Simulating hypervelocity impact and spacecraft breakup with discrete elements

The impact of a piece of space debris and an orbiting satellite usually results in the breakup and fragmentation of the satellite into thousands of new fragments of space debris. This complex phenomenon is being studied with a unique type of numerical simulation based on millions of small particles.

The increasing number of spacecraft launches in recent years continues to exacerbate the risks space debris poses to satellites around Earth’s orbits. A worst-case scenario, known as the Kessler syndrome, predicts a cascade of collisions as space debris impacts spacecraft causing catastrophic breakups. The fragments generated from such collisions join the growing quantity of space debris, each event further increasing the probability of more collisions. This ever-worsening cycle ends with certain Earth orbits rendered unusable for generations.

One key way of preventing the Kessler syndrome from becoming a reality is to better understand and model the complex phenomena that occur when spacecraft are hit by space debris traveling at a relative speed of up to 15,000 meters per second. A hypervelocity impact (HVI) is incredibly energetic, and even millimeter- to centimeter-sized debris fragments can knock out a small satellite. Larger impacts cause not only localized damage, but can also cause the breakup of large satellites.

When simulating HVI and satellite breakups with numerical methods, it can be challenging to accurately capture the transition of a material from a solid to a fragmented state with traditional continuum-based simulation codes such as finite-element methods. At Fraunhofer EMI, we have developed a new type of simulation approach based on the interaction of many millions of discrete particles to simulate spacecraft fragmentation events. Our discrete element method code, called MD-Cube, performs exceptionally well in modeling the transition from solid to fragmented state that occurs the during a HVI collision.

Simulating with millions of particles

Our discrete-element-method-based simulation code MD-Cube has been specially developed to accurately simulate fragmentation. This is achieved by using millions of small particles linked together by springs to create a solid material. The forces in the springs are collectively calibrated to approximate the macroscopic response of a given material. When the material is loaded, the springs fail upon reaching a predefined extension, leading to cracks and finally failure of the material. In this way, a natural and realistic fragmentation is achieved.

A key aspect of the success of MD-Cube in simulating fragmentation events is its highly developed parallelization scheme. MD-Cube is parallelized with the message passing interface (MPI) that allows the computationally intensive tasks of calculating particle interactions to be spread over hundreds of CPUs in parallel. The relative simplicity of particles as the fundamental building block of the simulation allows a huge number of particles to be used in a model, generally ranging in the tens of millions. This results in a very fine “resolution” of the simulated materials and allows the whole range of fragmented debris, from large chunks to dust-like particles, to be accurately reproduced.

Explosive fragmentation under hypervelocity impact

The explosive fragmentation seen in experimental HVI images is well captured and reproduced in MD-Cube simulations. Aluminum, for example, fails in a brittle manner in the immediate vicinity of a hypervelocity impact, leading to the formation of thousands of fragments. The MD-Cube simulations capture this well, particularly the wide-ranging distribution of fragment sizes.

While the majority of simulation parameters for a given material can be derived from generic material properties such as the bulk modulus, one simulation parameter needs to be calibrated based on HVI experimental data. We perform this calibration by directly comparing the shape, size and velocity of the fragment cloud between experimental and simulated images. We also calibrate the low-velocity (non-hypervelocity) mechanical behavior via comparisons with ballistic limit penetration studies.

Apart from isotropic aluminum, MD-Cube is currently also able to simulate anisotropic materials such as carbon-fiber-reinforced polymers (CFRP). 

CFRP is an important material in modern satellites, often replacing aluminum in many structural components of newer spacecraft. We are able to simulate the orthotropic nature of CFRP by assigning different types of springs in different directions, corresponding to the material properties of the carbon fiber and epoxy matrix, respectively. This approach not only captures the orthotropic behavior, but the unique pattern of delamination and generation of long, thin fibrous fragments is also completely captured. The ability to accurately predict, not only the number and size of fragments, but also the shape is one of the many advantages of simulating satellite impacts with MD-Cube.

The road to modeling spacecraft breakups

With the end goal of understanding and modeling the breakup of spacecraft after impact with orbital space debris, we apply MD-Cube to a variety of spacecraft impact scenarios. A CubeSat can be simplified as a hollow cubic box of ten centimeters side length made with thin plates, and filled with a number of internal thin plate components. Using such a model, we demonstrated MD-Cube the ability of MD-Cube to handle large simulations of tens of millions of particles by studying the fragment distributions following various impacts such as a small sphere impacting a CubeSat or a two-CubeSats collision.

Resulting fragment distributions correspond well to existing empirical models such as the NASA Satellite Breakup Model when simulating aluminum satellites. Applying similar comparisons with CFRP satellites highlights known discrepancies in existing empirical models that could potentially be improved using simulation results.

Satellites in full detail, down to individual screws and electrical components, can be accurately and efficiently modeled in MD-Cube via a simple import from a CAD program. We discretized ERNST, a 12U nanosatellite currently under development at Fraunhofer EMI, with 13.5 million particles to perform parameter studies investigating the breakup of this particular satellite under a variety of impact conditions. For the time being, only a single material can be chosen for the entire satellite, but plans are being made to allow multi-material configurations as well.

The strengths of MD-Cube in simulating fragmentation allows realistic satellite breakup scenarios to be investigated to a level of detail not previously possible. We study the breakup and fragment distribution resulting from the impact of ERNST with space debris of various shapes (sphere, rod, disk) and sizes. Another interesting aspect that we study is the effect of impacts on different parts of the satellite and from different directions. The resulting fragment distributions are compared and analyzed.

We believe that numerical simulations that specialize in fragmentation, such as MD-Cube, are a powerful tool to study in-orbit satellite breakups. Unlike ground-based experiments, the range of conditions and sheer number of parameter studies that can be efficiently conducted make them invaluable for developing new and improved empirical models that can be used to understand the ever-changing orbital environment around our Earth.