Skip to main content
SpringerLink
Log in

A constitutive formulation for anisotropic materials suitable for wave propagation computer programs—II

  • Originals
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

The constitutive relationships for an anisotropic material are established for shock wave propagation and nonlinear, large deformation computer programs, commonly referred to as hydrocodes. Stresses are formulated in terms of strains; the procedure for separating material compressibility effects (equation of state) from strength effects is formulated which permits the consistent calculation of stresses in the elastic regime, and allows the mean pressure to be defined in accordance with their scalar interpretations. Futher, this procedure permits the computation of inelastic response by scaling of deviatoric stresses, so the equivalent stress resides on a yield or failure surface, without changing the pressure. The procedure for computing the equivalent plastic strain and non-radial return to the yield surface, which results from a calculated overstress, is developed. Also, the transformation matrices for large deformation (rotation), necessary for transformation between material and geometric coordinates, are presented.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anderson, C. E.Jr. 1987: An overview of the theory of hydrocodes. Int. J. Impact Engng. 5(1–4): 33–60

    Google Scholar 

  • Anderson, C. E.Jr.; O'Donoghue, P. E.; Skerhut, D. (1990): A mixture theory approach for the shock response of composite materials. J. Composite Materials 24(11): 1159–1178

    Google Scholar 

  • Boresi, A. P.; Sidebottom, O. M.; Seely, F. B.; Smith, J. O. 1978: Advanced mechanics of materials, 3rd Edition, John Wiley and Sons

  • Dienes, J. K. 1979: On rotation and stress rate in deforming bodies. Acta Mechanica 32: 217–232

    Google Scholar 

  • Flanagan, D. P.; Taylor, L. M. 1987: An accurate numerical algorithm for stress integration with finite rotations. Comp. Meth. in Appl. Mech. and Engng. 62: 305–320

    Google Scholar 

  • Hill, R. 1948: A theory of yielding and plastic flow of anisotropic metals. Proc. Roy. Soc. Lond., Series A., 193: 281–297

    Google Scholar 

  • Hughes, T. J. R.; Winget, J. 1980: Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis. Int. J. Numer. Meths. Engng. 15(12): 1862–1867

    Google Scholar 

  • Johnson, G. R. 1981: Recent developments and analyses associated with the EPIC-2 and EPIC-3 codes. In: Wang, S. S.; Renton, W. J. (eds.): Advances in Aerospace Structures and Materials, ASME, 1981 AD-01, 141–147

  • Johnson, G. R.; Colby, D. D.; Vavrick, D. J. 1979: Three-dimensional computer code for dynamic response of solids to intense impulsive loads. Int. J. Num. Meth. In Engng. 14: 1865–1871

    Google Scholar 

  • Johnson, G. R.; Stryk, R. A. 1992: User instructions for the 1992 Version of the EPIC research code. Alliant Techsystems, Inc., Brooklyn Park, MN, December

    Google Scholar 

  • Jones, R. M. 1975: Mechanics of composite materials. Hemisphere Publishing Corporation, NY

    Google Scholar 

  • Malvern, L. E. 1969: Introduction to the mechanics of a continuous media. Prentice-Hall, Inc., Englewood Cliffs, NJ

    Google Scholar 

  • O'Donoghue, P. E.; Anderson, C. E.Jr.; Friesenhahn, G. J.; Parr, C. H. 1992: A constitutive formulation for anisotropic materials suitable for wave propagation computer programs. J. Composite Materials 26(13): 1860–1884

    Google Scholar 

  • Tsai, S. W.; Hahn, H. T. 1980: Introduction to composite materials. Technomic Publishing Co., Lancaster, PA

    Google Scholar 

  • Tuma, J. J. 1979: Engineering mathematics handbook. 2nd Edition, McGraw-Hill Book, Co.

  • Wilkins, M. L. 1964: Calculations of elastic-plastic flow. In: Adler, B.; Fernback, S.; Rosenberg, M. (eds.): Methods of Computational Physics, vol. 3, Academic Press, NY

    Google Scholar 

  • Wilkins, M. L. 1969: Calculation of elastic plastic flow. UCRL-7322, Rev. 1, Lawrence Livermore National Laboratory, Livermore, CA

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Structural Systems and Technology Division, Southwest Research Institute, 78228, San Antonio, TX, USA

    Ch. E. Anderson Jr.

  2. Alliant Techsystems, Inc., 55343, Hopkins, MN, USA

    P. A. Cox & G. R. Johnson

  3. Los Alamos National Laboratory, 87545, Los Alamos, NM, USA

    P. J. Maudlin

Authors
  1. Ch. E. Anderson Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. A. Cox
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. R. Johnson
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. J. Maudlin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by S. N. Atluri, 10 June 1994

Rights and permissions

Reprints and permissions

About this article

Cite this article

Anderson, C.E., Cox, P.A., Johnson, G.R. et al. A constitutive formulation for anisotropic materials suitable for wave propagation computer programs—II. Computational Mechanics 15, 201–223 (1994). https://doi.org/10.1007/BF00375030

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00375030

Keywords

Search

Navigation