MechanicsCore Level
Density & Rule of Mixtures
Estimate composite material density and elastic modulus upper and lower bounds using volume or mass fraction mixtures.
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Components Checklist
Fraction:
| Name | Density (g/cm³) | Fraction | Modulus (GPa, opt) | Delete |
|---|---|---|---|---|
Composite Properties
Calculated mixture bounds
Enter valid coordinates to compute mixture densities.
Formula: Rule of Mixtures
ρc = Σ V_i · ρ_i
Where:
ρc=Composite density (g/cm³)
Ec (Voigt)=Upper modulus bound: Σ (V_i · E_i) (GPa)
Ec (Reuss)=Lower modulus bound: 1 / Σ (V_i / E_i) (GPa)
V_i=Volume fraction of component i (0 to 1)
Scientific Assumptions & Methodology
- Fibers and matrix are assumed to be perfectly bonded with zero void fraction.
- Upper bound (Voigt/parallel model) assumes uniform strain across phases.
- Lower bound (Reuss/series model) assumes uniform stress across phases.
Limitations & Educational Warnings
- Actual composite modulus depends heavily on fiber length (continuous vs short), orientation (aligned vs random), and interface defects.
- Density calculation assumes no chemical reactions or volumetric volume expansion/contraction during blending.