewska J.: Energy-based limit conditions for transversally isotropic solids. Arch. Mech. 54, 497–523 (2002)MathSciNetMATHGoogle Scholar
- 11.Kowalczyk K., Ostrowska-Maciejewska J.: The influence of internal restrictions on the elastic properties of anisotropic materials. Arch. Mech. 56, 220–232 (2004)Google Scholar
- 12.Tsai S.W., Wu R.A.: A general theory of strength for anisotropic materials. J. Compos. Mater. 5, 58–80 (1971)CrossRefGoogle Scholar
- 13.Theocaris P.S.: Failure characterization of anisotropic materials by means of the elliptic paraboloid failure surface. Uspechi Mekhanikii (Advances in Mechanics) 10, 83–102 (1971)Google Scholar
- 14.Andrianopoulos N.P., Boulougouris V.C., Iliopoulos A.P.: On the separation of elastic strain energy in the general case of anisotropy: a direct approach. Arch. Mech. Eng. V.LIII(2), 153–163 (2006)Google Scholar
- 15.Burzyński, W.T.: Study of the strength hypotheses. Ph.D. thesis (in Polish). Lwow (1928)Google Scholar
- 16.Malvern L.E.: Introduction to the Mechanics of a Continuous Medium. Prentice Hall, Englewood Cliffs (1969)Google Scholar
- 17.Nye F.: Physical Properties of Crystals. Clarendon, Oxford (1957)MATHGoogle Scholar
- 18.Voigt W.: Lehrbuch der Kristallphysik. Teubner, Leipzig (1910)Google Scholar
- 19.Itskov M., Aksel N.: Elastic constants and their admissible values for incompressible and slightly compressible anisotropic materials. Acta Mechanica 157(1–4), 81–96 (2002)MATHCrossRefGoogle Scholar
Copyright information
© Springer-Verlag Wien 2013