Marina Trajković-Milenković, Otto T. Bruhns

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In elastoplasticity formulation constitutive relations are usually given in rate form, i.e. they represent relations between stress rate and strain rate. The adopted constitutive laws have to stay independent in relation to the change of frame of reference, i.e. to stay objective. While the objectivity requirement in a material description is automatically satisfied, in an Eulerian description, especially in the case of large deformations, the objectivity requirement can be violated even for objective quantities. Thus, instead of a material time derivative in the Eulerian description objective time derivatives have to be implemented. In this work the importance of the objective rate implementation in the constitutive relations of finite elastoplasticity is clarified. Likewise, it shows the overview of the most frequently used objective rates nowadays, their advantages and shortcomings, as well as the distinctive features of the recently introduced logarithmic rate.


finite deformations, objective rates, logarithmic rate, elastoplasticity, finite deformation decomposition

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Malvern, L. E., 1969, Introduction to the mechanics of a continuous medium, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 713 p.

Mićunović, M., 1990, Primenjena mehanika kontinuuma, Naučna knjiga, Beograd, 332 p.

Ogden, R. W., 1984, Non-linear elastic deformations, Dover Publications, Inc. Mineola, New York, 532 p.

Xiao, H., Bruhns, O.T. & Meyers, A., 1997, Hypo-elasticity model based upon the logarithmic stress rate, in: J. Elasticity, 47, pp. 51-68.

Xiao, H., Bruhns, O.T. & Meyers, A., 1998a, On objective corotational rates and their defining spin tensors, in: Int. J. Solids Structures, 35(30), pp. 4001-4014.

Xiao, H., Bruhns, O.T. & Meyers, A., 1998b, Strain rates and material spins, in: J. Elasticity, 52, pp. 1-41.

Bruhns, O.T., Meyers, A. & Xiao, H., 2004, On non-corotational rates of Oldroyd’s type and relevant issues in rate constitutive formulations, in: Proc. Roy. Soc. A, 460, pp. 909-928.

Xiao, H., Bruhns, O.T. & Meyers, A., 2005, Objective stress rates, path-dependence properties and non-integrability problems, in: Acta Mech., 176, pp. 135-151.

Lehmann, T., 1972, Anisotrope plastische Formänderungen, in: Romanian J. Techn. Sci. Appl. Mechanics, 17, pp. 1077-1086.

Trajković-Milenković, M., 2016, Numerical implementation of an Eulerian description of finite elastoplasticity, PhD Thesis, Ruhr University Bochum, Germany, 125 p.

Dienes, J. K., 1979, On the analysis of rotation and stress rate in deforming, in: Acta Mech., 32, pp. 217-232.

Simo, J. C. & Pister, K. S., 1984, Remarks on rate constitutive equations for finite deformation problems: computational implications, in: Comput. Meths. Appl. Mech. Engrg., 46, pp. 201-215.

Khan, A. S. & Huang, S., 1995, Continuum theory of plasticity, John Wiley& Sons, Inc., New York, 421p.

Bažant, Z. & Vorel, J., 2014, Energy-Conservation Error Due to Use of Green-Naghdi Objective Stress Rate in Commercial Finite-Element Codes and Its Compensation, in: ASME J. Appl. Mech., 81(2).

Xiao, H., Bruhns, O. T. & Meyers, A., 2000, The choice of objective rates in finite elastoplasticity: general results on the uniqueness of the logarithmic rate, in: P. Roy. Soc. A, 456, pp. 1865-1882.

Naghdi, P. M., 1990, A critical review of the state of finite elasoplasticity, in: Z. Angew. Math. Phys., 41, pp. 315-394.

Xiao, H., Bruhns, O. T. & Meyers, A., 2006, Elastoplasticity beyond small deformations, in: Acta Mech., 182, pp. 31-111.

Simo, J. C. & Hughes, T. J. R., 1998, Computational inelasticity, Springer-Verlag New York, Inc., 392 p.

Bruhns, O. T., Xiao, H. & Meyers, A., 1999, Self-consistent Eulerian rate type elastoplasticity models based upon the logarithmic stress rate, in: Int. J. Plasticity, 15, pp. 479-520.

Green, A. E. & Naghdi, P. M., 1965, A general theory of an elasto-plastic continuum, in: Arch. Ration. Mech. An., 18, pp. 251-281.

Truesdell, C., Noll, W. & Antman, S., 2004, The Non-Linear Field Theories of Mechanics, Volume 3 of The non-linear field theories of mechanics, Springer.

Bernstein, B., 1960, Hypoelasticity and elasticity, in Arch. Rat. Mech. Anal., 6, pp. 90-104.

Zaremba, S., 1903, Sur une forme perfectionée de la théorie de la relaxation, in Bull. Intern. Acad. Sci. Cracovie, pp. 594-614.


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