Research Programs from BAA - Mechanical Sciences

1.0 Overview

Research supported in the mechanical sciences portion of the Mechanical Sciences Division of the Army Research Office (ARO) is concerned with a broad spectrum of fundamental investigations in the disciplines of fluid dynamics, solid mechanics, structures and dynamics, and propulsion and energetics. Though many creative and imaginative studies concentrate on a particular sub-discipline, increasingly, new contributions arise from interdisciplinary approaches such as the coupling between aerodynamics and structures, combustion and fluid dynamics, or solid mechanics and structures as in the structural reliability areas. Additionally, several common themes run through much of these four sub-disciplines, for example, active controls and computational mechanics. Research in such areas is addressed within the context of the application rather than as a separate subject of study. Fluid dynamics research is primarily concerned with investigations in the areas of rotorcraft wakes, unsteady aerodynamics of dynamic stall and unsteady separation, and fundamental studies of micro-adaptive flow control. Solid mechanics include a wide array of research areas such as high strain rate phenomena, penetration mechanics, heterogeneous material behavior, and reliability of structures. The structures and dynamics area is focused on investigations in vehicle structural dynamics and simulation and air vehicle dynamics including rotor aeromechanics. Research in the propulsion and energetics area is concentrated on processes characteristic of reciprocating (diesel) and gas turbine engines and the combustion dynamics of propellants used for gun and missile propulsion.

1.1 Fluid Dynamics

Research in fluid dynamics supports the development of improved or new technology for advanced helicopters, small gas turbine engines, improved airdrop (parachute) systems, maneuverable high speed missiles and high performance gun-launched projectiles, and miniature unmanned air vehicles. While basic research studies that address the fundamental flow physics underlying these devices are solicited, innovative research in the specific topical thrust areas listed below is especially encouraged.

1.1.1 Vortex-Dominated Flows

In contrast to fixed-wing aircraft, rotorcrafts always operate under the influence of their own wakes. The prediction of rotor performance, vibratory loads, and blade-vortex interaction noise depends strongly on the accurate prediction of the rotor wake, and the prediction methodology of this wake remains one of the major challenges in fluid mechanics. Current computational fluid dynamics (CFD) approaches are computationally intensive, especially for Eulerian methodologies where the vorticity diffuses numerically through the grid points and makes predication inaccurate. The process by which vorticity is shed by the blade and rolls up to form vortex filaments is not now adequately simulated for rotorcraft load distributions. In fact, under certain flight conditions, multiple vortices are observed to form due to negative lift over the blade tip. The application of non-intrusive optical diagnostic techniques should yield new phenomenological understanding for the study of multiple vortices, wake structures, and wake development. New numerical algorithms or different techniques to increase accuracy and reduce the computational requirements are required.

1.1.2 Unsteady Aerodynamics

A high level of unsteady flow, which cannot be adequately predicted by steady or quasi-steady approaches, can characterize the flow field around many modern Army weapons systems. One classical example of very high Army relevance occurs on the retreating blade of a helicopter rotor, where the high angles of attack experienced by the retreating blade of the helicopter rotor leads to boundary-layer separation followed by load and pitching-moment overshoots. Mild separation causes increased vibration and reduces performance, while severe dynamic stall leads to unacceptably large vibratory loads and limits forward flight speeds, load, and maneuver capabilities. The physics of this flow phenomenon are known to depend on the Mach and Reynolds numbers of the flow, and hence, future research in this area needs to be performed under realistic flight conditions. Improved theoretical and numerical simulation is needed for understanding the unsteady separation process and evaluating concepts for separation control. The simulations must be capable of accounting for transition of the boundary layer (and under some circumstances, the transition in the separating free shear layer). Detailed experimental measurements of velocity and pressure are needed in the separating region for the fundamental understanding the separation process, the development of new turbulence models valid during the stall process, and the validation of numerical simulations: here, the current focus is on quantitative flow field measurements rather than merely quantitative measurements on the airfoil surface. These measurements will probably require the use of new non-intrusive optical methods. Combined experimental and numerical efforts towards control of unsteady separation using passive and active flow control (including the emerging field of Micro-Adaptive Flow Control) are also sought.

A second example of the importance of unsteady aerodynamics occurs on maneuvering missiles and projectiles. As future emphasis in flight vehicle control and "smart" systems pervades munitions design, advances in aerodynamic phenomena, such as dynamic high alpha separation, vortex shedding, control surface/vortex interaction, divert thruster/vehicle interaction, roll control stability, and propulsion system integration will be required. New composite material vehicles will have stringent thermodynamic limits and enhanced nonlinear aero elastic response to maneuver forces. Smart structures and micro-electro-mechanical systems (MEMS) technology will redefine control strategies, control surface shape, and control surface dynamics, consequently driving fluid dynamics into new areas of research. All of these developments require the prediction and experimental verification of complex nonlinear transient flow fields. This will require improved CFD for turbulent flow separation prediction, large eddy simulation, vehicle vortex interactions, and accurate computations of gross flow field response to MEMS boundary layer flow perturbations. Parallel developments in experimental techniques will be required to measure these complex flow fields to help verify and guide the predictive technology.

1.1.3 Micro Adaptive Flow Control

Micro-Adaptive Flow Control (MAFC) technologies enable control of large-scale aerodynamic flows using small-scale actuators. MAFC technologies combine adaptive control strategies with advanced actuator concepts like micro-scale synthetic jets: MEMS-based microactuators; pulsed-blowing, plasma actuators; and combustion actuators. These techniques are used to cause the delay, or prevention, of fluid flow separation; induce flow separation in previously unseparated flow; alter supersonic flow shock structure; or otherwise alter the large-scale flowfield and provide overall system benefit. Army systems for which MAFC is currently being investigated include on-blade controls; dynamic stall control on helicopter rotor blades; separation control for drag and buffet reduction on helicopters; surge and stall control within Army gas turbines; and dispersion reduction and terminal guidance of subsonic, transonic; and supersonic Army projectiles.

While recent successful demonstrations of the efficacy of MAFC technology have taken place, much of this research has tended to be somewhat Edisonian in nature. Basic research needs to enhance and focus the adoption of this technology include developing fundamental understanding of the method by which MAFC actuation alters the overall flowfield; developing of robust and efficient MAFC actuators featuring greater control authority and higher bandwidth; developing of computational analysis methodologies capable of accurately and efficiently predicting the effect of unsteady MAFC actuation on the entire flowfield; and the integrating of all these technologies into Army systems.

Technical Point of Contact: Dr. Frederick Ferguson, e-mail: frederick.ferguson1.ngo@mail.mil,(919) 549-4322.

1.2 Solid Mechanics

The light, lethal, survivable, continental United States (CONUS)-based modern Army with quick power projection capabilities around the globe has abiding interest in building the most effective fixed and mobile assets with advanced materials and systems. Weapons, platforms, ammunition, and ground structures are designed with severe weight and volume restrictions, and are frequently limited by material strength and failure. Innovative use of material combinations for specific applications necessitates understanding the behavior of materials and structures under complex and severe constraints. Solid mechanics research plays a crucial role in the prediction of strength, damage initiation and progression, and failure of Army material systems under extreme loading conditions, such as blast and impact. Two major research aims in solid mechanics are to reduce development cost by minimizing the need for expensive testing and to optimize performance. The program seeks approaches based on the underlying physics of solids that form the foundation of optimization tools to enhance performance, while minimizing weight and volume for the design of actual systems. The program focuses on the material and system response to blast, shock, impact, and penetration, as well as the mechanics of heterogeneous systems including computational modeling-based Solid Mechanics Research. Thrust areas related to the development of better protective systems against blast and impact loading are directly related to the challenges facing the current and future Army.Under these conditions, the Army faces research problems with the unique constraints of very high strain rates, large deformations, high pressures, and rapid changes in temperature. Hence, a fundamental understanding of the behaviors of a variety of complex materials and systems, including engineered materials and soft human tissue, is needed. Research approaches should consider the topological effects (both micro- and macro-scale), specific material geometry, layering, and interface properties on the response to blast and impact loading. In addition, it may also address non-traditional concepts including nanotechnology, biologically inspired hierarchical structures, active protection, and the functional degradation of electronic components. Interrelated analytical, experimental, and computational formulations are needed to address these difficult multi-physics problems. Predictive models, validated by well-characterized experiments, are needed to identify dominant mechanisms at relevant scales.

1.2.1 Blast, Shock, Impact, and Penetration

This research topic addresses the need to understand the response of Army assets to impact and explosive detonation. It integrates approaches based on finite deformation, high pressure and high strain-rate, damage, and failure mechanics. Research should be conducted through a combination of physically based experiments, analysis, and computations. No single material will fulfill all of the Army's functional requirements. Therefore, combinations of materials such as polymer-, metal-, and ceramic-matrix composites, ceramics, metals, active materials, and functionally graded materials will be needed to achieve the desired thermo-mechanical response. The complexity of Army systems comprised of these materials is compounded by their highly anisotropic and heterogeneous nature, and the severe gradients and complex stress states resulting from blast and impact loading environments. Paramount to this effort is a better understanding of the mechanics of interfaces and impact mechanisms, such as high velocity behaviors that might occur at the penetrator/target interface or within developing cracks at macroscopic and microscopic scales. An important aspect of this research area is the deformation and fracture of materials under high strain rates (up to 107 s-1), large strains (up to 500%), high temperatures (up to the melting point), and high pressures (up to 5 GPa). Innovative research on processes in materials and structures that absorb energy, deflect penetrators, and/or laterally disperse momentum is strongly encouraged.

Blast and impact into brittle materials presents special challenges due to cracking and comminution of material ahead of the penetrator, high-speed granular flow of comminuted material, and the mixing of eroded penetrator material and comminuted target material. Ceramics and geological materials exhibit extreme sensitivity to defects and loading histories, which may result in highly rate dependent failure strengths and the propagation of failure waves. Metals are susceptible to inelastic deformations leading to ductile failure under low to medium loading rates, but transition to more brittle behavior under higher loading rates. In addition, heat generation, and thermal softening occur in metals, further complicating the behavior of these materials under extreme loads and loading rates. Blast and impact of composite systems present still another set of challenges that result from their complex microstructure, material boundaries, and the number of different and coupled failure modes that may occur. Since personnel protection is a key objective for Army platforms, an understanding of the response of biological tissue to blast and impact is essential.

All of this requires greatly improved understanding, effective modeling, and efficient computational schemes. Because blast and impact events often involve erosion and sliding of both the projectile and the target, explicit modeling of these processes with friction-based theories and computational techniques are essential. Computational methods for treating discontinuities in a three dimensional context are required. These methods must concentrate not only on the techniques required to track a moving boundary, but also on the relevant physics and mechanics associated with those surfaces. Examples might include boundaries between dissimilar materials, shock fronts, elastic/plastic boundaries, phase boundaries, shear bands and cracks, as well as penetrator/target interfaces. Constitutive models should be three-dimensional and should allow for system nonlinearities.

In blast and impact environments, complex interactions between the shock and release waves usually initiate damage mechanisms in the target; accurate modeling of the target behavior will require controlled, high fidelity experiments. Therefore, innovative experimental techniques that incorporate high-speed data acquisition and imaging are necessary to capture the deformation processes and relative motion between surfaces. Accurate experimental techniques are required to delineate the nature, timing, and evolution of damage and failure in heterogeneous materials. An important aspect of this area of research is the development of novel experimental techniques that can be used to generate data for the wide ranges and combinations of strain rates, strains, temperatures, and pressures of interest.

1.2.2 Mechanics of Heterogeneous Systems

The mechanics of heterogeneous structures involves the development of integrated analytical, computational, and experimental approaches to investigate the response of hybrid structures that may include combinations of high strength and lightweight engineered composites, ceramics, and functionally graded materials. Heterogeneity at all scales should be considered, from nanomaterials to systems created through combinations of different materials at larger scales. Experimental and computational techniques are needed to optimize material microstructure as well as the topology of systems to provide the desired structural response for specific boundary and loading conditions. Physically based structural design guidelines for energy absorbing structural systems comprised of tailored combinations of materials and heterogeneities at different length and time scales are sought. There are continuing technology barriers that need to be overcome if reliable Army structures such as helicopters, ground vehicles, bridges, and weapons systems are to be designed, manufactured, and maintained over a long period of time. Of special interest to the Army is the thermo-mechanical response at strain rates encountered in high-speed impact or explosive loading. Probabilistic as well as deterministic approaches are encouraged. Phenomena of interest are wave propagation, scattering, dispersion, damage evolution, and failure.

At appropriate length and time scales, the quantitative prediction and measurement of parameters related to dominant heterogeneities and mechanisms are needed for specific material systems in order to relate nano and micro effects to the macro scale. Deterministic and statistical scaling methodologies for toughness, strength, and geometrical effects that account for the multitude and variability of heterogeneities such as interfaces, interphases, particulate dispersion, fiber volume fraction and distribution, constituent shape, and their combined effects on failure are needed. Innovative methods and models to control material properties and damage by graded interfaces, coatings, and mechanical impedance mismatches are required. Constitutive relations for multi-scale mechanisms should include failure and damage criteria, which are mechanism-based and experimentally verifiable. The determination of universal scaling laws that can be used to bridge physical scales would greatly enhance our understanding and prediction of phenomena such as inelastic deformations, localization, distributed damage and failure, and fragmentation.

1.2.3 Computational Modeling Based Solid Mechanics Research

Over the past decades, the finite element methods that were developed in the mechanics community have had a tremendous impact on engineering practice and Army designs. Although these methods have been highly effective for linear and some nonlinear analyses, substantial breakthroughs are needed for failure modeling and representations of blast and impact live-fire tests. Commercially developed algorithms that rely on the deletion of elements to model the nucleation and propagation of cracks are inadequate. These algorithms are highly sensitive to the size and mesh arrangement and distribution. Furthermore, no convergence theories or even empirical evidence of convergence has been obtained so far for these methods. New theories are needed that can overcome the limitations of traditional continuum fracture models that are based on crack tip singularities. New principles need to be devised for the construction of failure surfaces and cohesion strength. New methodologies are needed to account for energy dissipation due to crack progression, large-scale yielding, and interfacial separation. It has become important to be able to develop material properties in terms of subscale models because, with the rapid advent of new material systems, testing is becoming prohibitively time consuming and expensive. New theoretical approaches are needed to develop hierarchical methods for failure that account for the inherent statistical aspects of failure. Methodologies that explore fracture processes at the micro-scale and relate them to the meso- and macroscopic levels should be investigated. Computational models for the creation of free surfaces that are mesh independent and that incorporate evolving time-dependent boundary conditions and physically based failure initiation criteria need to be developed. These computational models should capture the complex interactions of failure processes and defects in three dimensions. To achieve the requisite accuracy in three-dimensional problems, effective adaptive methods that can treat crack propagation, shear band formation, and other failure modes are needed. The capability to model fragmentation, contact, and penetration is also of strong interest.

Technical Point of Contact: Dr. Larry Russell,Jr., e-mail:larry.c.russell8.civ@mail.mil, (919) 549-4211.

1.3 Complex Dynamics and Systems

Modern research concerning the dynamics of complex and innovative engineering systems to enable unprecedented Army operational capabilities requires a highly interdisciplinary approach spanning many aspects of engineering, mathematics, complexity science, and physics as well as the dynamics of biological systems. Numerous research needs of Army interest are driven by cooperative, complementary, stochastic, and sometimes conflicting interactions amongst interconnected dynamics and field phenomena ranging from thermal fluctuations in nanosystems to nonlinear aeroacoustically-induced vibrations to efficient and sustainable energy flows in interdependent systems. Consequently, the Complex Dynamics and Systems program encompasses a broad research spectrum and seeks to cultivate a cadre of avant-garde scientists, engineers, and mathematicians capable of skillfully transcending traditional disciplinary bounds to generate unprecedented foundational understanding and pivotal innovation across the full range of length scales concerning the underlying physics, information flow, mathematical modeling, and control of isolated or interdependent dynamical systems. Research fostered under the auspices of this program is typically positioned to benefit several ARL Major Laboratory Programs to include: mobility, power and energy, sensors, lethality, and trans-disciplinary network science. Further information on the programmatic thrust areas of greatest interest are detailed the paragraphs that follow.

Prospective investigators should submit a concise summary overview of their proposed research with explicit delineation of a fundamental hypothesis with outstanding and revolutionary scientific merit, other related scientific objectives, and clear articulation of a novel and sound technical approach to surmount relevant scientific challenges. This document should be no more than four pages and is an important process for gauging program interest and/or refinement of research objectives to suit programmatic needs. Ultimately, selection for funding is highly competitive and is due to a combination of factors including reviews from both academic and government subject matter experts, the program manager, current program investment areas, research diversity and balance requirements, and availability of funds.

1.3.1 Nonlinear Physics and Dynamical Systems

Nonlinear dynamics is a rich research endeavor of direct impact on a multitude of Army systems from nano/microsystems to conventional rotorcraft aeromechanics. Research in this thrust generally concern profound fundamental physical understanding and opportunistic exploitation of structural, multi-body and multi-physics dynamical systems whose state transition and control parameter behavior are necessarily characterized by either strong, smooth, or non-smooth nonlinearities; nonholonomic constraints; stochastic dynamics; or high-dimensional interactions with granular media and field phenomena. Research topics of interest are diverse and some examples include (but are not limited to): exploiting non-local and global coupling properties of high-dimensional dynamical systems; nonlinear multiphysics interactions and dynamics at the nanoscale; dynamical systems approaches to fundamental problems in biological autonomy, neuromechanics, and mobility; non-Lyapunov based stability theory of nonlinear systems; nonlinear inverse problems and system identification; geometric mechanics; chaotic and stochastic transitions; integrability and stability of nonholonomic systems; nonlinear aeroelasticity and wake/vortex/acoustic-field induced structural oscillations; de-stabilizing time-delays; multi-body and structural interactions within granular media of varying viscosity; nano- to macro-scale continuum field interactions (thermal, fluid, electromagnetic, photomechanical, viscoelastic); chaos, instabilities, bifurcations, chimera states, and synchronization of coupled nonlinear oscillators; high-frequency oscillations; non-smooth and stochastic excitations of nonlinear systems; nonlinear dynamics of multi-body hybrid translational/rotary systems with nonlinear/non-smooth connections; intelligent force perception, interpretation, and action in compliant environments; nonlinear physics of dissipation, slipping, and damping; or tightly coupled unsteady aeroelastic-rigid body dynamics. Inspiration from nature's solutions to problems relevant to micro-vehicle dynamics and robotics is of value, however, understanding how competing factors in biology lead to sub-optimal solutions that modern engineering science can overcome may lead to truly innovative solutions.

1.3.2 Multi-Dimensional and Dissipative Dynamical Systems

This thrust focuses on the mathematically rigorous methods and physics of continuous and discrete high-dimensional dynamical systems; the engineering science of complexity; renormalization, projection-operator, and uncertainty propagation methods in spatiotemporally heterogeneous dynamical systems; and development of a formalism for systems synthesis. Novel methods for the engineering analysis of high-dimensional linear, nonlinear, and stochastic dynamical systems is sought to include model order reduction, stability, bifurcations, attractors, uncertainty propagation, statistical fields, etc. In large-scale networks of interdependent dynamical systems, temporal anisotropy, spatial non-locality, and multiscale processes precipitate local dynamics to global responses in a non-straightforward manner such that ergodicity may only apply at certain spatiotemporal scales and hierarchies. Fundamental investigations are required to develop the abstract formalisms and frameworks guiding the scaling analysis, causality, energy and multidimensional information flow, hierarchal, adaptive dynamics, multi-objective synthesis, and new mathematical performance metrics of increasingly complex and dissipative (non-equilibrium) systems comprised of distributed, interdependent, and heterogeneous subsystems. The engineering science of complexity constitutes an effort to leverage the unprecedented insight from complex systems science regarding a wide variety of biological, economic, and social systems. While discovery and understanding of complex systems in nature, economics, and society are of profound value and impact, our ability exploit this knowledge to engineer the controllability, fragility, propensity for self-organization, and/or robustness of interdependent dynamical systems will demonstrate true mastery. Of particular interest are methods and techniques from complexity science, dynamical systems theory, non-equilibrium physics, differential topology, graph theory, stochastic calculus, percolation theory, and associated stability and control principles. Multiscale projection-operator methods and renormalization groups for novel reduced order modeling strategies for complex dynamical systems is of major interest. Within the context of the aforementioned theoretical approaches, characterization of the uncertainty propagation and non-Gaussian stochastic dynamics is of paramount significance. Determining, understanding, and manipulating the emergent behaviors, persistent or transient mathematical structures, self-similarity, chaotic and fractional dynamics, etc, will lead to unprecedented capabilities of complex engineered systems and high dimensional multi-scale simulation. Furthermore, research developing the formalism for systems synthesis and systems-level stochastic nonlinear inverse problem analysis is sought after, where deep understanding of the nonlinear and stochastic dynamics of complex systems drives optimal system modeling. The theoretical framework for determining the efficient allocation of computational resources or component characteristics for the optimum desired systems-level dynamics remains an open challenge and the intricate dynamics of multi-dimensional and complex systems bring about a wealth of challenges in this endeavor.

Technical Point of Contact: Dr. Samuel Stanton, e-mail: samuel.c.stanton2.civ@mail.mil, (410) 278-7777, (919) 549-4225.

1.4 Propulsion and Energetics

Propulsion and Energetics Research supports the Army's need for higher performance propulsion systems. These systems must also provide reduced logistics burden (lower fuel/propellant usage) and longer life than today's systems. Fundamental to this area are the extraction of stored, chemical energy and the conversion of that energy into useful work for vehicle and projectile propulsion. In view of the high temperature and pressure environments encountered in these combustion systems, it is important to advance current understanding of fundamental processes as well as to advance the ability to make accurate, detailed measurements for the understanding of the dominant physical processes and the validation of predictive models. Thus, research in this area is characterized by a focus on high pressure, high temperature combustion processes and on the peculiarities of combustion behavior in systems of Army interest.

1.4.1 Engines

Research on combustion in engines is focused on intermittent, reacting flows encountered in diesel combustion chambers and on continuous combustion characteristics of small, gas turbine combustors. Optimizing engine performance, through understanding and control of in-cylinder combustion dynamics, while retaining high power density, is a major objective. This focus leads to a strong emphasis on fuel injection processes, jet break-up, atomization and spray dynamics, ignition, and subsequent heterogeneous flame propagation. Research on heterogeneous flames requires supporting study into kinetic and fluid dynamic models, turbulent flame structure, soot formation and destruction, flame extinction, surface reactions, multiphase heat transfer, and other factors that are critical to an understanding of engine performance and efficiency. An additional consideration is the high pressure/temperature environment, encountered in advanced engines, which influences liquid behavior and combustion processes at near-critical and super-critical conditions. Of particular interest are investigations of fundamental characteristics related to highly stressed engines, such as elevated temperature combustion, accelerated mixing, and transient heat transfer. Engine performance degradation under low temperature conditions, due to reduced fuel volatility, high oil viscosity, poor atomization and vaporization, etc., is a major concern. Fundamental research is needed in many areas, including low temperature physical and chemical rate processes, instantaneous friction and wear mechanisms, and combustion instability effects at low temperatures. With advances in sensing, modeling, and control architectures, it is becoming possible to further optimize the performance of combustion systems. Providing the foundations for such active control is also a major goal of the program.

1.4.2 Propellant Combustion Processes

Research on propellant combustion processes is focused on understanding the dynamics of the planned and inadvertent ignition and subsequent combustion of energetic materials used for propulsion in gun and missile systems and in ordinance. The program is also addressing the characterization of advanced energetic materials, e.g., those based on nanoscale structures and/or ingredients. Basic research is needed in several areas, including, plasma- and laser-induced ignition; thermal pyrolysis of basic ingredients and solid propellants; flame spreading over unburned surfaces (particularly in narrow channels); surface reaction zone structure of burning propellants; chemical kinetics (including possible ion kinetics in the presence of plasmas) and burning mechanisms; propellant flame structures; characterization of physical and chemical properties of propellants and their pyrolysis products; and coupling effects among the ignition, combustion, and mechanical deformation/fracture processes with or without the presence of a plasma. The use of advanced combustion diagnostic techniques for reaction front measurements, flame structure characterization, and determination of reaction mechanisms is highly encouraged. This includes characterization of radiative and convective stimuli delivered by plasma injection sources as well as the thermal, kinetic, and mechanical responses of the propellant. Complementary model development and numerical solution of these same ignition and combustion processes are also essential. There is also need to understand the unplanned or accidental ignition of energetic materials due to stimuli such as electrostatic discharge, impact, friction, etc. This requires, for example, research on the processes of energy absorption and energy partitioning in the materials, the effect of mechanical damage on the ignition events, and other topics relating to the safety of energetic materials.

Technical Point of Contact: Dr. Ralph A. Anthenien, e-mail: ralph.a.anthenien2.civ@mail.mil, (919) 549-4317.

 

Last Update / Reviewed: April 16, 2012