Innovation 1: Simplification of Laminate Stiffness with Trace

Background

Traditional laminate stiffness involves predicting and measuring four elastic constants: longitudinal stiffness (ExE_xEx​), transverse stiffness (EyE_yEy​), shear modulus (EsE_sEs​), and Poisson’s ratio (νx\nu_xνx​). While measuring ExE_xEx​ is straightforward, predicting and testing for EyE_yEy​ and EsE_sEs​ are challenging.

Our breakthrough
We discovered TRACE, a single parameter that simplifies stiffness representation. Trace, the sum of the diagonal components of the stiffness matrix, represents the total elastic stiffness capability of a composite ply. It’s easier to use, understand, and determine experimentally.

Benefits

  • Simplified Stiffness Ranking: Composite materials can now be ranked by stiffness, much like metals (e.g., aluminum at 70 GPa, titanium at 110 GPa, and steel at 210 GPa).
  • Universal Laminate Partitioning: Laminate stiffness ratios remain constant across materials. For example:
    • For a [90/0] laminate:
      • E1=E2=0.47×Trace
      • E6=0.03×Trace
    • These values are consistent for carbon, Kevlar, glass, and even flax composites.

Material Comparisons Made Simple:
If Material A’s trace is 20% higher than Material B, all laminates of Material A are 20% stiffer than those of Material B.

Applications

  • Streamlined Testing:
    • Only ExE_xEx​ needs to be tested to determine trace. For carbon/epoxy composites, Trace=Ex/0.88
    • Testing can be approximated using the rule-of-mixtures: Ex=Vf . Ef
  • Effortless Deflection Calculations:
    • Deflections in beams and tubes can be directly compared using relative trace values, with no recalculations needed.
  • Broader Implications:
    • Trace links directly to other composite constants, such as U2​, making stiffness properties more accessible and comprehensible.