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Model Behavior

SwRI researchers are developing an advanced computer code to simulate high-velocity impact

Computed results of a complex projectile impacting a layered target at 2,000 meters per second (m/s).

By Gordon Johnson, Ph.D.

During the past 50 years there has been an ever-increasing effort to develop accurate computer-simulation capabilities for a wide range of physical events. Simulations can often be performed more quickly and inexpensively than experiments. They can look inside events to provide a clear understanding of the physical processes that occur and can be applied to events for which experiments cannot be performed. Also, the demonstrated ability to accurately simulate events on the computer generally indicates that an event is well understood.

One area of particular interest is the high-velocity impact of projectiles onto targets. Many of these applications are military-related, with projectiles ranging from small-caliber bullets to large-caliber tank ammunition, and targets from body armor for soldiers to heavy armor for large tanks. For armor designs, for instance, it is clear that it would be much more efficient for the designer to evaluate different concepts and materials on the computer, rather than the much slower and more expensive process of building and testing each concept. Closely related are the much-higher-velocity impacts that occur when space debris impacts Earth-orbiting structures and when meteorites impact the Earth.


Researchers in Southwest Research Institute's Computational Mechanics group, located in Minneapolis, are advancing the EPIC (Elastic-Plastic Impact Computations) computer code to simulate these high-powered events. Development of the EPIC code was begun by the author in the 1970s, and work to enhance and advance the code has continued since then. EPIC development has been funded by numerous Department of Defense and Department of Energy laboratories, and it is available to U.S. government organizations and their contractors. Although much progress has been made, researchers continue to address new applications and materials for the code.

Conversion of distorted finite elements into meshless particles.

For these applications, numerical algorithms are mathematical descriptions of the dynamic equations of motion and the response of materials under intense loading conditions. They are cast in a form of specific equations that can be efficiently processed on a computer. There are three important requirements for the numerical algorithms for high-velocity impact computations. They must be able to accurately represent the high distortions, the boundaries (edges of the materials) and interfaces (where two or more boundaries meet and contact one another), and the response of the materials (including failure) subjected to large strains, high strain rates, high temperatures and high pressures. The EPIC code is based on a Lagrangian formulation, which means that the grid is attached to the material. This allows for a good definition of boundaries and interfaces because the grid is attached to the boundaries and moves along with the movement of the boundary. In contrast, an Eulerian formulation allows the material to pass through a fixed grid, producing a loss of accuracy at boundaries and interfaces because there is no grid attached to the boundary.

Dr. Gordon R. Johnson is program director of the Computational Mechanics Section, located in Minneapolis. The section is part of SwRI’s Mechanical and Materials Engineering Division. Johnson specializes in developing computational algorithms and material models for intensive loading caused by high-velocity impact and explosive detonation.

An Eulerian code can readily represent the high distortions, but for a Lagrangian formulation this provides a greater challenge. Historically, most Lagrangian approaches for high-velocity impact have been based on a finite-element formulation, where the elements that carry stress, strain, temperature and such are attached to nodes that carry mass, position and velocity. When the elements become highly distorted, the formulations tend to fail and special numerical procedures, which themselves introduce inaccuracies, are required to keep the computations running. More recently, meshless particle algorithms have been developed, and these algorithms can carry all variables such as mass, position, velocity, stress, strain and temperature at the nodes. These meshless particle algorithms can handle large distortions because they have variable nodal connectivity, which means that a node can acquire new neighbor nodes, which are used to determine strain rates and stress gradients as the solution progresses. Unfortunately, meshless particle algorithms are less accurate and less efficient than finite element methods.

Computed and experimental results of fragmentation resulting from impact of a tungsten projectile onto a steel target at 1,020 m/s.

One unique characteristic of the EPIC code is that it uses both finite elements and meshless particles, and it automatically converts distorted finite elements into meshless particles as the solution progresses [1]. This allows the mildly distorted regions of the problem to be represented with finite elements that run faster and more accurately than meshless particles. Thus, only the highly distorted portions of the problem are represented with particles. Initially the entire mesh is composed of elements, and particles are generated only as needed. The particles are attached to the adjacent element sides when they are generated. They can contact and slide on other element faces, and they can interact with particles of other materials.

One computation that illustrates the capabilities of this approach involving the conversion of elements into particles is the impact of a tungsten core projectile with a copper sleeve against a target composed of three plates (aluminum, mild steel and a stronger steel). In this computation, many of the elements are converted into particles. There is contact and sliding between the three plates, and also between the copper sleeve and the tungsten core. Some of the particles attach to the adjacent finite elements, some slide on the finite elements, some fragment into multiple particles, some interact with particles of different materials, and some simply travel freely through space. It is clear that large distortions can be represented, and that the boundaries and interfaces are well defined.

Computed results of a tungsten projectile impacting a concrete target at velocities of 1,020 m/s (left) and 100 m/s (right).

Material models are very important for these high-velocity impact computations. Not only must models be available for a wide range of metals such as aluminum alloys, steel alloys and copper, but they must be available for other types of materials as well. Concrete, ceramics, fabrics and composites are common materials for targets, or armors, of interest. Generally, different models must be used for these different types of materials and constants for these models must be determined for each material. Determining constants requires numerous laboratory tests to quantify the effects of strain, strain rate, temperature and pressure for both strength and failure. This can be expensive and time-consuming, and the current EPIC library of almost 200 materials is the result of many years of effort.

A range of material models

In addition to developing the numerical algorithms, the EPIC team has developed models for a range of materials. Included are the Johnson-Cook models for strength [2] and failure [3] of metals, the Holmquist-Johnson-Cook model for concrete [4], the Johnson-Holmquist-Beissel model for ceramics [5] and the Johnson-Beissel-Cunniff models for fabrics and composites [6]. These models are intended to capture the important responses of the materials, but they are simple enough to be efficiently used in a computational framework. These models are widely used throughout the international computational community. Many of the current applications are concerned with protection of soldiers, vehicles and structures. Body armor is often composed of ceramic, composite and fabric materials; vehicle armor is often composed of metallic, composite and ceramics materials; and protective structures make extensive use of concrete.

Computed results of a jacketed projectile impacting a layered ceramic/aluminum target at 900 m/s.

As an example, SwRI researchers used the Johnson-Cook models for strength and failure to simulate a tungsten projectile perforating a steel plate. Metals can be very ductile, often experiencing strains well over 100 percent. The model formed a large number of different-sized fragments [7], and the computed distribution of fragment sizes was in good general agreement with experimental results. In a similar example with the same projectile, researchers used the Holmquist-Johnson-Cook concrete model because the target was concrete. Concrete is much weaker and less ductile than steel and the fragment size is much smaller than for the comparable velocity in the previous example. As the impact velocity is reduced, the fragment sizes become larger. It is clear that fragmentation is dependent on both impact velocities and materials. It is important to be able to predict the positions, velocities and masses of the fragments behind an armor or protective structure, such that the damage due to these fragments can be accurately assessed.

Another computation involved a jacketed projectile impacting a layered ceramic-aluminum target, which is representative of body armor. In this case, researchers used the Johnson-Holmquist-Beissel model. In this simulation a few major cracks formed in the ceramic and it broke into some large pieces. Generally, ceramics are very strong in compression, but much weaker in tension, and they exhibit little ductility. For this computation the ceramic failed in the finite elements and the conversion to particles occurred after failure, when the cracks began to open. Again, the Lagrangian nature of the approach provided a clear definition of the boundaries and interfaces.

Yet another instance where this technology proved valuable involved a hypervelocity impact of 6,150 meters per second, where an aluminum sphere impacted a thin aluminum plate. These high velocities are representative of the relative velocities that could occur in space, where the sphere represents space debris and the thin plate acts as a shield to break up the impacting projectile into a particulated debris cloud. The cloud then loads the next protected structure beneath the top plate over a large area. The response here is much different than for the lower ballistics velocities discussed previously. Even though the target plate is very thin, the high shock pressures and their reflections are much greater than the strength of the aluminum materials, and the sphere breaks into many small pieces. A more detailed analysis of this problem showed the computation was in good agreement with the fragment and temperature distributions observed in the experiment.[8]

Computed (left) and experimental (right) debris clouds from impact of an aluminum sphere onto a thin aluminum plate at 6,150 m/s.

Future work

Computational capabilities have been developed to the point that they can be very valuable for the design and analysis of systems involving high-velocity impact. Although there remains room for improvement to the numerical algorithms, a greater need is for material models representing the new materials that are being introduced into future projectiles and targets.


[1] Johnson, G.R. and R.A. Stryk. "Conversion of 3D Distorted Elements into Meshless Particles During Dynamic Deformation," International Journal of Impact Engineering, 28, 2003.

[2] Johnson, G.R. and W.H. Cook. "A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temperatures," Proceedings of Seventh International Symposium on Ballistics, The Hague, The Netherlands, 1983.

[3] Johnson, G.R. and W.H. Cook. "Fracture Characteristics of Three Metals Subjected to Various Strains, Strain Rates, Temperatures and Pressures," Engineering Fracture Mechanics, 21, 1985.

[4] Holmquist, T.J., G.R. Johnson and W.H. Cook. "A Computational Constitutive Model for Concrete Subjected to Large Strains, High Strain Rates and High Pressures," Proceedings of Fourteenth International Symposium on Ballistics, Quebec City, Canada, 1993.

[5] Johnson, G.R., T.J. Holmquist and S.R. Beissel. "Response of Aluminum Nitride (Including a Phase Change) to Large Strains, High Strain Rates and High Pressures," Journal of Applied Physics, 99, 2003.

[6] Johnson, G.R., S.R. Beissel and P.M. Cunniff. "A Computational Model for Composite Materials Subjected to Ballistic Impact," Proceedings of Second International Conference on Structural Stability and Dynamics, Singapore, 2002.

[7] Johnson, G.R., R.A. Stryk, C.A. Gerlach, T.J. Holmquist and N.L. Rowe. "A Quantitative Assessment of Computational Results for Behind Armor Debris," Proceedings of 23rd International Symposium on Ballistics, Tarragona, Spain, 2007.

[8]Beissel, S.R., C.A. Gerlach and G.R. Johnson. "Hypervelocity Impact Computations with Finite Elements and Meshfree Particles," International Journal of Impact Engineering, 33, 2006.

Questions about this article? Contact Johnson at (612) 460-488 or (210) 522-5625, or

Published in the Spring 2009 issue of Technology Today®, published by Southwest Research Institute. For more information, contact Joe Fohn.

Spring 2009 Technology Today
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