Project 1-2: Simulating Fracture and Penetration

Principal Investigator: Adrian Lew (Stanford)

Understanding the effects of ballistic impact of ammunition or shrapnel on human soft tissues has the potential to aid medical professionals in treating battlefield injuries, planning reconstructive surgery, and understanding more about wound healing processes. In addition, this knowledge can be used to evaluate various materials and designs for ammunition and armor. Human testing of this type is of course impractical. Blocks of alternative tissue simulants, called ballistic gels, are used instead.

Constructing computer simulations of material behavior under shock or ballistic impact is especially difficult because complex changes occur rapidly. A soft material such as a polymer or ballistic gel absorbs and dissipates energy from the impact, deforms, and cracks, in less than a few milliseconds. Building a computer simulation that captures all of these changes requires repeatedly solving millions of equations to create a series of “snapshots” taken at the rate of millions of frames per second and extending over several milliseconds. Each change affects the changes after it, and physical effects interact to alter the course of events. In addition, each snapshot comprises millions of small sections (finite elements) of a structure, each interacting with and affecting the behavior of the adjacent sections. The number of computations required to construct a realistic simulation can tax the resources of even the best high performance computers. Thus, it is necessary to frame the problem and program the computational codes in a way that uses computing resources efficiently, without sacrificing accurate results.

AHPCRC researcher and assistant professor Adrian Lew and graduate students Raymond Ryckman and Ramsharan Rangarajan (mechanical engineering department, Stanford University), are working with AHPCRC staff scientist Mark Potts (High Performance Technologies, Inc.) to create and adapt methods for modeling the evolution of domains (regions with uniform properties) and crack paths so that they function in a parallel processing environment.

The group is devising methods to simulate soft materials undergoing fracture and penetration. When they began their work, there were no existing simulation methods that were sufficiently robust to carry out accurate calculations over the time scale of an actual impact event. Because of the computational resources needed for such an endeavor, any computer codes would have to be scalable; that is, the codes would need to run well on any number of available processors. The group needed to develop algorithms for complex motions and interactions between the projectile and the target that would work well in such an environment.

At present, a model is being constructed for the effects of a bullet hitting a ballistic gel. Ballistic gel simulations under development include shock, penetration, and contact effects, and the way the gel absorbs energy from an impact. Lew foresees future efforts that incorporate aspects of material modeling: how does impact with tissue or a polymer differ from impact with wood, metal, or concrete? What happens when friction-generated heat partially melts the polymer or gel? What are the effects of a projectile tumbling within a fissure? How does a network of cracks form and spread? The Stanford group is planning to compare their simulations with experimental studies conducted at the University of California at Berkeley at a later stage of the project.

Breaking the Lock-Step
The AHPCRC group is currently working on a parallel code for nonlinear solid dynamics that incorporates an algorithm capable of asynchronously constructing the part of each snapshot corresponding to different spatial locations (parallel asynchronous time integration, or pAVI). This approach allows each section of a large problem to be computed at the speed and degree of detail that best suits the complexity of that section. This differs from conventional problem-solving approaches, in which differential equations for each of the millions of elements in a problem are integrated using the same time increments, using the same number of processors. Potts explains: “With the lock step approach, lots of computational time ends up getting devoted to solving nondescript sections of the problem using very small time steps where they otherwise could be solved using much larger time steps.”

For problems in which some sections are especially complex (e.g., complicated geometries, rapid shape changes), the time increments between individual calculations must be very small in order to capture the requisite degree of detail—in much the same way as high-speed video uses thousands of frames per second to capture the flight of a bullet or the impact of a falling drop of water. Dividing the complex parts of the problem among several processors allows for frequent updates without slowing down the overall process. Simpler or less important sections of the problem that do not require this degree of detail can proceed with fewer updates (larger time increments between calculations) and occupy fewer processors. Thus, the pAVI approach reduces the need for trade-offs between accuracy and efficiency.

Redrawing the Boundaries
The mathematical approach taken by the AHPCRC group is based on numerical methods for solving partial differential equations, which track physical quantities that change continuously over time. A mathematical representation of a soft structure, such as a ballistic gel, is divided into many small elements, each of which changes shape in response to the simulated ballistic impact. As these elements stretch and bend away from their initial shape, the mathematics describing them becomes more complex. At some point, the calculations must pause, and a process known as “remeshing” draws new reference gridlines onto the deformed soft body, based on localized displacement and velocity fields. This procedure may need to be repeated many times during the course of a simulation, and it slows the calculation process considerably.

The Stanford group uses an adaptive remeshing algorithm based on an immersed boundary method. This method, which is often used to simulate solid bodies moving through fluids (or gels, in this case), uses a mesh that encompasses the domain of the problem while only approximately following the boundaries between the soft body and the solid body passing through it. This makes generating the mesh much easier at the expense of complicating the imposition of boundary conditions. Implementing this concept for a three-dimensional problem is one of the major areas of research for this project, because of the ability of this method to overcome many of the difficulties associated with automatic mesh generation.

Ongoing Work
When many calculations are going on all at once, it is necessary to build elements into the computer code that keep the calculations on track and to weed out solutions that are mathematically correct, but physically meaningless. Toward this end, the group is investigating a new approach to control the high-frequency velocity oscillations that appear with the adoption of explicit time discretizations such as AVI. These oscillations are enhanced in the presence of shocks, typical of penetration problems or contact problems. This is critically important for modeling the amount and spatial distribution of energy absorbed by a ballistic gel when a bullet penetrates it.

Raymond Rickman is working on a rigid bodies algorithm that will model the contact between a bullet and a ballistic gel. He has begun parallel runs with the algorithm using Army computing clusters, and has shown that the problem is scalable. Ramsharan Rangarajan has demonstrated that a new immersed boundary method for solid mechanics with nonhomogeneous boundary conditions converges quadratically (a measure of how fast a calculation reaches a solution), as required by many solid mechanics problems. This algorithm is intended to be part of the automatic remeshing capability for the penetrating bullet problem.

Simulations for rigid body impact on elastic bodies have been performed using as many as 128 processors and 3 million degrees of freedom. Simulations for penetration have been started, using a model that incorporates a small pre-existing hole in the elastic medium. As the work progresses further, a penetration algorithm will be added so that the pre-opened hole will not be necessary. A self-contact algorithm is also in the works, which will enable the simulation of the cavity collapsing after the bullet passes through.

The AHPCRC group plans to adapt their method to model the rupture of the material by the projectile. They will also develop the first parallel version of the penetration problem in gelatin that will run scalably on HPC platforms. This year, they will perform the first parallel-explicit contact runs for the bullet.

Source: AHPCRC Bulletin, Vol. 1, Issue 3 (2009)