On a model for anisotropic creep of materials



We apply the concepts of proper moduli and states, revealing the structure of the generalized Hooke’s law, to a model of anisotropic steady-state creep of materials. The steady-state creep equations for incompressible materials are expressed in invariant form. The matrix of anisotropy coefficients of these materials reduces to block form with the nine independent components. We consider the special case of an orthotropic incompressible material for which the matrix of anisotropy coefficients corresponds to a nonor.


steady-state creep anisotropy coefficients proper anisotropy coefficients and proper states transversal isotropy orthotropy incompressibility 


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  1. 1.
    B. D. Annin and N. I. Ostrosablin, “Anisotropy of Elasticic Properties ofMaterials,” Prikl. Mekh. Tekhn. Fiz. 49(6), 131–151 (2008) [J. Appl. Mech. Tech. Phys. 49 (6), 998–1014 (2008)].MathSciNetGoogle Scholar
  2. 2.
    N. I. Ostrosablin, “Limit Criteria and a Model of Inelastic Deformation of Anisotropic Media,” Prikl. Mekh. Tekhn. Fiz. 52(6), 165–176 (2011) [J. Appl. Mech. Tech. Phys. 52 (6), 986–996 (2011)].MathSciNetGoogle Scholar
  3. 3.
    B. D. Annin and N. I. Ostrosablin, “Anisotropy Tensor of the Potencial Model of Steady Creep,” Prikl. Mekh. Tekhn. Fiz. 55(1), 5–12 (2014) [J. Appl. Mech. Tech. Phys. 55 (1), 1–7 (2014).Google Scholar
  4. 4.
    N. I. Ostrosablin, “About Invariants of the Rank 4 Tensor of Elasticity Moduli,” Sibirsk. Zh. Industr. Mat. 1 (1), 155–163 (1998).Google Scholar
  5. 5.
    Yu. N. Robotnov, Creep of Structural Components (Nauka, Moscow, 1966) [in Russian].Google Scholar
  6. 6.
    O. V. Sosnin, “On Anisotropic Creep of Materials,” Zh. Prikl. Mekh. Tekhn. Fiz. No. 6, 99–104 (1965).Google Scholar
  7. 7.
    A. C. Pipkin, “Constraints in Linearly ElasticMaterials,” J. Elast. 6(2), 179–193 (1976).CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    P. Podio-Guidugli and M. Vianello, “Internal Constraints and Linear Constitutive Relations for Eransversely Isotropic Materials,” Rend. Lincei. Mat. Appl. Ser. 9, 2(3), 241–248 (1991).MATHMathSciNetGoogle Scholar
  9. 9.
    C. A. Felippa and E. Oñate, “Stress, Strain and Energy Splittings for Anisotropic Elastic Solids under Volumetric Constraints,” Comput. Struct. 81(13), 1343–1357 (2003).CrossRefGoogle Scholar
  10. 10.
    C. A. Felippa and E. Oñate, “Volumetric Constraint Models for Anisotropic Elastic Solids,” Trans. ASME. J. Appl. Mech. 71(5), 731–734 (2004).CrossRefMATHGoogle Scholar
  11. 11.
    K. Kowalczyk-Gajewska and J. Ostrowska-Maciejewska, “The Influence of Internal Restrictions on the Elastic Properties of AnisotropicMaterials,” Arch. Mech. 56(3), 205–232 (2004).MATHMathSciNetGoogle Scholar
  12. 12.
    F. R. Gantmakher, Matrix Theory (Gostekhizdat, Moscow, 1954) [in Russian].Google Scholar
  13. 13.
    N. I. Ostrosablin, “Linear Invariant Irreducible Decomposition of the Rank 4 Tensor of Elasticity Moduli,” Dinamika Sploshn. Sredy No. 120, 149–160 (2002).Google Scholar
  14. 14.
    N. I. Ostrosablin, “Canonical Moduli and General Solution of Equations of a Two-Dimensional Static Problem of Anisotropic Elasticity,” Prikl. Mekh. Tekhn. Fiz. 51(3), 94–106 (2010) [J. Appl. Mech. Tech. Phys. 51 (3), 377–388 (2010)].MathSciNetGoogle Scholar

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© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Lavrent’ev Institute of HydrodynamicsNovosibirskRussia

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