Testing for Crash and Impact Material Models for CAE
Crash and impact simulations represent one of the most challenging areas of computer-aided engineering (CAE). Unlike quasi-static analyses, these simulations must account for the extreme and dynamic conditions that occur during high-energy events: large plastic deformations, rapid loading at high strain rates, complex and evolving stress states, and progressive degradation of material stiffness that leads ultimately to fracture.
A predictive material model for crashworthiness does far more than indicate the point at which a component will yield. It must describe the full sequence of events from initial yielding, through hardening and potential localization, to damage initiation and post-initiation softening, and finally to complete loss of load-carrying capacity. This requires models that combine rate-dependent plasticity, anisotropy, and stress-state-dependent fracture behavior.
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SAMP-1 and GISSMO Damage Models
Two advanced LS-DYNA material models widely adopted for the purpose of accurately capturing material behavior for crash and impact simulations are:
- SAMP-1 (Semi-Analytical Model for Polymers - 1): Initially developed for metals and later adapted for other materials, SAMP-1 captures elastic–plastic behavior with strain-rate sensitivity, incorporates anisotropic yield surfaces, and uses a unified damage law that applies across all stress states. Once damage initiates, stiffness and strength progressively degrade until the element is deleted from the simulation, allowing fracture to be represented in a physically consistent way.
- GISSMO (Generalized Incremental Stress-State dependent damage MOdel): A more flexible model that separates damage initiation and damage evolution for each stress state. This separation allows independent calibration of these phases for a range of loading paths, which can improve fracture prediction under complex crash loadings.
Both models require extensive, high-quality experimental data. In what follows, we outline relevant testing methodologies in detail, showing how they connect to the parameters in each model, and includes practical advice for calibration and validation.
Requirements for Crash and Impact Material Models
Beyond Quasi-Static Properties
Although quasi-static tensile and compression tests form the starting point for characterizing elastic modulus, yield strength, and strain-hardening behavior, they are insufficient for crash applications. Automotive and aerospace crash events often involve strain rates of 100 s⁻¹ or more, which can significantly alter material response. Under such conditions:
- Flow stress increases with strain rate in most metals and polymers, a phenomenon known as strain-rate hardening.
- Adiabatic heating from rapid deformation can locally reduce ductility and accelerate fracture.
- Fracture strain varies not only with rate but with the stress triaxiality, meaning that identical strain levels may cause failure under one stress state but not under another.
For this reason, a crash-oriented characterization program must go beyond static data. It should include multiple decades of strain rate, a range of stress states from shear to biaxial tension, and measurements of both the onset of damage and the progression to complete failure. The aim is to build a dataset that reflects the actual operating envelope of the component in service.
Stress State and Damage Modeling
Stress triaxiality, defined as the ratio of hydrostatic stress to von Mises equivalent stress, plays a decisive role in ductile fracture. Both SAMP-1 and GISSMO rely on its proper characterization, but they differ in how they use it.
In SAMP-1, a single unified curve relates fracture strain to triaxiality across all loading modes. GISSMO, on the other hand, allows a separate curve for each stress state, giving more freedom but requiring more data. In either case, the test plan must cover:
- Low triaxiality: shear-dominated loading, important for predicting failure in shear panels or weld seams.
- Medium triaxiality: smooth tensile tests, representing common uniaxial tension states.
- High triaxiality: notched tensile tests, which simulate constraint-induced fracture.
- Negative triaxiality: compression-dominated loading, relevant for crushing components.
By varying specimen geometry and loading configuration, these stress states can be generated and measured, providing the necessary input for damage modeling.
Testing for SAMP-1
Overview of SAMP-1 Parameters
The LS-DYNA MAT_187 implementation of SAMP-1 requires:
- Elastic constants: Young’s modulus and Poisson’s ratio, generally assumed rate-independent.
- Plastic flow curves: True stress–true strain data from quasi-static through high-rate testing.
- Yield surface definition: Capturing shear, compression, and tension behavior for anisotropic or asymmetric materials.
- Damage initiation curve: Equivalent plastic strain at fracture versus stress triaxiality.
- Damage evolution law: Describing the rate at which stiffness and strength decay after initiation.
- Failure criterion: Conditions under which elements are deleted from the simulation.
These parameters work together: flow curves define the hardening, the yield surface constrains the allowable stress combinations, and the damage law dictates how the material transitions from intact to failed.
Quasi-Static Elastic–Plastic Properties
Quasi-static tests provide the baseline from which rate effects are measured. A typical program includes:
- Smooth tensile tests at very low strain rates (0.01–1 s⁻¹) to determine modulus, yield strength, and plastic flow.
- Unloading tests to measure elastic recovery in the plastic range, aiding in volumetric plasticity modeling.
- Density measurements, using standards such as ASTM D792, to establish mass properties for simulations.
This baseline ensures that any observed differences at higher rates can be attributed to rate sensitivity rather than testing artifacts.
Yield Surface Definition
Accurately modeling yield across multiple loading paths requires more than just tensile data. Shear tests provide yield stress at low triaxiality, while compression tests — including combined-loading compression fixtures — capture behavior at negative triaxiality. Together with tensile data, these populate the yield surface in three-dimensional stress space, enabling SAMP-1 to predict initial yielding for arbitrary load paths.
Strain-Rate Sensitivity
The strain-rate dependence of the flow curve is established from tensile tests over several orders of magnitude in rate. For SAMP-1 calibration, this often includes:
- Quasi-static and intermediate rates (0.01–1 s⁻¹) on standard servo-hydraulic machines.
- High rates (10–100 s⁻¹) on specially configured servo-hydraulic machines or very high rates (up to 1000 s⁻¹) on servo-hydraulic high-speed tensile systems that apply a programmed displacement pulse to the specimen.
In the high-rate setup, local strain is measured with high-speed optical techniques such as DIC or high-speed video, synchronized with load measurement to produce accurate true stress–true strain curves even beyond uniform elongation. The data from these rates are fit to constitutive laws like Cowper–Symonds, ensuring that simulations capture realistic rate-hardening effects. For a more accurate yield surface calibration, testing at different rates for all triaxiality states is recommended, especially when testing polymers.
In essence, the final testing input for the model is a table containing failure/yield curves that define the respective surface. Typically, the calibration process consists of first generating the quasi-static curves, then scale-adjusting these for increasing strain rates across different modes of deformation based upon the rate dependency results from tensile testing. Such an approach works well for metals, but poorly for polymers since the scaling factors are not constant along the triaxiality range.
Damage Initiation and Evolution
In SAMP-1, damage initiation is determined by the equivalent plastic strain at fracture for each stress state. This is obtained by combining experimental fracture observations with inverse finite element analysis.
The evolution law then describes how quickly the material loses stiffness after initiation. Energy-based approaches integrate the area under the stress–strain curve after initiation; displacement-based approaches use the loss of load-carrying capacity over a measured displacement. In both cases, DIC is valuable for recording the local behavior without the noise introduced by grip slip or machine compliance.
Testing for GISSMO
Overview of GISSMO Parameters
GISSMO shares many requirements with SAMP-1 but treats damage initiation and evolution separately for each stress state. It also explicitly incorporates mesh-size effects, scaling fracture strain according to element length.
The required inputs are:
- Elastic–plastic flow curves for all relevant strain rates.
- Damage initiation curves for each stress state of interest.
- Damage evolution curves for each stress state.
- Mesh scaling parameters.
Quasi-Static and High-Rate Tests
The test suite for GISSMO is broader because each stress state has its own curve. It generally includes:
- Smooth tension for medium triaxiality.
- Notched tension for high triaxiality.
- Shear for low triaxiality.
- Compression for negative triaxiality.
- Biaxial tension for intermediate values around η ≈ 2/3.
At high rates, the same servo-hydraulic high-speed tensile systems are used. Each specimen type is tested across multiple strain rates so that the combined effects of rate and stress state are fully captured.
Calibration Strategy
Calibration proceeds by generating rate-dependent flow curves, extracting local fracture strains from DIC and inverse FEA for each stress state, fitting initiation and evolution curves separately, and applying mesh scaling laws. The result is a set of curves that together enable the model to predict fracture across a wide range of loading paths and element sizes.
Digital Image Correlation (DIC)
DIC has become a near-essential tool for crash-oriented testing. By capturing full-field displacement and strain data, it allows fracture strain to be measured at the exact point and moment of initiation. It also enables accurate determination of triaxiality from measured deformation fields and provides reliable data under high-speed conditions where traditional extensometers may fail.
Environmental and Anisotropy Effects
Materials used in crash-critical structures are often anisotropic, particularly rolled sheets and extrusions. To model directional fracture accurately, tests should be repeated at multiple orientations relative to the rolling direction. If crash conditions may involve elevated temperatures — for example, from under-hood fires — temperature-controlled testing is necessary to determine whether fracture strain decreases significantly.
Model Calibration Stages
SAMP-1 Calibration Stages
- Fit elastic constants from low-rate data.
- Generate flow curves across rates and fit to a rate law.
- Define the yield surface from shear, compression, and tension data.
- Build a unified damage curve from fracture data across stress states.
- Fit the damage evolution law from post-initiation data.
- Validate with structural crash tests without further tuning.
GISSMO Calibration Stages
- Generate flow curves across rates.
- Determine fracture strain for each stress state.
- Fit separate damage initiation curves for each state.
- Fit evolution damage curves for each state.
- Apply mesh scaling laws.
- Validate against component-level crash tests.
Structural Validation
Validation at the structural level ensures that the calibrated material model behaves correctly in realistic geometries. Typical validation components include axial crush tubes, three-point bend beams, and hat-section columns. Simulations are run with the calibrated material card, and results are compared to physical tests in terms of force–displacement curves, deformation patterns, and fracture locations.
Conclusion
Accurate crash and impact simulation depends on more than choosing an advanced damage model — it requires a carefully designed and executed test program that matches the model’s calibration needs. SAMP-1 offers the advantage of a unified damage law, which simplifies calibration and is often sufficient for many crash scenarios. GISSMO provides greater flexibility and potentially higher accuracy in complex loading situations by allowing separate treatment of initiation and evolution for each stress state, but at the cost of more extensive testing.
The common thread is the need for high-quality, multi-rate, multi-state experimental data. Servo-hydraulic high-speed tensile systems with optical strain tracking are well-suited to covering the strain-rate range of interest for automotive and aerospace crashes. Digital image correlation has emerged as a key enabling technology, ensuring accurate measurement of local fracture strains and post-initiation softening.
When integrated into a robust calibration and validation workflow, these testing methodologies provide the foundation for predictive crash simulations that can guide design decisions, reduce the need for costly prototypes, and improve safety outcomes. The investment in comprehensive characterization pays dividends in simulation reliability — and ultimately in the performance of the structures we trust to protect lives.
