Eric P. Fahrenthold

An improved hybrid particle-element method for hypervelocity impact simulation

An improved hybrid particle-finite element method has been developed for hypervelocity impact simulation. The method combines the general contact-impact capabilities of particle codes with the true Lagrangian kinematics of large strain finite element formulations. Unlike some alternative schemes which couple Lagrangian finite element models with smooth particle hydrodynamics, the present formulation makes no use of slidelines or penalty forces.

Hamilton’s Equations With Euler Parameters for Rigid Body Dynamics Modeling

A combination of Euler parameter kinematics and Hamiltonian mechanics provides a rigid body dynamics model well suited for use in strongly nonlinear problems involving arbitrarily large rotations. The model is unconstrained, free of singularities, includes a general potential energy function and a minimum set of momentum variables, and takes an explicit state space form convenient for numerical implementation. The general formulation may be specialized to address particular applications, as illustrated in several three dimensional example problems.

A hybrid particle-finite element method for hypervelocity impact simulation

Abstract Coupled particle-finite element methods have been suggested as an approach to modeling particular impact problems not well suited to simulation with conventional Eulerian, Lagrangian, or particle codes. An alternative hybrid particle-finite element technique has been developed, in which particles are used to model contact-impact and volumetric deformation while finite elements are employed to represent interparticle tension forces and elastic-plastic deviatoric deformation. The method has been implemented in a three dimensional code and applied to simulate representative hypervelocity impact problems.

Discrete Hamilton's equations for arbitrary Lagrangian-Eulerian dynamics of viscous compressible flow

Abstract A number of different arbitrary Lagrangian–Eulerian (ALE) formulations of continuum fluid and solid dynamics problems have been developed, to address applications where more conventional Lagrangian or Eulerian modeling techniques are difficult to apply. In general these ALE formulations are based on finite difference or weighted residual finite element solutions of the partial differential equations for the system. An alternative, energy based ALE model for fluid dynamics simulations may be obtained, by direct application of Hamiltons canonical equations to a finite element discretization of an open, deforming control volume. Formulated in terms of convected coordinates and incorporating an adaptive mesh scheme, this modeling approach yields a simple but general description of viscous compressible flows. Numerical application of the method demonstrates accurate results in the solution of several shock problems, whether the calculations are performed using a Lagrangian, an Eulerian, or an ALE mesh.

Eulerian Bond Graphs for Fluid Continuum Dynamics Modeling

The development of high resolution, general purpose models of viscous, compressible flows is extremely difficult with existing system dynamics modeling tools. Published work admits to significant limitations, with regards to the treatment of flow geometry, inertia effects, or mass and energy convection. Combining a finite element discretization scheme with a bond graph based model formulation procedure provides a very general purpose tool for continuum fluid system modeling.

Thermodynamics of continuum damage and fragmentation models for hypervelocity impact

Abstract General numerical models of hypervelocity impact problems must account for finite strain deformation, isochoric rate dependent plasticity, volumetric and deviatoric damage, and complex energy domain coupling. Incorporating all these effects into current damage and fragmentation models is difficult, given their limited thermodynamic framework. An alternative, systematic approach to the material model formulation process results in a general thermodynamic framework which can incorporate a variety of constitutive assumptions. Application of the method is illustrated by formulation of an elastic-viscoplastic damage model with finite strain kinematics, Grady-Kipp volumetric damage, Johnson-Holmquist deviatoric damage, and thermodynamic compuling through an entropy state. Hypervelocity impact simulations using the developed model show that predictions of fragment size and fracture surface area based on Grady-Kipp fragmentation theory vary significantly with the extent of plastic deformation, over a velocity range of five to ten kilometers per second.

Discrete Hamilton's equations for viscous compressible fluid dynamics

Abstract Lagrange’s and Hamilton’s equations are used extensively in numerical modeling of rigid body dynamics and continuum solid dynamics problems. The use of energy methods in viscous compressible flow problems has been by contrast rather limited, largely confined to the development of basic balance laws in partial differential equation form. However, finite element interpolation of the modeled flow field allows for the direct application of the discrete form of Hamilton’s equations to viscous compressible fluid dynamics in Eulerian frames. The resulting model is a true energy formulation, developed without reference to the partial differential balance equations which underlie conventional finite difference, weighted residual finite element, and finite volume methods.

Hamiltonian particle hydrodynamics

Abstract Particle-based hydrodynamics models offer distinct advantages over Eulerian and Lagrangian hydrocodes in particular shock physics applications. Particle models are designed to avoid the mesh distortion and state variable diffusion problems which can hinder the effective use of Lagrangian and Eulerian codes, respectively. However, existing particle-in-cell and smooth particle hydrodynamics methods employ particles which are actually moving interpolation points. The latter distinction has been emphasized in the more recent development of element-free Galerkin theory. As a result, general formulations of all of the aforementioned methods are based on the partial differential equation forms of the continuum balance laws which underlie conventional Eulerian and Lagrangian schemes. An alternative modeling methodology, based on the application of Hamiltons equations to a system of deforming physical particles, provides a fully Lagrangian, energy-based approach to shock physics simulations. Neither interpolations of field variables nor continuum balance laws are used to establish the state equations for the particle system. Mechanical and thermal interaction of the particles is accounted for by nonholonomic constraints which determine both particle entropy evolution and particle collision loads. Application of the method is illustrated by simulation of a wall shock problem.

A Lagrangian model for debris cloud dynamics simulation

Abstract A new modeling approach has been developed for computer simulation of hypervelocity impacts on multi-plate orbital debris shields. This approach links an Eulerian finite difference code for shield perforation calculations to a Lagrangian finite element code for debris cloud evolution simulations. Mixture theory is used to account for the presence of void space in the debris cloud.

Evaluation of Shear Thickening Fluid Kevlar for Large Fragment Containment Applications

Application of a shear thickening fluid (STF) treatment to neat Kevlar has been reported to improve fabric ballistic performance, for impacts of 0.22 caliber fragment simulating projectiles at velocities near 800 feet per second. In recent research, the authors have evaluated the ballistic performance of STF Kevlar in a series of impact experiments performed using larger projectiles and thicker targets, at impact velocities near 1,000 feet per second, including two different fabric boundary conditions. The experimental results indicate that under these test conditions, the impact protection afforded by STF Kevlar is at best equivalent to that provided by neat Kevlar at the same areal density. In addition, the ballistic performance of STF Kevlar was found to be strongly dependent on fabric target boundary conditions, with the best performance obtained in a friction sensitive target configuration that is not representative of current body armor, orbital debris shielding, or turbine blade containment systems.