2. Composite material fundamentals for crash simulation

Before a single element is generated in LS-DYNA, the analyst must decide what the material model is actually being asked to represent. A carbon-fiber/epoxy front crash rail, a glass-mat thermoplastic underbody shield, and a woven aramid helmet shell all fail by different mechanisms, and each demands a different constitutive description. This section establishes the material-science foundation that drives those choices: the distinct roles of fiber and matrix, the orthotropic elastic law, classical laminate theory (CLT) as the bridge from ply to stacking sequence, and the failure mechanisms that dominate under impact-rate loading.

Fiber and Matrix: Two Materials, Two Jobs

In a structural composite, the fiber carries the load and the matrix transfers it. This division of labor explains nearly every modeling decision that follows.

Reinforcing fibers — carbon (T300, T700, IM7), E-glass, and aramid — are stiff, strong, and brittle. Typical properties used as simulation inputs are:

• Carbon fiber (T700): E_f ≈ 230 GPa, tensile strength ≈ 4900 MPa, failure strain ≈ 2.1%, density ≈ 1.80 g/cm³
• E-glass fiber: E_f ≈ 72 GPa, tensile strength ≈ 3400 MPa, failure strain ≈ 4.8%, density ≈ 2.54 g/cm³
• Aramid (Kevlar 49): E_f ≈ 131 GPa, tensile strength ≈ 3000 MPa, failure strain ≈ 2.8%, density ≈ 1.44 g/cm³

The matrix — typically an epoxy, vinylester, or thermoplastic such as PA6 or PEEK — is compliant and comparatively weak, but it performs four essential functions: it binds fibers together, transfers shear stress between them, protects the fiber surface from moisture and abrasion, and governs the transverse and interlaminar response. A typical aerospace-grade epoxy has E_m ≈ 3.5 GPa, tensile strength ≈ 70 MPa, and failure strain of 3–5%. Note the two-order-of-magnitude stiffness gap between fiber and matrix: this is the physical origin of the strong orthotropy that makes composite modeling fundamentally different from metal modeling.

For crash simulation, the matrix is also the rate-sensitive constituent. Epoxy stiffness and strength increase measurably at strain rates above roughly 10 s⁻¹, and thermoplastic matrices exhibit even stronger rate dependence. LS-DYNA material cards such as *MAT_054/055 (enhanced composite damage) and *MAT_058 (Laminated Composite Fabric) expose rate-scaling factors or load-curve tables for this purpose; ignoring rate effects typically under-predicts peak force by 10–20% in a high-speed crush event.

Orthotropic Elasticity: Nine Constants, Not Two

An isotropic metal needs only E and ν. A unidirectional (UD) composite ply needs nine independent elastic constants: three moduli (E₁, E₂, E₃), three Poisson's ratios (ν₁₂, ν₁₃, ν₂₃), and three shear moduli (G₁₂, G₁₃, G₂₃). The convention used throughout this course is the standard one: direction 1 is along the fiber, direction 2 is transverse in-plane, and direction 3 is through-thickness. All sign conventions for stress and strain follow this material coordinate system unless a global system is explicitly stated.

For a UD carbon/epoxy ply, representative values are E₁ = 135 GPa, E₂ = E₃ = 9.5 GPa, G₁₂ = G₁₃ = 5.0 GPa, G₂₃ = 3.2 GPa, ν₁₂ = ν₁₃ = 0.30, ν₂₃ = 0.45. The ratio E₁/E₂ ≈ 14 means a ply loaded 10° off-axis loses roughly 60% of its axial stiffness — a sensitivity that makes fiber orientation mapping in the LS-DYNA *ELEMENT_SHELL / *PART_COMPOSITE definition critically important.

Two practical consequences follow. First, the through-thickness modulus E₃ is matrix-dominated and low; thin-shell assumptions are usually acceptable for in-plane crash loading but break down at bolted joints and impact contact zones. Second, the Poisson coupling ν₂₃ is high (0.4–0.5), so transverse contraction can be significant and should not be zeroed out for convenience.

Classical Laminate Theory: From Ply to Stacking Sequence

A real part is a stack of plies at different angles. CLT provides the transformation from ply-level stiffness to laminate-level response through the ABD matrix:

[ N ]   [ A  B ] [ ε⁰ ]
[   ] = [      ] [    ]
[ M ]   [ B  D ] [ κ  ]

A_ij = Σ Q̄_ij^(k) · (z_k − z_{k−1})        extensional stiffness
B_ij = ½ Σ Q̄_ij^(k) · (z_k² − z_{k−1}²)    coupling stiffness
D_ij = ⅓ Σ Q̄_ij^(k) · (z_k³ − z_{k−1}³)    bending stiffness

Here Q̄ is the transformed reduced stiffness of each ply, and z_k are the ply interface coordinates measured from the laminate mid-plane. The B matrix is zero for symmetric laminates, which is why crash-critical structures are almost always laid up symmetrically — an unsymmetric laminate couples extension and bending, producing warpage and unpredictable crush behavior.

Consider a representative automotive laminate [0/±45/90]_s with 0.2 mm plies, giving a 1.6 mm total thickness. The 0° plies dominate axial stiffness, the ±45° plies carry shear and torsion, and the 90° plies stabilize against transverse cracking. In LS-DYNA this is entered as eight integration points through the shell thickness in *PART_COMPOSITE, with each integration point assigned its own material angle. A common error is to define the ply angles relative to the global X-axis when the part's local coordinate system is rotated; the resulting stiffness error can exceed 30% and is invisible in the input deck unless the *DEFINE_COORDINATE_SYSTEM is checked.

Failure Mechanisms Under Impact

Composites do not yield; they fail by discrete, interacting mechanisms. For crash simulation the four that matter most are:

Under impact, these mechanisms interact. A low-velocity impact produces matrix cracking first, which triggers delamination, which reduces the buckling resistance of the sublaminate and finally causes fiber compression failure. At high velocity, the sequence compresses: fiber failure and delamination occur nearly simultaneously, and the energy absorption is dominated by fragmentation rather than progressive crushing.

Worked Example: Building a Ply Definition

Suppose a side-impact beam uses T700/epoxy UD tape with the following measured properties: ρ = 1.55 g/cm³, E₁ = 135 GPa, E₂ = 9.5 GPa, G₁₂ = 5.0 GPa, ν₁₂ = 0.30, X_T = 2200 MPa, X_C = 1200 MPa, Y_T = 55 MPa, Y_C = 200 MPa, S = 75 MPa. The layup is [0/90/±45]_s with 0.25 mm plies.

1. Compute total thickness: 8 plies × 0.25 mm = 2.0 mm.
2. Assign integration points: 8 through-thickness points, one per ply, in *PART_COMPOSITE.
3. Set ply angles: 0°, 90°, +45°, −45°, −45°, +45°, 90°, 0° (symmetric).
4. Select *MAT_054 with the Chang-Chang failure criterion and enable rate scaling via the LCSS load curve.
5. Verify the B matrix is zero by confirming symmetry; if the part is not symmetric, expect warpage in the simulation and correct the layup.

After running a 5 m/s axial crush, check three things: the peak force should fall within 10% of the experimentally measured value; the specific energy absorption (SEA) should be reported in kJ/kg and compared against the target for the material class (typically 40–80 kJ/kg for carbon/epoxy crush tubes); and the failure pattern should show progressive splaying rather than a single catastrophic fracture. If the model shows an instantaneous load drop to zero, the damage evolution parameters are too brittle — reduce the softening slope or increase the element characteristic length in the regularization.

The chain shown above is the mental model to carry into every composite crash model: constituents define ply properties, ply properties plus stacking sequence define laminate stiffness through CLT, and the laminate stress state activates one or more failure mechanisms whose interaction determines the energy absorption. When an LS-DYNA result looks wrong — too stiff, too brittle, or too soft — the diagnosis almost always traces back to one link in this chain: a mis-oriented ply, a missing rate factor, or a failure criterion applied to the wrong stress component.