Invariant based approaches in the design of composite laminates

S.L.J. Millen, Brian Falzon, M. Ali Aravand*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
75 Downloads (Pure)


Invariant based approaches have been proposed to simplify the design and analysis of composite materials, in particular, for generating design allowables. Of these invariants, Trace, more recently referred to as Tsai’s Modulus, a material property derived from the plane stress stiffness matrix, can be used to help with preliminary design. However, in literature this has mainly focussed on unidirectional composites. The present work extends the application of invariants to woven and hybrid composites, i.e. the latter made with both unidirectional and woven laminae, and provides appropriate validation for the use of invariants in design. A novel approach to implement Tsai’s Modulus and determine the three-dimensional stiffness matrix of a woven specimen is proposed. Omni failure envelopes have been proposed in literature and these have been extended to accommodate hybrid specimens with both unidirectional and woven laminae. This work shows that Tsai’s Modulus and invariants can be used as an initial design tool in order to establish the likely properties of a given layup and material combination for use in preliminary design. Property predictions at the laminate level, Ex, Ey, νxy and Gxy, were within ±10% of experimental values for highly complex laminate stacking sequences and material combinations.
Original languageEnglish
Article number108526
JournalComposites Science and Technology
Early online date28 Oct 2020
Publication statusPublished - 20 Jan 2021


  • Laminate
  • Mechanical properties
  • Elastic properties
  • Failure criterion
  • Tsai’s Modulus


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