A Visual Mo del for Blast Waves and Fracture by Michael Ne A thesis submitted in conformity with the requirements for the degree of Master of Science Department of Computer Science University of Toronto c Copyright by Michael Ne A Visual Mo del for Blast Waves and Fracture Michael Ne Department of Computer Science University of Toronto Abstract Explosions generate extreme forces and pressures They cause massive displacement deformation and breakage of nearby ob jects The chief damage mechanism of high ex plosives is the blast wave which they generate A practical theory of explosives blast waves and blast loading of structures is presented This is used to develop a simplied visual mo del of explosions for use in computer graphics A heuristic propagation mo del is develop ed which takes ob ject o cclusions into account when determining loading The study of fracture mechanics is summarized This is used to develop a fracture mo del that is signicantly dierent from those previously used in computer graphics This mo del propagates cracks within planar surfaces to generate fragmentation patterns Visual re sults are presented including the explosive destruction of a brickwall and the shattering of a window iii Acknowledgements It is a pleasure to write acknowledgements at the end of a body of work First of all it gives you a chance to thank the p eople that have made the work p ossible Second it indicates that the work is nally done To b egin I would liketothankmy sup ervisor Eugene Fiume His insightcontributed greatly to this work and his passionate nature was an imp ortant source of inspiration My second reader Michiel van de Panne provided thoughtful and thorough feedback that signicantly improved this thesis More than this he made himself available throughout this work to answer my numerous questions I am also grateful to James Stewart and Demetri Terzop olous for useful discussions My fellow students in DGP provided imp ortant help during this work and also made DGP a fun place to b e Id like to thank some wonderful friends for providing an imp ortant source of distrac tion Whether it was late night stories of Taiwanese pop stardom driving across the continent with me to jump in the o cean or just getting me out of the lab for a few hours thanks for b eing there Finallytomy family Mom Diane Grandma Eunice Grampa Ken and Chris tine sister for years of loveand supp ort how can I begin to thank you This work was nancially supp orted through a Post Graduate Scholarhsip from the Natural Science and Engineering Research Council v vi Contents Intro duction Motivation Comparison to Conventional Animation Contributions of This Work A Practical Theory of Explosions Intro duction Dening an Explosion A Picture of an Explosion Damage Mechanisms of Explosives Detonations The ZND Mo del of Explosions The RankineHugoniot Relations Mo delling Explosions The Mathematical Approach Hydro co des Mo delling Explosions The Blast Curve Approach Scaling Equations for Predicting Peak Static Overpressure The Pressure Pulse Surface Eects Transp ort Medium Other Damage Mechanisms The Interaction of Blast Waves and Structures vii General Picture Small Blast Wave Large Ob ject Reections Dynamic Loading Lump ed Mass Ob ject Mo dels PressureImpulse Diagrams Primary and Secondary Missiles Solving for Ob ject Motion Mo delling Glass Blast Wave Mo del Determining a Mo delling Approach Selection of aWave Mo del Geometry Mo del General Mo del Prop erties QuasiStatic Mo delling User Control Blast Curves Elements of the Mo del Panels Ob jects The Simulator Blowing Up aBrick Wall A Heuristic Propagation Mo del Intro duction Propagation Mo del Basic Idea Building the Data Testing viii Mo delling Fracture Intro duction The Physical Basis of Fracture Background Denitions Fracture Mechanics Fracture Typ es Fast Fracture Material Flaws Wave Eects Crack Propagation Previous Mo dels of Fracture A New Fracture Mo del Basic Algorithm Bit Bucket FragmentTracing Results and Algorithm Enhancements Blowing Out a Window Tessellation Sampling and Panel Denition Inertial Tensor Centre of Mass Results A Comparison to Exp erimental Results Future Work Conclusions and Future Directions Improvements and Extensions to the Base Mo del Geometry Improvements to the Fracture Mo del Conclusion ix Bibliography x List of Figures The explosion of a spherical charge of TNT Detonation is initiated at the centre of the charge The detonation wave spreads outwards until it reaches the airexplosive b oundary Most of the energy and released gas is forced outwards as the primary blast wave Some of the waves energy is reected back towards the middle This wave b ounces o the centre of detonation and travels outwards again eventually forming the secondary blast wave The secondary wave is signifanctly less powerful than the primary wave Primary fragments consist of pieces of the explosives casing which are accelerated outwards Secondary fragments are nearby ob jects which the blast wave accelerates outwards Note that secondary fragment is placed abnormally close to the explosive in this diagram for illustrative purp oses ZND Mo del of a detonation frontmoving through a section of explosive Sho ck front Hugoniot curve and Rayleigh line Detonation fronthugoniot curve and Rayleigh line Hugoniot curves and Rayleigh lines including a reaction progress variable A comparison of the Bro de and Henrych equations to exp erimental re sultsfrom Pressure pulse as a function of time Impulse as a function of time approximated bytwo dierent triangle pulses Pressure pulses at four dierent radii xi When a blast wave strikes an ob ject it reects o it diracts around it and generate stress waves in it These three waves with their correct directions are shown here for a blast wave striking a rectangular ob ject Coecient of reection versus angle for three dierent pressures Notice that C R increases at the mach stem transition from Pressure prole versus time for the front side and rear faces resp ectively of a rectangular prism shap ed ob ject Resistance versus Displacement PressureImpulse diagram to determine damage threshold Translatory Pressure versus Time S T The blast curves for static overpressureP S and scaled pulse p erio d W as a function of scaled distance Z from These curves are for shp er ical TNT charges explo ded in air at ambient conditions The blast curves for scaled wavevelo cityU and dynamic pressure q s as a function of scaled distance Z from These curves are for shp erical TNT charges explo ded in air at ambient conditions r as a function of b oth angle of incidence The reection co ecientC and static overpressure from Each curve corresp onds to a sp ecic static overpressure bar as lab elled The brick pattern used for the brick wall Eight equally time spaced frames from an animation of a brickwall blowing apart Frontview Images are ordered from left to right Six equally time spaced frames from an animation of a brickwall blowing apart View p oint is b elow the wall lo oking up Images are ordered from left to right .