Skip to main content
Log in

Quadrilateral isoparametric finite elements for plane elastic Cosserat bodies

  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

4-node, 8-node and 8(4)-node quadrilateral plane isoparametric elements are used for the solution of boundary value problems in linear isotropic Cosserat elasticity. The patch test is applied to validate the finite elements. Engineering problems of stress concentration around a circular hole in plane strain condition and mechanical behaviors of heterogeneous materials with rigid inclusions and pores are computed to test the accuracy and capability of these three types of finite elements.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Lake, R.: Materials with structural hierarchy. Nature, 361(11), 511–515 (1993)

    Google Scholar 

  2. Vardoulakis, I., Graf, B.: Calibration of constitutive models for granular materials using data from biaxial experiments. Geotechnique, 35(3), 299–317 (1985)

    Google Scholar 

  3. de Borst, R.: Simulation of strain localization: a reappraisal of the Cosserat continuum. Eng. Comput., 8, 317–332 (1991)

    Google Scholar 

  4. Cosserat, E., Cosserat, F.: Theorie des Corps Deformables. Hermann Paris 1909

  5. Mindlin, R.D.: Stress functions for a Cosserat continuum. Int. J. Solids Struct., 1, 265–271 (1965)

    Google Scholar 

  6. Aifantis, E.C.: On the microstructural original of certain inelastic models. Journal of Engineering Materials and Technology, 106, 326–334 (1984)

    Google Scholar 

  7. Zhang, H.W., Zhang, X.W.: A combined parametric quadratic programming and precise integration method based dynamic analysis of elastic-plastic hardening/softening problems. Acta Mechanica Sinica, 18(6), 638–648 (2002)

    Google Scholar 

  8. Huang, W., Bauer, E.: Numerical investigations of shear localization in a micro-polar hypoplastic material. Int. J. Numer. Anal. Meth. Geomech., 27, 325–352 (2003)

    Google Scholar 

  9. Adhikary, D.P., Dyskin, A.V.: A Cosserat continuum model for layered materials. Comput. & Geo., 20(1), 15–45 (1997)

  10. Mori, K., Shiomi, M., Osakada, K.: Inclusion of microscopic rotation of powder particles during compaction in finite element method using Cosserat continuum theory. Int. J. Numer. Meth. Eng., 42, 847–856 (1998)

    Google Scholar 

  11. Providas, E., Kattis, M.A.: Finite element method in plane Cosserat elasticity. Comput. & Struct., 80, 2059–2069 (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hongwu Zhang.

Additional information

The project supported by the National Natural Science Foundation of China (10225212, 50178016, 10421002) and the Program for Changjiang Scholars and Innovative Research Team in University of China The English text was polished by Keren Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, H., Wang, H. & Liu, G. Quadrilateral isoparametric finite elements for plane elastic Cosserat bodies. ACTA MECH SINICA 21, 388–394 (2005). https://doi.org/10.1007/s10409-005-0041-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-005-0041-y

Keywords

Navigation