Simulating a vehicle's crashworthiness is one of the most difficult, yet crucial, challenges facing automotive engineers today. The physical phenomena that constitute a vehicle crash are extremely complex and the time frame of the event is brief. Material deformation occurs in a split second — and has life-or-death consequences.
The intent of crashworthiness simulation is to model, as realistically as possible, exactly what happens during a vehicle impact. What happens is that parts and assemblies crush, buckle, twist, shear, stretch and tear. Acceleration acts on the bodies of vehicle occupants. An analysis model that accurately simulates the physics involved will contribute enormously to vehicle safety.
And it can contribute cost effectively. Consider that a physical crash test can happen only once, but a valid crash model can run hundreds of simulations at a fraction of the expense.
New technologies for crashworthiness simulation are continually being invented by some developers of FEA software. At ABAQUS, we've had the opportunity to collaborate with researchers at BMW Group on a number of technical initiatives in this area. Here's a look at some of the tools we've developed to offer improved predictions of vehicle structural crashworthiness and occupant safety. Most of these developments are supported by advances in high-performance computing.
Material Failure Modeling
BMW and other automotive manufacturers are actively exploring the potential of new structural materials to reduce vehicle weight and improve crashworthiness. The materials include various aluminum and magnesium alloys, as well as advanced high-strength steels. But these materials sometimes fail differently than the conventional portfolio of automotive structural materials.
Take aluminum, for example. Experimental studies show that metal sheets and thin-walled extrusions made of aluminum alloys may undergo ductile failure due to nucleation, growth and coalescence of voids in the material. Cracks within shear bands may cause shear failure. Other failures are caused by localized instabilities.
To give engineers a better understanding how these newer structural materials fail during crash-loading conditions, we have implemented a general framework for material failure modeling into ABAQUS software. During crashworthiness simulation, the material stiffness is degraded progressively after damage initiation in accordance with the specified damage evolution response. Engineers can specify one or more damage-initiation criteria — including ductile, shear, forming limit diagram, Müschenborn-Sonne forming limit diagram and Marciniak-Kuczynski criteria.
BMW's researchers have determined that the Müschenborn-Sonne forming limit diagram criteria is particularly useful for predicting material necking for their applications. At deformation levels outside the forming limit, the material will likely exhibit failure such as necking or tearing. And the advantage of using the Müschenborn-Sonne forming limit diagram is that it takes into account the effects of the deformation path on the limit strains of sheet metals, whereas the traditional forming limit diagram is valid only for linear strain paths.
With ABAQUS, crash analysts can also incorporate manufacturing effects into their simulations. By capturing strain that actually exists in the sheet metal before a crash occurs, the simulation is able to better reflect physical reality (see Figures 1a-1d). The damage framework in ABAQUS is applicable across a wide range of industries. For example, it can also be used in a manufacturing setting to simulate metal cutting.
Automotive assemblies often contain thousands of spot welds. The manner in which spot welds undergo damage and fail during a crash can obviously influence a vehicle's structural crashworthiness. One of the most useful tools we have developed for crashworthiness simulation in ABAQUS is a mesh-independent fastener to simulate spot welds.
Fastener technology in ABAQUS has evolved over several years of collaboration with customers. A fastener is a computationally efficient 1D idealization that simulates the behavior of a “point-to-point” connection between two or more surfaces. A typical fastener joining two surfaces consists of a connector element plus two constraints, called distributing couplings, that identify the connecting surfaces. Engineers can draw from the extensive library of kinematic and constitutive behaviors that are available with our connector elements to assemble any type of fastener they can imagine. Deformable spotwelds are normally modeled using a bushing-type connection to describe the kinematics. Either elasticity or rigid plasticity with damage and failure describe the constitutive response.
What makes the fastener mesh independent is the ability of distributing couplings to “smear” the connection across a region of FE mesh (see Figures 2a and 2b). Traditionally, each fastener would be identified with a specific node location, so all the spot-weld locations would have to be redefined whenever the model was remeshed. Mesh-independent fasteners contribute to modeling efficiency and save a great deal of time for engineers in many industries. For example, mesh-independent fasteners are also used to simulate rivets in the aerospace industry.
Looking ahead, automotive manufacturers are investigating the benefits of using structural adhesives to join assemblies. Adhesive bonds may offer more strength and better noise management than spot-welded joints. To simulate how structural adhesives perform during a vehicle crash, engineers can use a feature in ABAQUS software called cohesive elements, which model the deformation and failure of adhesive joints where bonded parts interface. ABAQUS also supports innovative applications for automotive composites and is currently evaluating several composite failure models for crash analysis.
To predict what will happen to the occupants of a vehicle during a crash, engineering analysts model the interaction of crash dummies with automotive seats, seat belt restraint systems and supplemental air bags. In ABAQUS, the seat belt restraint system is modeled using a series of specific connector elements. These are 1D idealizations that represent the particular kinematics of connection points in the restraint system. One is a special pulley-type connector called a slipring.
The slipring connector element allows a line or cable to change its direction of travel as though it were moving around a pulley. The slipring models the behavior of the seat belt during a crash, as loading from the displaced dummy model causes the belt material to flow and stretch across attachments. As Figure 3 shows, six slipring elements are used to model the seat belt, starting where the belt spools from the retractor device inside the B-pillar. Different connectors model the behavior of the seat belt retractor device and of the pretensioner.
Slipring connectors also have applications outside the automotive industry in fields such as civil engineering and offshore engineering, where they can be used to model cable systems.
In ABAQUS, the modeling of airbag supplemental restraints is based on the concept of surface-based fluid cavities. The surface of the airbag structure is defined with regular finite elements, but the fluid inside the bag is not meshed. Instead, the gas is defined by a constant pressure that propagates from an inflator and is felt instantaneously throughout the airbag. As the simulation progresses, deformation of the fluid-filled structure is coupled to the pressure of the contained fluid on the cavity boundary. Surface-based fluid cavities are also used in the manufacturing industry to model the blow molding process.
Like many FEA models, airbag models are validated by comparing simulation results with experimental data. The airbag manufacturer develops the product, performs physical tests and measures the physical response of the system. A simulation is then devised to model the physical test. The more simulation results correlate with experimental results, the more confident the manufacturer can be in using the model to predict the performance of airbag designs.
Figure 4 shows results from a simulated impactor test of a deployed side-curtain airbag. (The airbag model was provided by Autoliv GmbH.) In this simulation, the airbag is divided into 18 chambers to approximate the nonuniform distribution of gases and the pressure gradients observed during unfolding. Each chamber is modeled as a surface-based fluid cavity. The airbag skin is represented by membrane elements and uses a special fabric material model that is available in ABAQUS. The impactor is modeled as a rigid body with a total mass of 7.2 kg and an initial velocity of 4,500 mm/s toward the deploying airbag. The results of the simulation show close correlation with physical tests.
To better support crash modeling and similarly complex simulations, ABAQUS has advanced its parallel computing speed using the domain decomposition method. The idea is to divide the simulation model into separate domains and run each domain on a different CPU. Where domains connect, there is an exchange of information to ensure consistent computational order. Ideally the model is decomposed so every CPU is doing approximately the same amount of work (see Figure 5).
In the case of crash simulation, which involves significant buckling behavior, very slight numerical differences arising from the order in which information is exchanged between domains can lead to noticeable inconsistencies in results when the same model is run using different numbers of domains. Our implementation of parallel computing takes extra steps to minimize these effects and to provide repeatable results. And with repeatability comes confidence that a simulation is accurate.