Skip to main content
SpringerLink
Log in

Using a Smoothing Averaging Operator to Evaluate Macroscopic Parameters in Structurally Inhomogeneous Materials

  • Published:
Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

A smoothing averaging operator is used in passing from structural to macroscopic modeling of the stress–strained state of an article from a composite material taking into account finite strains. A model is constructed using an integral operator, in which the macroscopic laws of conservation of energy and mass and the equation of motion have the ordinary form used to describe processes in homogeneous materials. As an example, macroscopic parameters are evaluated in a system consisting of an ensemble of inclusions in an infinite matrix.

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

  1. R.I. Nigmatulin, Dynamics of Multiphase Media, Part 1, Hemisphere, New York (1991).

    Google Scholar 

  2. L.S. Bennethum and J.H. Cushman, “Multiscale, hybrid mixture theory for swelling systems.1.Balance laws," Int.J.Eng.Sci., 34, 125–145 (1996).

    Google Scholar 

  3. L.S. Bennethum, M.A. Murad, and J.H. Cushman, “Macroscale thermodynamics and the chemical potential for swelling porous media," Transp.Porous Media, 39, 187–225 (2000).

    Google Scholar 

  4. W.G. Gray and S.M. Hassanizadeh, “Macroscale continuum mechanics for multiphase porous-media ow including phases, interfaces, common lines and common points," Adv.Water Res., 21, 261–281 (1998).

    Google Scholar 

  5. C.K. Chui, An Introduction to Wavelets, Academic Press (2001).

  6. I.M. Dremin, O.V. Ivanov, and V.A. Nechitailo, “Wavelets and their use,"Usp.Fiz.Nauk., 171, No.5, 465–501 (2001).

    Google Scholar 

  7. J.-S. Chen, C. Pan, C.-T. Wu, and W.K. Liu, “Reproducing kernel particle methods for large deformation analysis of nonlinear structures," Comput.Meth.Appl.Mech.Eng., 139, 195–227 (1996).

    Google Scholar 

  8. J.-S. Chen, C. Pan, and C.-T. Wu, “Large deformation analysis of rubber based on a reproducing kernel particle method," Comput.Mech., 19, 211–227 (1997).

    Google Scholar 

  9. E. Hardee, K.-H. Chang, I. Grindeanu, et al. “A structural nonlinear analysis workspace (SNAW) based on meshless methods," Adv.Eng.Software, 30, 153–175 (1999).

    Google Scholar 

  10. W.K. Liu, S. Hao, T. Belytschko, et al., “Multiple scale meshfree methods for damage fracture and localization," Comput.Mater.Sci., 16, 197–205 (1999).

    Google Scholar 

  11. A.E. Green, “On Cauchy's equations of motion," Z.Angew.Math.Phys., 15, 290–292 (1964).

    Google Scholar 

  12. A.L. Svistkov, O.K. Garshin, S.E. Evlampieva, and S.N. L.ebedev, “Iterative computational method for calculating stress strained states in ensembles of inclusions,” in: Mekh.Komposit.Mat.Strukt., 5, No.2, 17–28 (1999).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mechanics of Continua, Ural Division, Russiand Academy of Sciences, Perm', 614013

    A. L. Svistkov & S. E. Evlampieva

Authors
  1. A. L. Svistkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. E. Evlampieva
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Svistkov, A.L., Evlampieva, S.E. Using a Smoothing Averaging Operator to Evaluate Macroscopic Parameters in Structurally Inhomogeneous Materials. Journal of Applied Mechanics and Technical Physics 44, 727–735 (2003). https://doi.org/10.1023/A:1025520823726

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1025520823726

Search

Navigation