Equivalent inhomogeneity method for evaluating the effective elastic properties of unidirectional multi-phase composites with surface/interface effects

Sofia G. Mogilevskaya, Steven L. Crouch, Henryk K. Stolarski, Adrien Benusiglio

Research output: Contribution to journalArticlepeer-review

67 Scopus citations

Abstract

A new technique is presented for evaluating the effective properties of linearly elastic, multi-phase unidirectional composites. Various effects on the fiber/matrix interfaces (perfect bond, homogeneously imperfect interfaces, uniform interphase layers) are allowed. The analysis of nano-composite materials based on the Gurtin and Murdoch model of material surface is also included. The basic idea of the approach is to construct a circular inhomogeneity in an infinite plane whose effects on the displacements and stresses at distant points are the same as those of a finite cluster of inhomogeneities (fibers of circular cross-section) arranged in a pattern representative of the composite material in question. The elastic properties of the equivalent inhomogeneity then define the effective elastic properties of the material. The volume ratio of the composite material is found after the size of the equivalent circular inhomogeneity is defined in the course of the solution procedure. This procedure is based on a semi-analytical solution of a problem of an infinite plane containing a cluster of non-overlapping circular inhomogeneities subjected to loading at infinity. The method works equally well for periodic and random composites and - importantly - eliminates the necessity for averaging either stresses or strains. New results for nano-composite materials are presented.

Original languageEnglish (US)
Pages (from-to)407-418
Number of pages12
JournalInternational Journal of Solids and Structures
Volume47
Issue number3-4
DOIs
StatePublished - Feb 2010

Keywords

  • Effective properties
  • Surface effects
  • Unidirectional multi-phase composites

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