Composite Materials Analysis — Overview
From the carbon fiber wings of a commercial airliner to the lightweight hood of a sports car, composite materials push structural performance beyond what metals can achieve. This guide explains how to model, analyze, and predict failure in composite structures using FEA.
1. Why Composites in CAE? CFRP, GFRP, and Sandwich Panels
Composite materials combine two or more constituents to achieve properties neither provides alone. In structural engineering, the dominant systems are:
CFRP — Carbon Fiber Reinforced Polymer
Highest specific stiffness and strength among structural materials. Used in aerospace primary structure, motorsport chassis, and high-end sporting goods. Expensive; brittle in the matrix direction.
GFRP — Glass Fiber Reinforced Polymer
Lower cost than CFRP, good corrosion resistance, electrically transparent. Wind turbine blades, marine hulls, automotive body panels. Higher density and lower stiffness than carbon.
Sandwich Panels
Two thin stiff face-sheets bonded to a light core (Nomex honeycomb, foam, balsa). Extremely high bending stiffness per unit weight. Critical failure mode is face-sheet wrinkling or core shear failure.
The key challenge in composite CAE is that these materials are anisotropic — their stiffness and strength depend on direction. A unidirectional CFRP ply may be 10× stiffer along the fibers than transverse to them. This directional dependence requires specialized analysis theory and software tools that go far beyond isotropic material models.
2. Classical Laminate Theory (CLT): The [A][B][D] Stiffness Matrices
Classical Laminate Theory (CLT) — also called Classical Laminated Plate Theory (CLPT) — extends thin plate bending theory to multi-ply laminates with arbitrary ply orientations. The central result is the laminate constitutive law relating mid-plane strains \(\{\varepsilon^0\}\), curvatures \(\{\kappa\}\), in-plane stress resultants \(\{N\}\), and moment resultants \(\{M\}\):
$$\begin{bmatrix} \{N\} \\ \{M\} \end{bmatrix} = \begin{bmatrix} [A] & [B] \\ [B] & [D] \end{bmatrix} \begin{bmatrix} \{\varepsilon^0\} \\ \{\kappa\} \end{bmatrix}$$2.1 The A, B, D Matrices
Each matrix is assembled by integrating the ply-level transformed stiffness \([\bar{Q}]_k\) through the laminate thickness:
$$A_{ij} = \sum_{k=1}^{N} [\bar{Q}_{ij}]_k (z_k - z_{k-1})$$ $$B_{ij} = \frac{1}{2}\sum_{k=1}^{N} [\bar{Q}_{ij}]_k (z_k^2 - z_{k-1}^2)$$ $$D_{ij} = \frac{1}{3}\sum_{k=1}^{N} [\bar{Q}_{ij}]_k (z_k^3 - z_{k-1}^3)$$where \(z_k\) is the distance from the laminate mid-plane to the top of ply \(k\).
- [A] — Extensional stiffness: Relates in-plane loads to mid-plane strains. Depends only on total thickness and ply orientations (not order).
- [B] — Coupling stiffness: Couples in-plane loads to curvatures, and moments to mid-plane strains. Non-zero for asymmetric laminates — causes warping when heated or loaded in-plane.
- [D] — Bending stiffness: Relates moments to curvatures. Depends on ply order (outer plies contribute most, proportional to \(z^3\)).
2.2 Ply Angle Effects on Laminate Behavior
The ply orientation angle \(\theta\) (measured from the global x-axis to the fiber direction) transforms the ply stiffness components through trigonometric transformation. Key practical effects:
- 0° plies: Maximum axial stiffness and strength. Drive tensile/compressive capacity.
- 90° plies: Transverse stiffness. Resist loads perpendicular to the main direction.
- ±45° plies: Shear stiffness and torsional resistance. Critical for shear panels and torque tubes.
- Quasi-isotropic [0/±45/90]s: Equal stiffness in all in-plane directions. Common in structures with multi-directional loading.
3. Failure Criteria: Hashin, Puck, Tsai-Wu, Tsai-Hill
Composite failure prediction requires criteria that distinguish between matrix cracking, fiber fracture, and delamination — failure modes unknown in isotropic metals. The most widely used criteria are:
3.1 Tsai-Hill Criterion
Based on Hill's anisotropic yield criterion, Tsai-Hill combines all stress components into a single scalar index. Failure is predicted when:
$$\left(\frac{\sigma_1}{X}\right)^2 - \frac{\sigma_1 \sigma_2}{X^2} + \left(\frac{\sigma_2}{Y}\right)^2 + \left(\frac{\tau_{12}}{S}\right)^2 = 1$$where \(X\), \(Y\) are longitudinal and transverse strengths, and \(S\) is shear strength. Note: this criterion uses X for both tension and compression, which is a limitation.
3.2 Tsai-Wu Criterion
Tsai-Wu generalizes to different tensile and compressive strengths through additional interaction terms:
$$F_1\sigma_1 + F_2\sigma_2 + F_{11}\sigma_1^2 + F_{22}\sigma_2^2 + F_{66}\tau_{12}^2 + 2F_{12}\sigma_1\sigma_2 = 1$$where \(F_1 = 1/X_t - 1/X_c\), \(F_{11} = 1/(X_t X_c)\), etc. The interaction term \(F_{12}\) requires biaxial test data and is often set to \(-1/2\sqrt{F_{11}F_{22}}\) for conservative estimates.
3.3 Hashin Criteria (Most Popular in FEA)
Hashin's criteria (1980) separate the failure index into physically distinct modes, making them ideal for progressive damage modeling:
Fiber tension failure (\(\sigma_1 > 0\)):
$$F_f^{(t)} = \left(\frac{\sigma_1}{X_t}\right)^2 + \left(\frac{\tau_{12}}{S_L}\right)^2 = 1$$Fiber compression failure (\(\sigma_1 < 0\)):
$$F_f^{(c)} = \left(\frac{\sigma_1}{X_c}\right)^2 = 1$$Matrix tension failure (\(\sigma_2 > 0\)):
$$F_m^{(t)} = \left(\frac{\sigma_2}{Y_t}\right)^2 + \left(\frac{\tau_{12}}{S_L}\right)^2 = 1$$Matrix compression failure (\(\sigma_2 < 0\)):
$$F_m^{(c)} = \left(\frac{\sigma_2}{2S_T}\right)^2 + \left[\left(\frac{Y_c}{2S_T}\right)^2 - 1\right]\frac{\sigma_2}{Y_c} + \left(\frac{\tau_{12}}{S_L}\right)^2 = 1$$3.4 Puck Criterion
Puck's criterion (1996) is physically the most rigorous, based on Mohr-Coulomb fracture mechanics. It predicts the fracture plane orientation within the matrix and distinguishes three matrix failure modes (A, B, C) based on the sign and magnitude of transverse stresses. It requires more material parameters but gives better accuracy for highly loaded matrix-dominated lay-ups. Widely used in the German aerospace industry (DLR, Airbus) and increasingly adopted in Abaqus UMAT implementations.
4. Shell Elements for Composites: Section Stacking and Through-Thickness Integration
In FEA, composite laminates are most efficiently modeled with layered shell elements. The key features to understand:
4.1 Section Stacking Definition
The laminate is defined by specifying each ply's thickness, fiber orientation, and material. In Abaqus:
*SHELL SECTION, ELSET=wing_skin, COMPOSITE, OFFSET=MID
** thickness, section_points, material, angle
0.000125, 3, CFRP_T300, 0.
0.000125, 3, CFRP_T300, 45.
0.000125, 3, CFRP_T300, -45.
0.000125, 3, CFRP_T300, 90.
0.000125, 3, CFRP_T300, 90.
0.000125, 3, CFRP_T300, -45.
0.000125, 3, CFRP_T300, 45.
0.000125, 3, CFRP_T300, 0.
** [0/45/-45/90]s symmetric laminate4.2 Integration Points Through Thickness
Each ply uses integration points through its thickness to capture the linear stress variation. Typically 3 points per ply suffice for linear analysis; for nonlinear or damage analysis, 5 points per ply improve accuracy. The section_points parameter in Abaqus controls this.
Output is requested at specific section points (SP1 = bottom, SP3 = top for 3-point integration). In post-processing, always check stresses at both top and bottom of the critical plies — the failure index can differ significantly between faces.
4.3 Continuum Shell vs. Conventional Shell
- Conventional shell (S4R, S8R): 2D mid-surface mesh, thickness specified as section property. Best for thin laminates. Cannot capture out-of-plane normal stress \(\sigma_{33}\).
- Continuum shell (SC8R in Abaqus): 3D solid-looking element with actual top/bottom surfaces. Models out-of-plane compression. Essential near cutouts, thick sections, and bonded joints where interlaminar stresses dominate.
5. Progressive Damage Modeling: UMAT and VUMAT
Failure criteria like Hashin tell you when a ply fails, but not what happens next. Progressive damage modeling (PDM) degrades the ply stiffness after failure initiation, redistributing loads to remaining plies until final structural failure.
The standard degradation scheme reduces affected stiffness components to near-zero after failure:
- Fiber failure: Set \(E_1 \to 0\), \(G_{12} \to 0\), \(G_{13} \to 0\)
- Matrix failure: Set \(E_2 \to 0\), \(G_{12} \to 0\), \(\nu_{12} \to 0\)
5.1 UMAT/VUMAT Implementation
Abaqus provides Hashin damage built-in (*DAMAGE INITIATION, CRITERION=HASHIN + *DAMAGE EVOLUTION), but custom behavior requires a user material subroutine:
! Key UMAT state variables for composite damage
! SDV1 = fiber tension damage variable d_ft (0=intact, 1=failed)
! SDV2 = fiber compression damage variable d_fc
! SDV3 = matrix tension damage variable d_mt
! SDV4 = matrix compression damage variable d_mc
! Degraded stiffness (example for matrix damage):
! E2_eff = E2 * (1 - d_mt) * (1 - d_mc)
! G12_eff = G12 * (1 - d_mt) * (1 - d_mc)For explicit dynamics (crash, impact), use VUMAT — the vectorized version that operates on batches of integration points for computational efficiency. Progressive damage under impact loading in CFRP panels is a common application in automotive hood and aerospace bird-strike certification.
6. Delamination: CZM and VCCT
Delamination — separation between plies — is the most dangerous failure mode in composites because it is often invisible on the surface and can cause sudden loss of compression strength (delamination growth reduces effective ply count, triggering buckling at a fraction of the undamaged critical load).
6.1 Cohesive Zone Model (CZM)
CZM places cohesive elements at the ply interface. These elements follow a traction-separation law:
- Initiation: When the traction exceeds a critical value (Mode I: interlaminar tensile strength; Mode II: shear strength), damage begins.
- Evolution: Stiffness degrades with continued opening until the critical fracture energy \(G_c\) is consumed.
- Final failure: Element is deleted when \(G = G_c\).
The mixed-mode fracture criterion is typically:
$$\left(\frac{G_I}{G_{Ic}}\right)^\alpha + \left(\frac{G_{II}}{G_{IIc}}\right)^\beta = 1$$With \(\alpha = \beta = 1\) (linear BK criterion) or Benzeggagh-Kenane (BK) exponent fitted to mixed-mode fracture toughness data.
** Abaqus CZM cohesive element definition
*COHESIVE SECTION, ELSET=interface_layer, RESPONSE=TRACTION SEPARATION, THICKNESS=SPECIFIED
1.0, ! thickness
*SURFACE INTERACTION, NAME=cohesive_prop
*COHESIVE BEHAVIOR
Knn, Kss, Ktt ! interface stiffnesses [N/mm³]
*DAMAGE INITIATION, CRITERION=MAXS
t0_n, t0_s, t0_t ! normal and shear strengths [MPa]
*DAMAGE EVOLUTION, TYPE=ENERGY, MIXED MODE BEHAVIOR=BK, POWER=1.45
Gnc, Gsc, Gtc ! fracture toughnesses [N/mm]6.2 Virtual Crack Closure Technique (VCCT)
VCCT is a fracture mechanics approach that computes the strain energy release rate (SERR) at a crack front from the forces and displacements of adjacent nodes. It is suitable for propagating a pre-existing delamination (known crack front location). The SERR in Mode I is:
$$G_I = -\frac{1}{2 \Delta a} F_{z,i} \cdot \delta_{z, i-1}$$where \(\Delta a\) is the crack extension length, \(F_{z,i}\) is the nodal force at the crack tip, and \(\delta_{z,i-1}\) is the relative opening displacement one element behind the tip. VCCT is numerically simpler than CZM but requires a mesh with a predefined crack — it cannot nucleate new delaminations from an intact interface.
7. Software: Abaqus Composite Layup and ANSYS ACP
7.1 Abaqus — Composite Manager and Damage
Abaqus CAE includes a Composite Layup editor for graphical ply stacking definition. Key workflow:
- Create composite layup in the Property module — define ply orientations using global, edge-based, or local coordinate systems (critical for curved surfaces).
- Use
*SHELL SECTION, COMPOSITEor the CAE layup editor for uniform laminates; for variable ply drops, use multiple section assignments. - For damage, use the built-in
HASHINinitiation + energy-based evolution for a quick first pass. - Post-process failure indices per ply per element with
HSNFTCRT,HSNFCCRT,HSNMTCRT,HSNMCCRToutput variables.
7.2 ANSYS ACP (Ansys Composite PrepPost)
ACP is a dedicated pre- and post-processing tool for composites integrated with ANSYS Mechanical/Workbench. Key capabilities:
- Draping simulation: ACP can simulate fiber draping on complex double-curved surfaces, computing the actual fiber angle deviation from the nominal lay-up — critical for accurate buckling and strength analysis of compound-curved panels.
- Rosette definition: Multiple coordinate system types (Parallel, Radial, Edge-wise) control fiber direction mapping on curved geometry.
- Ply-level post-processing: Plot failure indices, reserve factors, and damage initiation location per ply in a user-friendly 3D viewer.
- Coupling to Mechanical: ACP Pre creates the layered section data; ACP Post reads solver results and provides ply-level visualization.
7.3 Other Tools
- HyperWorks (OptiStruct): Good composite optimization capabilities — ply thickness and orientation optimization with manufacturing constraints (balanced, symmetric).
- ESAComp: Dedicated laminate analysis tool by Altair, excellent for rapid CLT calculations and failure envelope generation.
- Nastran PCOMP: Define composite laminates in Nastran with
PCOMPproperty card; pair withCQUAD4shell elements.
8. Articles in This Section
Q&A: Understanding Composite Analysis
Professor, I need to analyze a CFRP bracket for an aircraft. My colleague said "just use isotropic aluminum properties as an approximation" to save time. Is that acceptable?
Please don't do that — it's a common shortcut that can give dangerously wrong answers. CFRP stiffness in the fiber direction can be 5 to 10 times higher than transverse to the fibers. If you lump everything into an isotropic average, you'll get the wrong load distribution, wrong deflections, and completely miss the critical failure mode — which is almost always matrix cracking or delamination, not fiber fracture. Those modes have no analog in aluminum. The whole value of doing a composite analysis is capturing the ply-level behavior correctly.
Okay, understood. So I need to set up a proper composite layup. The part is a [0/90/0] lay-up — only three plies. Does CLT apply to something that simple, or is it only for thick laminates?
CLT applies perfectly well to three plies — it's valid for any number of plies as long as the laminate is "thin" relative to its in-plane dimensions, which most structural panels satisfy. Your [0/90/0] is actually symmetric — the 0° plies are mirror images about the 90° center ply — so the B matrix is zero. That's a good thing: no bending-stretching coupling, no warping after cure. For your bracket analysis, the D matrix will tell you the bending stiffness, and the A matrix handles in-plane loads. The dominant failure modes to watch for are delamination at the 0°/90° interfaces and matrix cracking in the 90° ply under transverse tension.
What's the difference between Tsai-Wu and Hashin? My company uses Tsai-Wu but I see Hashin everywhere in papers. Which one should I actually trust?
Both are widely used, but they serve different purposes. Tsai-Wu gives you a single scalar failure index that tells you "is this ply about to fail, yes or no?" — useful for initial design screening. Hashin gives you separate failure indices for fiber tension, fiber compression, matrix tension, and matrix compression. That distinction matters enormously for understanding what kind of failure is happening and for progressive damage modeling — you can't degrade stiffness properly if you don't know which failure mode activated. In practice: use Tsai-Wu for quick first-pass margin checks, Hashin (or Puck) when you need to understand failure mode and want to implement damage progression.
I've heard about delamination being catastrophic. How do I even know if my model is at risk? The surfaces of the part look fine in my stress plots.
That's exactly the dangerous thing about delamination — it's driven by out-of-plane stresses that conventional shell element models don't capture at all. A regular shell model with in-plane Hashin failure criteria will completely miss delamination risk. To detect it, you need to check interlaminar shear stress \(\tau_{13}\) and \(\tau_{23}\), and interlaminar normal stress \(\sigma_{33}\) — these are the stresses that peel the plies apart. The highest risk zones are near free edges (where interlaminar stresses spike sharply due to the free-edge effect), near ply drop-offs, at fastener holes, and at bondline terminations. For those regions, switch to continuum shell (SC8R) or 3D solid elements to capture the full stress state.
What about the cohesive zone model — it seems really powerful but also really complicated to set up. Are there simple rules for picking the interface parameters?
CZM does require care with parameters, but there are practical guidelines. The penalty stiffness Knn should be high enough to prevent spurious compliance before damage, but not so high it causes numerical ill-conditioning — a value of \(10^5\) to \(10^6\) N/mm³ is typical for epoxy interfaces. The interface strengths t0_n and t0_s come from standard fracture specimens: DCB (double cantilever beam) test gives Mode I toughness GIc, ENF (end-notched flexure) gives Mode IIc. If you don't have test data, use literature values for the specific prepreg system — HTA/6376 CFRP typically has GIc ≈ 0.3 N/mm and GIIc ≈ 0.8 N/mm. One practical trap: use a mesh small enough that at least 3–5 cohesive elements span the cohesive zone length Lc ≈ E·GIc/t0² to avoid mesh-size dependent results.
ANSYS ACP keeps coming up in job postings. Is it significantly better than just defining composite sections manually in Abaqus? What does ACP actually add?
ACP's biggest advantage is for complex curved structures — think a doubly curved fuselage panel or a wind turbine blade with twist and taper. When you drape a flat fabric over a compound curve, the fiber angles deviate from the nominal lay-up angles. ACP has a draping simulation engine that computes this deviation across the surface and feeds the actual (not nominal) fiber angles into the stress analysis. That can make a 10–20% difference in predicted buckling load or failure index. For a flat bracket or simple panel, yes, manually defining sections in Abaqus is perfectly fine. But for complex aerospace or wind energy geometries, ACP is genuinely worth the learning investment.