3. Airbag fabric material modeling

An airbag is not a rigid pressure vessel. It is a woven nylon or polyester membrane that stretches, shears, vents gas through its own pores, and stiffens as it deforms faster. If you model the cushion as a rigid shell or a simple linear-elastic surface, the deployment kinematics will look plausible but the internal pressure history, the contact forces on the occupant, and the timing of full inflation will all be wrong. This chapter covers the three constitutive ingredients that make a fabric model behave like real fabric in LS-DYNA: hyperelastic membrane behavior (isotropic and anisotropic), permeability, and strain-rate dependence.

Why Fabric Is Not a Simple Elastic Material

Woven fabric carries load almost entirely in tension along its yarn directions. It has negligible bending stiffness, it is nearly incompressible in the plane, and it exhibits a nonlinear stiffening response as yarns straighten and lock. A linear elastic MAT_001 with a single modulus cannot reproduce the J-shaped stress–strain curve, and it will over- or under-predict the pressure peak during the critical first 30 ms of deployment.

LS-DYNA offers two practical routes for fabric:

• Isotropic hyperelastic membrane — *MAT_FABRIC with an isotropic strain-energy formulation, or *MAT_HYPERELASTIC_RUBBER (MAT_077) restricted to membrane elements. Suitable when the weave is balanced (equal warp and weft yarns) and the loading direction is not strongly biased.
• Anisotropic hyperelastic membrane — *MAT_FABRIC (MAT_034) with orthotropic elastic moduli, or *MAT_ANISOTROPIC_HYPERELASTIC (MAT_295) when you need a full strain-energy function with distinct warp/weft contributions.

In practice, MAT_034 is the workhorse for airbag cushions because it combines orthotropic stiffness, optional permeability, and optional strain-rate scaling in a single card. MAT_295 is preferred when the fabric undergoes large shear and you need a physically consistent hyperelastic potential rather than a piecewise elastic curve.

Isotropic Hyperelastic Formulation

For a balanced weave, the strain-energy density can be written as a function of the first and second invariants of the right Cauchy–Green tensor. A common choice is a Mooney–Rivlin form:

W = C10 (I1 - 3) + C01 (I2 - 3)

where I1 = λ1² + λ2² + λ3²
      I2 = λ1²λ2² + λ2²λ3² + λ3²λ1²
      λi = principal stretch ratios

For a thin membrane, plane stress is assumed (σ3 = 0), and the in-plane Cauchy stresses follow from the derivatives of W with respect to the stretches. In LS-DYNA, MAT_077 takes C10 and C01 directly. A typical coated nylon 6.6 fabric at quasi-static rates gives C10 ≈ 2.5 MPa and C01 ≈ 0.3 MPa, but these must be fitted to your own biaxial test data — do not copy them blindly.

Anisotropic Hyperelastic Formulation

Real airbag fabric is orthotropic: warp and weft directions have different stiffness, and the shear response is nonlinear. MAT_034 defines the membrane as orthotropic elastic with optional hyperelastic correction, while MAT_295 uses a strain-energy function decomposed into fiber and matrix contributions:

W = W_matrix(I1, I2) + W_fiber(I4, I6)

I4 = a0 · C · a0   (warp fiber invariant)
I6 = b0 · C · b0   (weft fiber invariant)

a0, b0 = unit vectors along warp and weft in reference configuration

The fiber terms typically use an exponential or power-law form to capture the stiffening as yarns straighten. In MAT_295 you supply the fiber direction vectors, the matrix constants, and the fiber stiffness parameters. The key practical point: the reference configuration must be the flat, undeformed fabric pattern, not the folded cushion. If you define fiber directions on the folded mesh, the warp/weft orientation will be wrong after unfolding.

For MAT_034, the orthotropic elastic card requires EA, EB, EC, PRBA, PRCA, PRCB, and GAB. A representative coated nylon at 20 °C and 50 % RH might use EA = 800 MPa (warp), EB = 700 MPa (weft), EC = 50 MPa (through-thickness, mostly for stability), GAB = 30 MPa. Again, these are illustrative starting points, not validated material data.

Permeability: The Fabric Leaks on Purpose

An airbag must vent gas to absorb energy. Permeability is the volumetric flow rate of gas through the fabric per unit area per unit pressure difference. In LS-DYNA, MAT_034 and MAT_295 support permeability via the PERM flag and a permeability curve or constant.

The simplest model is a constant Darcy permeability:

Q = K * A * ΔP / μ

Q  = volumetric flow rate
K  = permeability coefficient (m²)
A  = fabric area
ΔP = pressure difference across fabric
μ  = gas dynamic viscosity

In practice, fabric permeability is not constant — it increases with pressure and with strain because the weave opens up. LS-DYNA allows a pressure-dependent permeability curve (LCPERM) or a strain-dependent option. For a driver-side airbag, a typical coated fabric might have K ≈ 1e-12 m² at low pressure, rising to 5e-12 m² at 200 kPa. Uncoated fabric can be an order of magnitude higher.

Strain-Rate Effects

Airbag fabric is strain-rate sensitive. At deployment rates (strain rates of 100–1000 s⁻¹), nylon can be 30–80 % stiffer than at quasi-static rates. LS-DYNA handles this in two ways:

• Rate-dependent scaling curve — LCRATE in MAT_034 scales the stress by a factor as a function of strain rate. You supply a table of (strain rate, scale factor).
• Rate-dependent hyperelastic constants — in MAT_295, the fiber stiffness parameters can be defined as functions of strain rate via a load curve.

A typical rate-scaling table for nylon 6.6 fabric might look like this:

These values are illustrative. The correct approach is to run tensile tests at multiple rates on your actual fabric and fit the scaling curve. If you cannot test, use published data for the same yarn type and coating, and document the assumption.

Putting It Together: A Practical Modeling Workflow

The figure below shows how the three ingredients interact in a deployment simulation. The fabric constitutive model receives strain and strain rate from the membrane elements, computes stress via the hyperelastic potential, and simultaneously computes gas flow through the permeability model. The internal pressure then feeds back into the membrane equilibrium.

The workflow in practice: start with a flat pattern mesh, assign MAT_034 with orthotropic elastic constants fitted to biaxial tests, add a rate-scaling curve from high-speed tensile tests, and enable permeability with a pressure-dependent curve. Run a single-element tension test first to verify the stress–strain response matches your coupon data. Then run a static inflation of the folded cushion to check for element inversion or negative volume. Only after these checks should you run the full deployment with the inflator model.

Common Pitfalls and How to Detect Them

• Element inversion during folding — often caused by too-stiff bending behavior or insufficient membrane formulation. Use ELFORM=9 (membrane) or ELFORM=16 (fully integrated shell with membrane option) and check the negative volume message in the output.
• Pressure too high or too low — check permeability first, then inflator mass flow. A factor-of-two error in permeability is common when using uncoated fabric data for coated fabric.
• Unrealistic occupant force — often a sign that strain-rate scaling is missing. At deployment rates, the fabric is much stiffer than the quasi-static curve suggests.
• Warp/weft swap after unfolding — verify fiber direction vectors in the reference configuration. A 90° error will make the cushion deploy asymmetrically.

With the fabric model in place, the next step is to connect it to the inflator gas source and the folded geometry. That is where the material model meets the deployment kinematics.