Scale effects in materials with random distributions of needles and cracks

Research output: Contribution to journalArticlepeer-review

Abstract

According to a classical prescription of micromechanics, a representative volume element (RVE) is well defined when the response under uniform displacement (Dirichlet) boundary condition becomes the same as that under uniform stress (Neumann) boundary condition. We study the convergence of both responses in anti-plane elasticity of sheets with non-periodic, random distributions of thin needle-shaped inclusions. By lowering the stiffness of inclusions and increasing their aspect ratio (up to 100), we approach the situation of cracks embedded in a matrix. We show that, with the needles' stiffness decreasing and their slenderness growing, the RVE tends to be very large. The statistics of the first and second invariants of both response tensors are very well modeled by a Beta probability distribution. For moderate aspect ratio needles, the coefficient of variation of the second invariant is found to stay at about 0.5 irrespective of the window size, the mismatch in stiffness between the inclusions and the matrix, and the needle aspect ratio.

Original languageEnglish (US)
Pages (from-to)883-893
Number of pages11
JournalMechanics of Materials
Volume31
Issue number12
DOIs
StatePublished - Dec 1 1999
Externally publishedYes

ASJC Scopus subject areas

  • Materials Science(all)
  • Instrumentation
  • Mechanics of Materials

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