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Further Developments of Physically Based Invariants for Nonlinear Elastic Orthotropic Solids

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Abstract

Recently, Rubin and Jabareen (J. Elast. 90:1–18, 2008) introduced six physically based invariants for nonlinear elastic orthotropic solids which are measures of distortions that cause deviatoric Cauchy stress. Three of these invariants include three dependent functions that characterize the distortion in a hydrostatic state of stress. In particular, these invariants can be used without the need to place additional restrictions on the strain energy function to model the distortion in a hydrostatic state of stress. The objective of this research note is to modify the definitions of the remaining three invariants. These new invariants have clear physical interpretations that can be measured in experiments.

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References

  1. deBotton, G., Hariton, I., Socolsky, E.A.: Neo-Hookean fiber-reinforced composites in finite elasticity. J. Mech. Phys. Solids 54, 533–559 (2006)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  2. Criscione, J.C., Hunter, W.C.: Kinematics and elasticity framework for materials with two fiber families. Continuum Mech. Thermodyn. 15, 613–628 (2003)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  3. Criscione, J.C., Humphrey, J.D., Douglas, A.S., Hunter, W.C.: An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelasticity. J. Mech. Phys. Solids 48, 2445–2465 (2000)

    Article  MATH  ADS  Google Scholar 

  4. Criscione, J.C., Douglas, A.S., Hunter, W.C.: Physically based strain invariant set for materials exhibiting transversely isotropic behavior. J. Mech. Phys. Solids 49, 871–897 (2001)

    Article  MATH  ADS  Google Scholar 

  5. Ericksen, J.L., Rivlin, R.S.: Large elastic deformations of homogeneous anisotropic materials. Arch. Ration. Mech. Anal. 3, 281–301 (1954)

    MathSciNet  MATH  Google Scholar 

  6. Flory, P.: Thermodynamic relations for high elastic materials. Trans. Faraday Soc. 57, 829–838 (1961)

    Article  MathSciNet  Google Scholar 

  7. Rubin, M.B., Jabareen, M.: Physically based invariants for nonlinear elastic orthotropic materials. J. Elast. 90, 1–18 (2008)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Technion—Israel Institute of Technology, 32000, Haifa, Israel

    M. B. Rubin

  2. Faculty of Civil and Environmental Engineering, Technion—Israel Institute of Technology, 32000, Haifa, Israel

    M. Jabareen

Authors
  1. M. B. Rubin
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  2. M. Jabareen
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Correspondence to M. B. Rubin.

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Rubin, M.B., Jabareen, M. Further Developments of Physically Based Invariants for Nonlinear Elastic Orthotropic Solids. J Elast 103, 289–294 (2011). https://doi.org/10.1007/s10659-010-9276-3

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  • DOI: https://doi.org/10.1007/s10659-010-9276-3

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