On the applicability of generalized strain measures in large strain plasticity

  • Mikhail Itskov
Conference paper

Abstract

In the present paper two thermodynamically consistent large strain plasticity models are examined and compared in finite simple shear. The first model (A) is based on the multiplicative decomposition of the deformation gradient, while the second one (B) on the additive decomposition of generalized strain measures. Both models are applied to a rigid-plastic material described by a von Mises-type yield criterion. Since both models include neither a hardening nor a softening law, a constant shear stress response, even for large amounts of shear, is expected. Indeed, model A exhibits true constant shear stress behavior independent of the elastic material law. This is not, however, the case for model B so that its applicability under finite shear deformations may be questioned.

Keywords

Simple Shear Deformation Gradient Plastic Strain Rate Additive Decomposition Large Strain Plasticity 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Mandel, J. (1972): Plasticité classique et viscoplasticité. (CISM course no. 97). Springer, ViennaMATHGoogle Scholar
  2. [2]
    Aravas, N. (1992): Finite elastoplastic transformations of transversely isotropic metals. Internat. J. Solids Structures 29, 2137–2157MATHCrossRefGoogle Scholar
  3. [3]
    Cleja-Ţigoiu, S. (2000): Nonlinear elasto-plastic deformations of transversely isotropic material and plastic spin. Internat. J. Engrg. Sci. 38, 737–763MathSciNetCrossRefGoogle Scholar
  4. [4]
    Häusler, O., Schick, D., Tsakmakis, Ch. (2004): Description of plastic anisotropy effects at large deformations. II. The case of transverse isotropy. Internat. J. Plasticity 20, 199–223MATHCrossRefGoogle Scholar
  5. [5]
    Seth, B.R. (1964): Generalized strain measure with applications to physical problems. In: Reiner, M., Abir, D. (eds.): Second-order effects in elasticity, plasticity and fluid dynamics. Jerusalem Academic Press, Jerusalem, pp. 162–172Google Scholar
  6. [6]
    Hill, R. (1968): On constitutive inequalities for simple materials. I. J. Mech. Phys. Solids 16, 229–242MATHCrossRefGoogle Scholar
  7. [7]
    Ogden, R.W. (1984): Nonlinear elastic deformations. Ellis Horwood, ChichesterMATHGoogle Scholar
  8. [8]
    Papadopoulos, P., Lu, J. (1998): A general framework for the numerical solution of problems in finite elasto-plasticity. Comput. Methods Appl. Mech. Engrg. 159, 1–18MATHCrossRefGoogle Scholar
  9. [9]
    Hill, R. (1950): The mathematical theory of plasticity. Clarendon Press, OxfordMATHGoogle Scholar
  10. [10]
    Papadopoulos, P., Lu, J. (2001): On the formulation and numerical solution of problems in anisotropic finite plasticity. Comput. Methods Appl. Mech. Engrg. 190, 4889–4910MATHCrossRefGoogle Scholar
  11. [11]
    Miehe, C., Apel, N., Lambrecht, M. (2002): Anisotropic additive plasticity in the logarithmic strain space: modular kinematic formulation and implementation based on incremental minimization principles for standard materials. Comput. Methods Appl. Mech. Engrg. 191, 5383–5425MATHMathSciNetCrossRefGoogle Scholar
  12. [12]
    Schröder, J., Gruttmann, F., Löblein, J. (2002): A simple orthotropic finite elastoplasticity model based on generalized stress-strain measures. Comput. Mech. 30, 48–64MATHCrossRefGoogle Scholar
  13. [13]
    Itskov, M. (2002): The derivative with respect to a tensor: some theoretical aspects and applications. ZAMM Z. Angew. Math. Mech. 82, 535–544MATHMathSciNetCrossRefGoogle Scholar
  14. [14]
    Truesdell, C., Noll, W. (1965): The nonlinear field theories of mechanics. In: Flügge, S. (ed.): Handbuch der Physik. Band III/3. Springer, Berlin, pp. 1–602Google Scholar
  15. [15]
    Lee, E.H. (1969): Elastic-plastic deformation at finite strains. J. Appl. Mech. 36, 1–6MATHGoogle Scholar
  16. [16]
    Lubliner, J. (1990): Plasticity theory. Macmillan, New YorkMATHGoogle Scholar
  17. [17]
    Brousse, P. (1988): Optimization in mechanics: problems and methods. North-Holland, AmsterdamGoogle Scholar
  18. [18]
    Carlson, D.E., Hoger, A. (1986): The derivative of a tensor-valued function of a tensor. Quart. Appl. Math. 44, 409–423MATHMathSciNetGoogle Scholar
  19. [19]
    Itskov, M., Aksel, N. (2002): A closed-form representation for the derivative of nonsymmetric tensor power series. Internat. J. Solids Structures 39, 5963–5978MATHMathSciNetCrossRefGoogle Scholar
  20. [20]
    Itskov, M. (2003): Application of the Dunford-Taylor integral to isotropic tensor functions and their derivatives. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 459, 1449–1457MATHMathSciNetCrossRefGoogle Scholar
  21. [21]
    Itskov, M. (2003): Computation of the exponential and other isotropic tensor functions and their derivatives. Comput. Meth. Appl. Mech. Engrg. 192, 3985–3999MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2005

Authors and Affiliations

  • Mikhail Itskov
    • 1
  1. 1.Dept. of Applied Mechanics and Fluid Dynamics, Lehrstuhl für Technische Mechanik und StrömungsmechanikUniversity of BayreuthBayreuthGermany

Personalised recommendations