Rebecca M. Brannon

An Evaluation of the Material Point Method

The theory and algorithm for the Material Point Method (MPM) are documented, with a detailed discussion on the treatments of boundary conditions and shock wave problems. A step-by-step solution scheme is written based on direct inspection of the two-dimensional MPM code currently used at the University of Missouri-Columbia (which is, in turn, a legacy of the University of New Mexico code). To test the completeness of the solution scheme and to demonstrate certain features of the MPM, a one-dimensional MPM code is programmed to solve one-dimensional wave and impact problems, with both linear elasticity and elastoplasticity models. The advantages and disadvantages of the MPM are investigated as compared with competing mesh-free methods. Based on the current work, future research directions are discussed to better simulate complex physical problems such as impact/contact, localization, crack propagation, penetration, perforation, fragmentation, and interactions among different material phases. In particular, the potential use of a boundary layer to enforce the traction boundary conditions is discussed within the framework of the MPM.

Verification tests in solid mechanics

Code verification against analytical solutions is a prerequisite to code validation against experimental data. Though solid-mechanics codes have established basic verification standards such as patch tests and convergence tests, few (if any) similar standards exist for testing solid-mechanics constitutive models under nontrivial massive deformations. Increasingly complicated verification tests for solid mechanics are presented, starting with simple patch tests of frame-indifference and traction boundary conditions under affine deformations, followed by two large-deformation problems that might serve as standardized verification tests suitable to quantify accuracy, robustness, and convergence of momentum solvers used in solid-mechanics codes. These problems use an accepted standard of verification testing, the method of manufactured solutions (MMS), which is rarely applied in solid mechanics. Body forces inducing a specified deformation are found analytically by treating the constitutive model abstractly, with a specific model introduced only at the last step in examples. One nonaffine MMS problem subjects the momentum solver and constitutive model to large shears comparable to those in penetration, while ensuring natural boundary conditions to accommodate codes lacking support for applied tractions. Two additional MMS problems, one affine and one nonaffine, include nontrivial traction boundary conditions.

Experimental and numerical investigation of shock-induced full vaporization of zinc

Abstract A systematic computational and experimental study is presented on shock-induced full vaporization of zinc resulting from record-high impact speeds recently achieved on the Sandia Hyper-Velocity Launcher. In these experiments, a thin target plate of zinc is impacted by a tantalum flier plate at speeds ranging from 8 to 10.1 km/s, producing pressures from 3 Mbar to over 5.5 Mbar and temperatures as high as 39000 K (∼ 3.4 eV). Such high pressures produce essentially full vaporization of the zinc because the thermodynamic release isentropes pass into the vapor dome near the critical point. To characterize vapor flow, the velocity history produced by stagnation of the zinc expansion products against a witness plate is measured with velocity interferometry. For each experiment, the time-resolved experimental interferometer record is compared with wavecode calculations using an analytical equation of state, called ANEOS, that is known to have performed well at lower impact speeds (less than ∼7 km/s) where vaporization is negligible. Significant discrepancies between experiment and calculation are shown to exist under conditions of the more recent higher impact speeds in excess of 7 km/s. Numerical predictions underestimate witness-plate velocity for impact speeds up to about 9 km/s but overestimate witness-plate velocity for impact speeds exceeding 9 km/s. This qualitative change in the character of the discrepancy is conjectured to occur when the temperature on the release isentrope at the critical density lies above the critical temperature. These experiments can be used to develop and refine models representing the dynamics of the shock-induced vaporization process.

Crack behavior of ballistically impacted ceramic

A hot isostatically pressed (HIP) assembly of titanium alloy encapsulated AD995 ceramic, subjected to ballistic impact, is studied in detail. The crack behavior of ceramic confined in this way is studied in a combined experimental and computational effort. Fabrication of the HIP assembly is described. An experiment in which an assembly was impacted with a Lexan impactor at 1560 m/s is discussed, and the resulting deformation of the assembly and cracking of the ceramic are characterized. The Statistical Crack Mechanics (SCM) model for brittle materials is briefly described. The implementations of this model into the Lagrangian code PRONTO and into the Eulerian code CTH are described and used to further study the response of the ceramic during the experiment.

Concomitant evolution of wear and squeaking in dual‐severity, lubricated wear testing of ceramic‐on‐ceramic hip prostheses

Ceramic‐on‐ceramic (CoC) hip bearings were tested in short‐term wear tests with a systematically varied contact force. Continuous vibration and intermittent surface roughness measurements were obtained to elucidate potential causes of in vivo hip joint squeaking. The three‐phase test comprised alternating cycles of edge loading (EL) and concentric articulation (CA), always using ample serum lubricant. A 50,000‐cycle wear trial in which the contact force during CA was distant from the heads wear patch yielded no squeaking and practically no liner roughening. In 10‐cycle trials of an edge‐worn head coupled with a pristine liner, the contact force was varied in magnitude and point of application; immediate, recurrent squeaking occurred only when the contact force exceeded a critical threshold value and was centered upon the heads wear patch. In a 27,000‐cycle wear trial with the contact force applied near the margin of the heads wear patch, recurrent squeaking emerged progressively as the liners inner surface was roughened via its articulation with the worn portion of the head. The results reveal key conditions that yield recurrent squeaking in vitro in various scenarios without resorting to implausible dry conditions. A fundamental theory explains that hip squeaking is induced by myriad stress waves emanating from asperity collisions; yet, the root cause is edge loading.

Application of Uintah-MPM to shaped charge jet penetration of aluminum

The capability of the generalized interpolation material point (GIMP) method in simulation of penetration events is investigated. A series of experiments was performed wherein a shaped charge jet penetrates into a stack of aluminum plates. Electronic switches were used to measure the penetration time history. Flash x-ray techniques were used to measure the density, length, radius and velocity of the shaped charge jet. Simulations of the penetration event were performed using the Uintah MPM/GIMP code with several different models of the shaped charge jet being used. The predicted penetration time history for each jet model is compared with the experimentally observed penetration history. It was found that the characteristics of the predicted penetration were dependent on the way that the jet data are translated to a discrete description. The discrete jet descriptions were modified such that the predicted penetration histories fell very close to the range of the experimental data. In comparing the various discrete jet descriptions it was found that the cumulative kinetic energy flux curve represents an important way of characterizing the penetration characteristics of the jet. The GIMP method was found to be well suited for simulation of high rate penetration events.

ONR MURI project on soil blast modeling and simulation

Current computational modeling methods for simulating blast and ejecta in soils resulting from the detonation of buried explosives rely heavily on continuum approaches such as Arbitrary Lagrangian-Eulerian (ALE) and pure Eulerian shock-physics techniques. These methods approximate the soil as a Lagrangian solid continuum when deforming (but not flowing) or an Eulerian non-Newtonian fluid continuum when deforming and flowing at high strain rates. These two extremes do not properly account for the transition from solid to fluid-like behavior and vice versa in soil, nor properly address advection of internal state variables and fabric tensors in the Eulerian approaches. To address these deficiencies on the modeling side, we are developing a multiscale multiphase hybrid Lagrangian particle-continuum computational approach, in conjunction with coordinated laboratory experiments for parameter calibration and model validation. This paper provides an overview of the research approach and current progress for this Office of Naval Research (ONR) Multidisciplinary University Research Initiative (MURI) project.

Determining a Surrogate Contact Pair in a Hertzian Contact Problem

Laboratory testing of contact phenomena can be prohibitively expensive if the interacting bodies are geometrically complicated. This work demonstrates means to mitigate such problems by exploiting the established observation that two geometrically dissimilar contact pairs may exhibit the same contact mechanics. Specific formulas are derived that allow a complicated Hertzian contact pair to be replaced with an inexpensively manufactured and more easily fixtured surrogate pair, consisting of a plane and a spheroid, which has the same (to second-order accuracy) contact area and pressure distribution as the original complicated geometry. This observation is elucidated by using direct tensor notation to review a key assertion in Hertzian theory; namely, geometrically complicated contacting surfaces can be described to second-order accuracy as contacting ellipsoids. The surrogate spheroid geometry is found via spectral decomposition of the original pairs combined Hessian tensor. Some numerical examples using free-form surfaces illustrate the theory, and a laboratory test validates the theory under a common scenario of normally compressed convex surfaces. This theory for a Hertzian contact substitution may be useful in simplifying the contact, wear, or impact testing of complicated components or of their constituent materials.

Visualization of geologic stress perturbations using Mohr diagrams

Huge salt formations, trapping large untapped oil and gas reservoirs, lie in the deepwater region of the Gulf of Mexico. Drilling in this region is high-risk and drilling failures have led to well abandonments, with each costing tens of millions of dollars. Salt tectonics plays a central role in these failures. To explore the geomechanical interactions between salt and the surrounding sand and shale formations, scientists have simulated the stresses in and around salt diapirs in the Gulf of Mexico using nonlinear finite element geomechanical modeling. In this paper, we describe novel techniques developed to visualize the simulated subsurface stress field. We present an adaptation of the Mohr diagram, a traditional paper-and-pencil graphical method long used by the material mechanics community for estimating coordinate transformations for stress tensors, as a new tensor glyph for dynamically exploring tensor variables within three-dimensional finite element models. This interactive glyph can be used as either a probe or a filter through brushing and linking.

A simple surrogate test method to rank the wear performance of prospective ceramic materials under hip prosthesis edge-loading conditions

This research has developed a novel test method for evaluating the wear resistance of ceramic materials under severe contact stresses simulating edge loading in prosthetic hip bearings. Simply shaped test specimens - a cylinder and a spheroid - were designed as surrogates for an edge-loaded, head/liner implant pair. Equivalency of the simpler specimens was assured in the sense that their theoretical contact dimensions and pressures were identical, according to Hertzian contact theory, to those of the head/liner pair. The surrogates were fabricated in three ceramic materials: Al2 O3 , zirconia-toughened alumina (ZTA), and ZrO2 . They were mated in three different material pairs and reciprocated under a 200 N normal contact force for 1000-2000 cycles, which created small (<1 mm(2) ) wear scars. The three material pairs were ranked by their wear resistance, quantified by the volume of abraded material measured using an interferometer. Similar tests were performed on edge-loaded hip implants in the same material pairs. The surrogates replicated the wear rankings of their full-scale implant counterparts and mimicked their friction force trends. The results show that a proxy test using simple test specimens can validly rank the wear performance of ceramic materials under severe, edge-loading contact stresses, while replicating the beginning stage of edge-loading wear. This simple wear test is therefore potentially useful for screening and ranking new, prospective materials early in their development, to produce optimized candidates for more complicated full-scale hip simulator wear tests.