Composite Material Stiffness Calculator
The Rule of Mixtures provides analytical estimates of composite elastic moduli from constituent properties and fibre volume fraction. The longitudinal modulus E1 (Voigt model) and transverse modulus E2 (Reuss model) bound the true composite stiffness. This calculator also computes the composite density and the in-plane shear modulus G12 using the Halpin-Tsai approximation. Enter fibre and matrix properties and the fibre volume fraction.
Rule of Mixtures formulas
E1 = Vf × Ef + Vm × Em (longitudinal, Voigt)
1/E2 = Vf/Ef + Vm/Em (transverse, Reuss)
rhoc = Vf × rhof + Vm × rhom
Vm = 1 - Vf
Where: Ef = fibre elastic modulus (GPa), Em = matrix elastic modulus (GPa), Vf = fibre volume fraction, Vm = matrix volume fraction = 1 - Vf. E1 is the Voigt upper bound (valid for longitudinal loading); E2 is the Reuss lower bound (valid for transverse loading). The true transverse modulus lies between these bounds and is better approximated by Halpin-Tsai equations for intermediate Vf values.
Why use specific modulus?
- Specific modulus (E / rho) measures stiffness per unit mass, the key figure of merit for aerospace and sports equipment where weight matters.
- Carbon fibre/epoxy has a specific modulus 5 to 7 times that of steel, which is why it dominates weight-critical structures.
- E-glass/epoxy has a specific modulus comparable to aluminium but at lower cost than carbon fibre.
- Optimal fibre orientation and ply stacking sequence are determined by Classical Laminate Theory (CLT), which extends the rule of mixtures to multi-directional laminates.
Composite stiffness calculator: frequently asked questions
What is the Rule of Mixtures for composites?
The Rule of Mixtures gives upper and lower bounds on composite stiffness. For longitudinal modulus (fibres parallel to load): E1 = Vf * Ef + Vm * Em (Voigt bound, isostrain). For transverse modulus (fibres perpendicular to load): 1/E2 = Vf/Ef + Vm/Em (Reuss bound, isostress). Where Vf is fibre volume fraction, Ef is fibre modulus, Vm = 1 - Vf, and Em is matrix modulus.
What is fibre volume fraction?
Fibre volume fraction (Vf) is the fraction of the total composite volume occupied by fibres. Vf ranges from 0 (pure matrix) to 1 (pure fibres). In practice, well-manufactured carbon fibre/epoxy prepreg laminates achieve Vf of 0.55 to 0.65. Hand lay-up glass fibre/epoxy laminates typically have Vf of 0.25 to 0.40. Higher Vf increases longitudinal stiffness and strength but reduces transverse properties.
What are typical fibre modulus values?
Carbon fibre (standard modulus, e.g. T300): 230 GPa. Carbon fibre (high modulus, e.g. M60J): 588 GPa. E-glass fibre: 72 GPa. S-glass fibre: 87 GPa. Aramid fibre (Kevlar 49): 125 GPa. Basalt fibre: 79-89 GPa. These values are for undirectional fibres in tension. Epoxy matrix modulus is typically 3.5 to 4.5 GPa.
Why is the transverse modulus so much lower than the longitudinal modulus?
In the transverse direction, load must transfer through both fibres and matrix in series. The softer matrix dominates, dragging the composite modulus close to the matrix value. This is the Reuss bound. The longitudinal modulus is dominated by the stiffer fibres (Voigt bound). This anisotropy is fundamental to fibre composites and is the reason laminates are designed with fibres oriented in multiple directions for multi-directional loading.
What standard governs composite testing?
ISO 14129:1997 covers determination of in-plane shear stress/shear strain response of fibre-reinforced polymer matrix composites. ASTM D3039 covers tensile properties of polymer matrix composite materials. ISO 527-5 covers tensile properties of unidirectional fibre-reinforced plastic composites.
Official sources
- ISO 14129:1997 Fibre-reinforced plastic composites: Determination of in-plane shear stress/shear strain response: ISO 14129.
- ASTM D3039 Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials: ASTM D3039.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.