📚 Course ContentsChapter 4 Material modeling for impactor and target structures

4. Material modeling for impactor and target structures

In a virtual linear impactor simulation, the accuracy of the predicted force–displacement response depends far more on the constitutive models assigned to the striker, the target plate, and any polymeric components than on mesh density or solver settings. A linear impactor test typically drives a rigid or deformable striker into a flat or curved target at velocities between 1 and 10 m/s, producing strain rates that range from quasi-static in the far field to several hundred per second near the contact zone. Capturing that range requires three modeling decisions: an elastic–plastic backbone, a strain-rate scaling law, and a failure criterion that removes elements or degrades stiffness at the correct moment.

Elastic–Plastic Backbones for Metals

For metallic targets such as aluminum 6061-T6 or mild steel, the plastic response is usually described with a piecewise-linear hardening curve. In LS-DYNA this is *MAT_PLASTIC_KINEMATIC (MAT_003); in Abaqus it is the classical metal plasticity model with isotropic or kinematic hardening. The input is a table of true stress versus true plastic strain, converted from engineering data using:

sigma_true = sigma_eng * (1 + eps_eng)
eps_true   = ln(1 + eps_eng)
eps_pl     = eps_true - sigma_true / E

A common error is to enter engineering stress directly. For a 6061-T6 coupon with a 0.2% offset yield of 276 MPa and an ultimate of 310 MPa at 12% engineering strain, the true ultimate stress is approximately 347 MPa and the true plastic strain at that point is about 0.105. Feeding the engineering values underestimates the energy absorbed by roughly 8–12%, which shifts the predicted peak force downward and delays the onset of failure.

Isotropic hardening is adequate when the load path is monotonic, as in a single impactor strike. Kinematic hardening becomes necessary when the target experiences reverse loading, for example a rebound that plastically re-yields the contact region. For a linear impactor with a single forward stroke, isotropic hardening with a von Mises yield surface is normally sufficient and computationally cheaper.

Strain-Rate Dependence

Metals exhibit a measurable increase in flow stress with strain rate. The two most common scaling laws in impactor work are the Cowper–Symonds model and the Johnson–Cook model. Cowper–Symonds scales the yield stress by a factor:

sigma_y(dot_eps) = sigma_y0 * [1 + (dot_eps / D)^(1/p)]

where D and p are fitted constants. For aluminum 6061-T6, representative values are D = 6500 s^-1 and p = 4; for mild steel, D = 40 s^-1 and p = 5. These are illustrative fits, not universal constants, and should be re-fitted if the alloy temper or supplier changes.

Johnson–Cook separates rate and temperature effects:

sigma = (A + B*eps_pl^n) * (1 + C*ln(dot_eps/dot_eps_0)) * (1 - T_star^m)

For room-temperature impactor tests the thermal term is often set to unity, reducing the model to a rate-sensitive power law. The practical difference is that Cowper–Symonds multiplies the entire yield surface, while Johnson–Cook scales the flow stress after hardening. At the strain rates typical of a 5 m/s impactor strike (10–500 s⁻¹), both give similar results for aluminum; for polymers the choice matters much more.

Polymers: Rate Sensitivity and Pressure Dependence

Polymeric components—bumper fascia, energy absorbers, or a polycarbonate target window—cannot be represented by metal plasticity. Their yield stress depends strongly on strain rate and on hydrostatic pressure, and they often exhibit post-yield softening followed by draw. Suitable models include *MAT_PLASTICITY_POLYMER (MAT_089), *MAT_SAMP-1 (MAT_187), or *MAT_CRUSHABLE_FOAM (MAT_063) for expanded foams.

For a solid polymer such as polycarbonate, a practical workflow is:

Obtain tensile stress–strain curves at three or more strain rates (e.g., 0.001, 0.1, 10 s⁻¹).
Fit the elastic modulus and yield stress at each rate; the modulus is nearly rate-independent, while yield stress may rise 30–60% over that range.
Enter the curves into MAT_089, which interpolates between them using the current effective strain rate.
Define a pressure cutoff or tensile failure strain to capture brittle fracture under triaxial tension.

For foams, the input is a nominal stress–strain curve in compression with a plateau and densification region. The key parameters are the plateau stress, the densification strain, and the tensile cutoff stress. A common mistake is to use the tensile curve for a foam that is loaded in compression; the plateau stress in tension is typically 30–50% lower.

Failure Criteria

Failure in impactor simulations is usually triggered by one of four criteria:

Criterion	Typical use	Key parameter
Equivalent plastic strain	Ductile metals	`eps_f` at failure
Maximum principal stress	Brittle polymers, glass	`sigma_max`
Johnson–Cook damage	High-rate metals	`D1–D5`
GISSMO / damage	Sheet metals, crash	Instability + failure curve

For a linear impactor target plate, equivalent plastic strain with element deletion is the simplest defensible choice. Set eps_f from a notched tensile test rather than a smooth coupon, because the stress triaxiality at the notch is closer to that under the impactor. A smooth-coupon value of 0.12 may overpredict failure strain by a factor of two compared with a notched specimen at 0.05–0.07.

Element deletion removes mass and can artificially soften the structure. For thin plates, prefer a damage variable that degrades stiffness to zero over a defined displacement rather than instant deletion. In LS-DYNA, *MAT_ADD_EROSION with a displacement-based criterion is more stable than a pure strain trigger.

Calibration and Verification

After assigning the models, verify them against a simple coupon or plate test before running the full impactor. A useful check is a single-element or small-patch simulation loaded at the target strain rate; the predicted yield stress should match the fitted curve within 5%. Then run a plate impact at low velocity and compare the force–time trace. If the peak force is too high, the yield stress or rate scaling is overestimated; if the failure occurs too early, the failure strain is too low or the mesh is too coarse at the contact zone.

Always document the source of each material curve—coupon test, supplier datasheet, or literature fit—and the strain rate at which it was measured. A model that is accurate at 0.001 s⁻¹ may be wrong by 40% at 100 s⁻¹.

The figure summarizes how the striker and target material definitions feed into the constitutive response and ultimately into the predicted force–time trace. The strain-rate bar at the bottom reminds the analyst that a single rate-independent curve is rarely adequate: the contact zone and the far field operate in different regimes, and the model must interpolate between them.

Practical Checklist Before Running the Full Model

Confirm that all stress–strain input is in true stress and true plastic strain.
Check that the strain-rate constants were fitted over the rate range actually present in the simulation.
Verify that the failure criterion was calibrated with a specimen whose stress triaxiality matches the impact region.
Run a single-element verification at the expected strain rate and compare yield stress to the fitted curve.
Run a low-velocity plate impact and compare peak force and failure displacement before committing to the full impactor run.

When these steps are followed, the material model becomes a calibrated predictive tool rather than a set of default values. The remaining uncertainty is then dominated by contact definition and mesh refinement, which are addressed in the next stage of the workflow.