Hybrid particle‐element method for an unstructured hexahedral mesh

Abstract

SUMMARYHamiltonian models of high-velocity impact dynamics, based on a hybrid particle-element kinematic scheme, offer an energy conserving description of general contact-impact, perforation, and fragmentation physics with applications in a number of important engineering fields. Published work on these models has considered only a uniform finite element mesh, requiring curved surfaces and many target and projectile geometries to be represented in an approximate fashion. In recent research, the authors have developed a new formulation suitable for application to any solid model described by an unstructured hexahedral mesh. The formulation incorporates a new algorithm, which constructs an ellipsoidal particle discretization of the mass distribution described by a general hex mesh and a new density interpolation suitable for use with general ellipsoidal arrays whose particles vary in mass, shape, and spatial orientation. Application of the method in the simulation of high-velocity impact problems shows good agreement with experiment, for both smoothly graded and deliberately distorted hexahedral meshes.

Nonholonomic Hamiltonian method for meso-macroscale simulations of reacting shocks

“…They range from weighted residual solution methods for partial differential equations (at the continuum scale) to discrete Hamiltonian methods (at the molecular scale). Extending previous research by the second author and co-workers [1,2], this research is developing the first unified approach to multiscale reacting shock physics simulation.…”

“…generalized conservative and nonconservative forces, true and quasi coordinates, holonomic and nonholonomic systems, virtual work, etc.) [3] as well as previous work by the second author and co-workers extending general Hamiltonian formulations to shock physics applications, in both Eulerian and Lagrangian frames [1,2]. Interested readers are referred to the later three references (and numerous papers cited therein) for a more detailed description of the general method.…”

“…The internal energy evolution equations are again nonholonomic constraintsU =U wrk +U irr (5) and in this case include mechanical power and irreversible entropy production terms. The degenerate Hamilton's equations for the internal energies determine the Lagrange multipliers associated with the constraints, and a virtual work expression is introduced to account for external loads [2]. The final evolution equations for the particle positions, internal energies, and momenta take an explicit state space form.…”

“…Since the examples model shock compression, tensile fracture is not simulated. However, the hybrid-particle element method used at the mesoscale has been validated in three dimensional simulations of shock fragmentation processes [2]. Fracture and fragmentation at the macroscale may be represented using a history state variable dependent constitutive model [8].…”

“…The simulation results show pronounced temperature peaks in the void containing regions. Note that the hybrid-particle element method used at the mesoscale eliminates the need for legacy contact-impact modeling methods (such as master-slave nodes) by representing all contact-impact physics using singular particle kernels [2]; contact forces are thereby determined from the particle pressures, and penalty springs are avoided. The second hot spot (mesoscale) model employs mixture theory to simulate mixed solid-gas particle thermodynamics.…”