Remodelling in statistically oriented fibre-reinforced materials and biological tissues

Alfio Grillo*, Gabriel Wittum, Aleksandar Tomic, Salvatore Federico

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


We present a mathematical model of structural reorganisation in a fibre-reinforced composite material in which the fibres are oriented statistically, i.e. obey a probability distribution of orientation. Such a composite material exemplifies a biological tissue (e.g. articular cartilage or a blood vessel) whose soft matrix is reinforced by collagen fibres. The structural reorganisation of the composite takes place as fibres reorient, in response to mechanical stimuli, in order to optimise the stress distribution in the tissue. Our mathematical model is based on the Principle of Virtual Powers and the study of dissipation. Besides incompressibility, our main hypothesis is that the composite is characterised by a probability density distribution that measures the probability of finding a family of fibres aligned along a given direction at a fixed material point. Under this assumption, we describe the reorientation of fibres as the evolution of the most probable direction along which the fibres are aligned. To test our theory, we compare our simulations of a benchmark problem with selected results taken from the literature.

Original languageEnglish (US)
Pages (from-to)1107-1129
Number of pages23
JournalMathematics and Mechanics of Solids
Issue number9
StatePublished - Oct 1 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2013 SAGE Publications.


  • Remodelling
  • dissipation
  • statistical composites
  • two-layer dynamics

ASJC Scopus subject areas

  • General Mathematics
  • General Materials Science
  • Mechanics of Materials


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