Summary
In finite homogeneous deformation processes, the principal triad generally rotates with respect to a material element during the deformation. The material derivative of the logarithmic strain is no longer simply related to the rate of deformation tensor, and this is exemplified herein. A mathematical procedure is provided for the analysis and the derivations vations are formulated using the co-rotational rate technique in hope, that this technique may be extended to other applications in future modeling. It will be apparent in the article that the co-rotational rate formulation provides a convenient mathematical procedure for handling problems in finite deformation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Love, A. E. H.: A treatise on the mathematical theory of elasticity. New York: Dover Pub.. 1944.
Murnagham, F. D.: Finite deformations of an elastic solid. Amer. J. Math.59, 235 to 260 (1937).
Truesdell, C. A., Toupin, R. A.: Encyclopedia of physics,3 (Flügge, A., ed.) Berlin: Springer 1954.
Green, A. E., Zerna, W.: Theoretical elasticity. O. U. P. 1954.
Hsu, T. C.: A study of large deformations by matrix algebra. J. Strain analysis1, 313–321 (1966).
Choi, C. H., Hsu, T. C.: Mohr circle for large and small strains in two-dimensional deformations. J. Strain Analysis6, 62–69 (1971).
Parks, V. J., Durelli, A. J.: On the definitions of strain and their use in large-strain analysis. Exp. Mechs.7, 279–280 (1976).
Walak, J., Parks, V. J.: Evaluation of large strains in industrial applications. J. Testing and Evaluation2, 533–540 (1974).
Bredendick, F.: Visioplastische Deformations- und Spannungsermittlung. Die Technik4, 247–251 (1969).
Regazzoni, G., LeDouaron, A., Montheillet, F.: A new method for the analysis of a non-stationary two-dimensional flow and its application to the closed-die forging of a Rib. J. Mech. Working Technology5, 281–296 (1981).
Sowerby, R., Duncan, J.L., Sklad, M. P.: Engineering strains in large pressings. Sheet Metal Industries, pp. 290–293 (May 1983).
Sowerby, R., Chakravarti, P. C.: The determination of the equivalent strain in finite homogeneous deformation processes. M. R. & D. Report No.179, McMaster University, Hamilton, Ontario, Canada, 1983.
Chu, E., Sowerby, R., Soldaat, R., Duncan, J. L.: Strain measurement over large area of an industrial stamping. Proc. 13th Biennial Congress of IDDRG, February 1984.
Chu, E.: The determination of strain in finite homogeneous deformation processes. Proc. NAMRC-XIII, pp. 170–175 (May 1985).
Hill, R.: On constitutive inequalities for simple materials—I. J. Mechs. Phys. Solids16, 229 (1968).
Hill, R.: Constitutive inequalities for isotropic elastic solids under finite strain. Proc. Roy. Soc.A 314, 457 (1970).
Stören, S., Rice, J. R.: Localized necking in thin sheets. J. Mechs. Phys. Solids23, 421 (1975).
Dienes, J. K.: On the analysis of rotation and stress rate in deforming bodies. Acta Mechanica32, 217–232 (1979).
Hill, R.: Aspects of invariance in solid mechanics, in: Advances in Applied Mechanics18, 1 (1978).
Sowerby, R., Chu, E.: Rotations, stress rates and strain measures in homogeneous deformation processes. Int. J. Solids and struct.20, 1037 (1984).
Hutchinson, J., Neale, K.: Finite strainJ 2 deformation theory. Technical Report, Division of Applied Sciences, Harvard 1980.
Gurtin, M. E., Spear, K.: On the relationship between the logarithmic strain rate and the stretching tensor. Int. J. Solids and Struct.19, 437 (1983).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chu, E. Aspects of strain measures and strain rates. Acta Mechanica 59, 103–112 (1986). https://doi.org/10.1007/BF01177063
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01177063