Hamilton's equations with Euler parameters for hybrid particle-finite element simulation of hypervelocity impact

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Shivarama, Ravishankar Ajjanagadde

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Hypervelocity impact studies (impact velocities > 1 km/sec) encompass a wide range of applications including development of anti-terrorist defense and orbital debris shield for the International Space Station (ISS). The focus of this work is on the development of a hybrid particle-finite element method for orbital debris shield simulations. The problem is characterized by finite strain kinematics, strong energy domain coupling, contact-impact, shock wave propagation and history dependent material damage effects. A novel hybrid particle finite element method based on Hamilton’s equations is presented. The model discretizes the continuum of interest simultaneously (but not redundantly) into particles and finite elements. The particles are ellipsoidal in shape and can translate and rotate in three dimensional space. Rotation is described using Euler parameters. Volumetric and contact impact effects are modeled using particles, while strength is modeled using conventional Lagrangian finite elements. The model is general enough to accommodate a wide range of material models and equations of state.