Composite Materials (`composites`)

Composite Materials

Design laminate layups and composite section behavior

Standards catalog

Validation: indicative · Method band: advanced-numerics

Open calculator

Indicative method: Indicative closed-form or numerical model

Assumptions

Linear elastic material behavior unless noted otherwise.
User is responsible for load combinations and load factors per the selected design code.
Design standard (US/EU/ISO) sets unit defaults and screening check labels — not a full code worksheet.

Limitations

Professional screening / indicative workspace — does not replace a licensed PE or official code compliance review.
Where specialized evaluators are not implemented, checks map solver outputs to catalog templates for orientation only.

Engineering checks

Check	IND	US	EU	ISO
Effective modulus	implemented	—	—	—
Strength utilization	implemented	—	—	—

Purpose

Analyze laminated composite layups using classical lamination theory (CLT) for effective stiffness, ply stresses, and failure screening with common failure criteria. Supports symmetric and general stacking sequences.

Physics & theory

Each ply has orthotropic properties referenced to fiber direction: $E_{1}, E_{2}, G_{12}, ν_{12}$ . Under plane stress, reduced stiffness $Q$ relates stress to strain in ply coordinates. Rotated plies transform $Q$ to global coordinates via angle $θ$ .

Lamination theory sums ply contributions through thickness: extensional stiffness $A$ , coupling $B$ , and bending $D$ . Midplane strains $ϵ^{0}$ and curvatures $κ$ from applied loads yield ply stresses in each layer. Failure criteria (max stress, Tsai–Hill, Tsai–Wu) screen ply-by-ply.

Symmetric layups eliminate extension–bending coupling ( $B = 0$ ); asymmetric stacks require full $ABD$ inversion.

Governing equations

{N M} = [A B B D] {ϵ^{0} κ}

A = k \sum Q_{k} (z_{k + 1} - z_{k})

F_{Tsai - Hill} = \frac{σ _{1}^{2}}{X ^{2}} - \frac{σ _{1} σ _{2}}{X ^{2}} + \frac{σ _{2}^{2}}{Y ^{2}} + \frac{τ _{12}^{2}}{S ^{2}} \leq 1

Numerical method

CLT matrix assembly (engine): ply stack input builds $ABD$ matrices; load vector solved for midplane response; ply stresses and failure indices computed layer by layer.

Inputs

Parameter	Description
Ply materials	$E_{1}, E_{2}, G_{12}, ν_{12}$ , strengths
Layup sequence	Angles and thicknesses
Applied $N_{x}, N_{y}, N_{x y}, M_{x}, M_{y}, M_{x y}$	Loads per unit width
Failure criterion	Max stress, Tsai–Hill, Tsai–Wu

Outputs

Effective moduli, midplane strains/curvatures, ply stresses per layer, failure index, first-ply failure load factor.

Design codes & checks

Indicative: Effective modulus and strength utilization
US: MIL-HDBK-17-3F composite guidance (reference)
EU: EN 1999-1-3 aluminium structures with bonded panels (context)

Assumptions & limitations

Linear elastic CLT; no progressive damage or delamination propagation.
Plane stress, thin laminate; no transverse shear (no FSDT unless extended).
No moisture/temperature residual strains unless user offsets added.
Manufacturing defects and open-hole effects not included.

References

Jones, R. M. Mechanics of Composite Materials, 2nd ed. Taylor & Francis.
MIL-HDBK-17-3F. Composite Materials Handbook, Volume 3.
Herakovich, C. T. Mechanics of Fibrous Composites. Wiley.
ASTM D3039/D3039M. Tensile Properties of Polymer Matrix Composites.
PhyCalcPro verification benchmarks in src/data/verification/ where available for this module.
Beer, F. P., et al. Mechanics of Materials, 8th ed. McGraw-Hill — foundational stress and deformation theory.

Maintainer note: Domain-rich behavior and higher model/assumption complexity.

Composite Materials

Assumptions

Limitations

Engineering checks

Composite Materials (composites)

Composite Materials (`composites`)