Statistical shear lag model-Unraveling the size effect in hierarchical composites

Xiaoding Wei, Tobin Filleter, Horacio D. Espinosa*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


Numerous experimental and computational studies have established that the hierarchical structures encountered in natural materials, such as the brick-and-mortar structure observed in sea shells, are essential for achieving defect tolerance. Due to this hierarchy, the mechanical properties of natural materials have a different size dependence compared to that of typical engineered materials. This study aimed to explore size effects on the strength of bio-inspired staggered hierarchical composites and to define the influence of the geometry of constituents in their outstanding defect tolerance capability. A statistical shear lag model is derived by extending the classical shear lag model to account for the statistics of the constituents' strength. A general solution emerges from rigorous mathematical derivations, unifying the various empirical formulations for the fundamental link length used in previous statistical models. The model shows that the staggered arrangement of constituents grants composites a unique size effect on mechanical strength in contrast to homogenous continuous materials. The model is applied to hierarchical yarns consisting of double-walled carbon nanotube bundles to assess its predictive capabilities for novel synthetic materials. Interestingly, the model predicts that yarn gauge length does not significantly influence the yarn strength, in close agreement with experimental observations.

Original languageEnglish (US)
Pages (from-to)206-212
Number of pages7
JournalActa Biomaterialia
StatePublished - May 1 2015


  • Defect tolerance
  • Hierarchical composites
  • Load transfer
  • Shear lag
  • Size effect

ASJC Scopus subject areas

  • Biotechnology
  • Biomaterials
  • Biochemistry
  • Biomedical Engineering
  • Molecular Biology

Fingerprint Dive into the research topics of 'Statistical shear lag model-Unraveling the size effect in hierarchical composites'. Together they form a unique fingerprint.

Cite this