A micro-mechanics perspective to the invariant-based approach to stiffness

A. Arteiro, L. F. Pereira, M. A. Bessa, C. Furtado, P. P. Camanho

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)


To simplify the analysis and characterisation of composite laminates, an invariant-based approach to stiffness that takes the trace of the plane stress stiffness matrix as a material property was recently proposed. In the present work, a study based on micro-mechanical models brings new insight to this invariant-based approach. The Rule of Mixtures and the Halpin-Tsai models are used to establish the relations between the fibre volume fraction, the fibre/matrix stiffness ratios, and the trace-normalised engineering constants of unidirectional laminae and multidirectional laminates. For sufficiently high longitudinal fibre/matrix stiffness ratios and for fibre volume fractions between 50% and 70%, typical of advanced CFRPs, the variation of the trace-normalised longitudinal Young's modulus is within 6% for unidirectional laminae and within 1% for multidirectional laminates, supporting the definition of an invariant-based approach to stiffness based on a Master Ply concept and laminate factors derived thereof, defining clearly a domain of applicability of the invariant theory and confirming the empirical observations of the past.

Original languageEnglish
Pages (from-to)72-80
JournalComposites Science and Technology
Publication statusPublished - 2019


  • A. Laminate
  • A. Polymer-matrix composites (PMCs)
  • C. Elastic properties
  • C. Laminate theory
  • C. Micro-mechanics

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