The Betz process for minimizing the energy loss of single propellers is extended to the propeller operating in radially varying inflow, with a view toward the development of optimum stern propulsion for bodies of revolution. Assuming the usual lifting-line treatment of the propeller blades, an application of the isoperimetric problem in the calculus of variations is directed toward minimizing the energy loss while maintaining constant total thrust. Resulting expressions describe the optimum radial distribution of induced velocity in terms of an undetermined multiplier. The magnitude of the required total thrust, in turn, fixes the value of this multiplier, making the solution determinate. Inclusion of blade-profile drag at a later point in the development serves to determine an optimum propeller diameter for minimum over-all energy loss. The method gains in accuracy as the ratio of blade number to advance ratio increases, due to an approximation in the relation between the circulation and induced velocity.

Engineering measurements of internal friction in metals have been obtained from the decay characteristics of tuning forks of metals of interest. A damping program at Battelle Memorial Institute, conducted for the Office of Scientific Research and Development, called for such measurements at temperatures up to 1500 F, and it was necessary to develop suitable apparatus for obtaining accurate results at those elevated temperatures. A photoelectric method of measuring tine amplitude decay, using shutters on a vibrating fork to modulate light directed at a photocell, was developed. It proved to give very satisfactory results and had none of the mechanical difficulties in operation and uncertainties in results that were encountered at high temperatures when platinum-wire Sauereisen-cemented strain gages were used. It was necessary to reduce energy losses from the fork to its support by using a compliant coupling. This suspension worked so well that the lower limit of decrement measurements was probably determined by acoustic losses. It is believed that such losses added less than 0.00004 to the decrements of steel forks. This report includes details of construction of the equipment and reviews tests performed to establish its accuracy.

When an elastic sphere collides with another perfectly elastic body, part of the initial kinetic energy is lost in starting elastic waves in the two bodies. The energy thus dissipated can be calculated by previous analytical methods only when it is a small fraction of the initial kinetic energy. This paper develops an approximate analytical method for this calculation which is applicable even when the greater part of the energy is dissipated. Thus in a particular case where the energy dissipated is 90 per cent of the original kinetic energy, an error of only 0.7 per cent is made. The new element in this analysis is the introduction of a “normalized” interaction force which is necessarily quite insensitive to one’s ignorance of the exact interaction force. The powerfulness of the method is illustrated by a complete survey of the problem of impact of spheres with beams fixed at each end. Graphs are constructed showing the variation of the coefficient of restitution with the length of the beam and the mass of the sphere. Impacts with multiple blows are excluded. It is found that when the mass of the sphere is kept constant, the coefficient of restitution has a minimum for a certain optimal beam length, and is independent of the beam length for values greater than twice the optimal length. The coefficient is a minimum when the period of the fundamental mode of vibration is approximately equal to 2.4 times the time of contact. The method is also applied to the impact of spheres with large thin plates. The semiempirical formula of Raman is derived. Although this analytical method cannot be applied to impacts with multiple blows, it nevertheless gives the conditions for such multiple blows.

The subject matter considered in this paper deals with the mathematical investigation of heat flow in an annular disk of uniform thickness. Originally, the investigation was carried on in connection with the design of fins for increasing the heat transfer in various kinds of heat exchangers and engines. The results of the study, however, might easily be applied to a number of other problems, since by altering the boundary conditions slightly one may use the same basic equations for calculating the temperature distribution and heat transmission in grinding wheels and disk clutches. The study of the problem in connection with fin design has brought forth other solutions for special cases of the general proposition considered here. The particular results obtained by previous investigators can be readily found from the general equations given in this paper. In order to assist in the numerical solution of the somewhat complicated equations a chart for evaluating the mathematical expressions has been included.

Fatigue resistance is crucial for the engineering application of metals. Polycrystalline metals with highly oriented nanotwins have been shown to exhibit a history-independent, stable, and symmetric cyclic response [Pan et al., 2017, Nature 551, pp. 214-217]. However, a constitutive model that incorporates the cyclic deformation mechanism of highly oriented nanotwinned metals is currently lacking. This study aims to develop a physically based model to describe the plastic deformation of highly oriented nanotwinned metals under cyclic loading parallel to the twin boundaries. The theoretical analysis is conducted based on non-uniform distribution of twin boundary spacing measured by experiments. During cyclic plasticity, each twin lamella is discretely regarded as a perfect elastoplastic element with a yielding strength depending on its thickness. The interaction between adjacent nanotwins is not taken into consideration according to the cyclic plasticity mechanism of highly oriented nanotwins. The modeling results are well consistent with the experiments, including the loading-history independence, Masing behavior, and back stress evolution. Moreover, the dissipation energy during cyclic deformation can be evaluated from a thermodynamics perspective, which offers an approach for the prediction of the fatigue life of highly oriented nanotwins. The cyclic plasticity modeling and fatigue life prediction are unified without additional fatigue damage parameters. Overall, our work lays down a physics-informed framework that is critical for the precise prediction of the unique cyclic behaviors of highly oriented nanotwins.

Two types of non-holonomic constraints (imposing a prescription on velocity) are analyzed, connected to an end of a (visco)elastic rod, straight in its undeformed configuration. The equations governing the nonlinear dynamics are obtained and then linearized near the trivial equilibrium configuration. The two constraints are shown to lead to the same equations governing the linearized dynamics of the Beck (or Pflüger) column in one case and of the Reut column in the other. Although the structural systems are fully conservative (when viscosity is set to zero), they exhibit flutter and divergence instability. In addition, the Ziegler's destabilization paradox is found when dissipation sources are introduced. It follows that these features are proven to be not only a consequence of “unrealistic non-conservative loads” (as often stated in the literature); rather, the models proposed by Beck, Reut, and Ziegler can exactly describe the linearized dynamics of structures subject to non-holonomic constraints, which are made now fully accessible to experiments.

Three-dimensional coil structures assembled by mechanically guided compressive buckling have shown potential in enabling efficient thermal impedance matching of thermoelectric devices at a small characteristic scale, which increases the efficiency of power conversion, and has the potential to supply electric power to flexible bio-integrated devices. The unconventional heat dissipation behavior at the side surfaces of the thin-film coil, which serves as a “heat pump,” is strongly dependent on the geometry and the material of the encapsulating dissipation layer (e.g., polyimide). The low heat transfer coefficient of the encapsulation layer, which may damp the heat transfer for a conventional thermoelectric device, usually limits the heat transfer efficiency. However, the unconventional geometry of the coil can take advantage of the low heat transfer coefficient to increase its hot-to-cold temperature difference, and this requires further thermal analysis of the coil in order to improve its power conversion efficiency. Another challenge for the coil is that the active thin-film thermoelectric materials employed (e.g., heavily doped Silicon) are usually very brittle, with the fracture strain less than 0.1% in general while the overall device may undergo large deformation (e.g., stretched 100%). Mechanical analysis is therefore necessary to avoid failure/fracture of the thermoelectric material. In this work, we study the effect of coil geometry on both thermal and mechanical behaviors by using numerical and analytical approaches, and optimize the coil geometry to improve the device performance, and to guide its design for future applications.

The failure of materials with some sort of loading is a well-known natural phenomenon, and the reliable prediction of the failure of materials is the most important issue for many different kinds of engineering materials based on safety considerations. Classical strength theories with complex loadings are based on some sort of postulations or assumptions, and they are intrinsically empirical criteria. Due to their simplicity, classical strength theories are still widely used in engineering, and they are very easy to incorporate into any finite element code. Recently, a new methodology was proposed by the author. Instead of establishing empirical models, the material failure process was modeled as a nonequilibrium process. Then, the strength criterion was established with the rational stability analysis for the failure process. In this study, the author tried to use this idea to develop a rational thermodynamic strength theory and to make the theory easy to use in engineering, similar to the classical strength criteria. It was found that the predictions of the rational energy strength theory were very reasonable compared to the experimental data even if no postulation was taken. Through the analysis, it seemed that the strength problem could be efficiently tackled using the rational nonequilibrium energy model instead of using some sort of empirical assumptions or models.

For two combinations of a dimensionless rotational damping parameter and a dimensionless inertial coupling parameter, we consider free response of a rectilinearly vibrating linearly sprung primary mass inertially coupled to damped rotation of a second mass, for which Gendelman et al. (2012, “Dynamics of an Eccentric Rotational Nonlinear Energy Sink,” ASME J. Appl. Mech. 79(1), 011012) developed equations of motion in the context of a rotational nonlinear energy sink (NES) with no direct damping of the rectilinear motion. For dimensionless initial rectilinear displacements comparable with those considered by Gendelman et al., we identify a region in the motionless projection of the initial condition space (i.e., for zero values of the initial rectilinear and rotational velocities) in which every initial condition leads to a previously unrecognized zero-energy solution, with all initial energy dissipated by rotation. We also show that the long-time nonrotating, rectilinear solutions of the type found by Gendelman et al. are (orbitally) stable only in limited ranges of amplitude. Finally, we show how direct viscous damping of rectilinear motion of the primary mass affects dissipation, and that results with no direct rectilinear dissipation provide excellent guidance for performance when direct rectilinear dissipation occurs. Some applications are discussed.

We investigate the normal impact of a rigid sphere on a half-space of elasto-plastic auxetic/metal foam using the finite element method. The dependence of the coefficient of restitution, peak force, maximum displacement, and contact duration on the yield strain, impact velocity, and elastic and plastic Poisson’s ratio is analyzed. For a given elastic Poisson’s ratio, the coefficient of restitution generally decreases with an increase in the plastic Poisson’s ratio and impact velocity. When the plastic Poisson’s is maintained constant, the coefficient of restitution increases with an increase of the elastic Poisson’s ratio. These trends are explained using plastic energy dissipation. The energy dissipation trends are further investigated by decomposing it into deviatoric and hydrostatic parts. For a given impact velocity, the peak force is relatively insensitive to most of the elastic and plastic Poisson’s ratio combinations. We also show that for the cases where the elastic and plastic Poisson’s ratios are equal, the coefficient of restitution is relatively insensitive to their actual values. These findings can guide researchers to identify the right elastic and plastic Poisson’s ratio combinations so that lattice materials with exceptional energy absorbing capacity can be designed using topology optimization.

The thermo-mechanical response of an additively manufactured photopolymer-particulate composite under conditions of macroscopic uniaxial compression without lateral confinement at overall strain rates of 400–2000 s −1 is studied. The material has a direct-ink-written unidirectional structure. Computations are performed to quantify the effects of microstructure attributes including anisotropy, defects, and filament size on localized deformation, energy dissipations, and temperature rises. To this effect, an experimentally informed Lagrangian finite element framework is used, accounting for finite-strain elastic–plastic deformation, strain-rate effect, failure initiation and propagation, post-failure internal contact and friction, heat generation due to friction and inelastic bulk deformation, and heat conduction. The analysis focuses on the material behavior under overall compression. Despite relatively low contribution to overall heating, friction is localized at fracture sites and plays an essential role in the development of local temperature spikes unknown as hotspots. The microstructural attributes are found to significantly affect the development of the hotspots, with local heating most pronounced when loading is transverse to the filaments or when the material has higher porosities, stronger inter-filament junctions, or smaller filament sizes. Samples with smaller filament sizes undergo more damage, exhibit higher frictional dissipation, and develop larger hotspots that occur primarily at failure sites.

In nature, hair-like whiskers are used to detect surrounding information, such as surface texture and air flow field. The detection requires a comprehensive understanding of the relationship between whisker deformation and the contact force. With a whisker being modeled as a slender beam, the contact problem cannot be solved by small deformation beam theory and thus requires a new mechanical model to build up the relationship between whisker deformation and the contact force. In this work, the contact problem between a whisker and a round obstacle is solved, considering three factors: large deformation of the whisker, size of the obstacle, and frictional effect of the interface. Force and energy histories during the contact are analyzed under two motion modes: translation and rotation. Results show that the rotational mode is preferred in nature, because rotation of a whisker over an obstacle requires less energy for frictional dissipation. In addition, there are two types of detachment during the slip between the whisker and the obstacle. The detachment types are dependent on the whisker’s length and can be explained by the buckling theory of a slender beam.

Capture of a prey by spider orb webs is a dynamic process with energy dissipation. The dynamic response of spider orb webs under prey impact requires a multi-scale modeling by considering the material microstructures and the assembly of spider silks in the macro-scale. To better understand the prey capture process, this paper addresses a multi-scale approach to uncover the underlying energy dissipation mechanisms. Simulation results show that the microstructures of spider dragline silk play a significant role on energy absorption during prey capture. The alteration of the microstructures, material internal friction, and plastic deformation lead to energy dissipation, which is called material damping. In addition to the material damping in the micro-scale modeling, the energy dissipation due to drag force on the prey is also taken into consideration in the macro-scale modeling. The results indicate that aerodynamic drag, i.e., aero-damping, plays a significant role when the prey size is larger than a critical size.

A metallic microparticle impacting a metallic substrate with sufficiently high velocity will adhere, assisted by the emergence of jetting—the splash-like extrusion of solid matter at the periphery of the impact. In this work, we compare real-time observations of high-velocity single-microparticle impacts to an elastic–plastic model to develop a more thorough understanding of the transition between the regimes of rebound and bonding. We first extract an effective dynamic yield strength for copper from prior experiments impacting alumina spheres onto copper substrates. We then use this dynamic yield strength to analyze impacts of copper particles on copper substrates. We find that up to moderate impact velocities, impacts and rebound velocities follow a power-law behavior well-predicted on the basis of elastic-perfectly plastic analysis and can be captured well with a single value for the dynamic strength that subsumes many details not explicitly modeled (rate and hardening effects and adiabatic heating). However, the rebound behavior diverges from the power-law at higher impact velocities approaching bonding, where jetting sets on. This divergence is associated with additional lost kinetic energy, which goes into the ejection of the material associated with jetting and into breaking incipient bonds between the particle and substrate. These results further support and develop the idea that jetting facilitates bonding where a critical amount of bond formation is required to effect permanent particle deposition and prevent the particle from rebounding.

A polymeric gel contains a crosslinked polymer network and solvent. Gels can swell or shrink in response to external stimuli. Two typical kinetic processes are involved during the deformation of gels: the viscoelastic and poroelastic responses. Viscoelasticity of gels is generated from local rearrangement of the polymers, while poroelasticity is generated from solvent migration. The coupled time-dependent behaviors of gels can be formulated by coupling a spring-dashpot model with a diffusion–deformation model. Different combinations of spring and dashpot and different ways of dealing with the coupling between solvent migration and rheological models—either through the spring or dashpot—induce significantly different constitutive behaviors and characteristic time-dependent responses of gels. In this work, we quantitatively study how different rheological models coupled with solvent migration affect the transient behavior of gels. We formulate the visco-poroelastic gel theory for the Maxwell model, the Kelvin–Voigt model, and the generalized standard viscoelastic model. In addition, for generalized standard viscoelastic model, we also discuss the different coupling through the secondary spring or the dashpot. The models are implemented into finite element codes, and the transient-state simulations are performed to investigate the time-dependent deformation and frequency-dependent energy dissipation of different rheologically implemented gel models. The result shows that different combinations of spring and dashpot give the gel solid-like properties and liquid-like properties under different time scales; in addition, the coupling of solvent migration with the dashpot in the rheological model results in restrictions of solvent migration under certain length scales.

We analyze the operation of melting probes as a Stefan problem for the liquid/solid interface surrounding the probe. We assume that the liquid layer is thin and, therefore, amenable to analysis by the lubrication theory. The resulting Stefan problem is solvable in the closed form. The solution determines the dependence of the penetration speed on the temperature differential between the probe and the surrounding ice, the size, shape and weight of the probe, the viscosity of liquid water and the thermal properties of solid ice.

Aluminum is reduced from alumina by the Hall–Héroult electrolysis process in which the anode is utilized as the positive electrode. The quality of the prebaked anode plays a crucial rule in the efficiency of the aluminum electrolysis process. To produce high-quality anodes in the aluminum industry, the anode baking process calls for a deep understanding of mechanisms that govern the evolution of the anode mixture properties under the high-temperature condition. Therefore, the aim of this paper is to establish a thermo-chemo-poromechanical model for the baking anode by using the theory of reactive porous media based on the theory of mixtures within the thermodynamic framework. For this purpose, an internal state variable called “shrinking index” is defined to characterize the chemical progress of the pitch pyrolysis in the anode skeleton, and the Clausius–Duhem inequality is developed according to the Lagrangian formalism. By introducing a reduced Green–Lagrange strain tensor, a Lagrangian free energy is formulated to found a set of state equations. Then, the thermodynamic dissipation for this pyrolyzing solid–gas mixture is derived, and a constitutive model linking the chemical pyrolysis with the mechanical behavior is achieved. A dissipation potential is consistently defined to ensure the non-negativeness of the thermodynamic dissipation and to obtain the constitutive laws for viscous behaviors. Field equations governing the volatile diffusion and the heat transfer through the draining mixture body are derived from the entropy balance.

The elasto-plastic indentation of auxetic and metal foams is investigated using the finite element method. The contributions of yield strain, elastic, and plastic Poisson’s ratio on the indentation hardness are identified. For a given yield strain, when the plastic Poisson’s ratio is reduced from 0.5, the indentation hardness decreases first and then increases. This trend was found to be valid for a wide of yield strains. For yield strains less than 0.08, the hardness of auxetic materials is much larger when compared with materials having positive plastic Poisson’s ratio. As the plastic Poisson’s ratio approaches −1, the elastic deformations dominate over the plastic deformations. The plastic dissipation, when compared with the elastic work, is lower for materials with negative Poisson’s ratio. There is no effect of elastic Poisson’s ratio on the indentation hardness when the plastic Poisson’s ratio is more than −0.8. When the plastic Poisson’s ratio is less than −0.8, the hardness increases with a decrease of elastic Poisson’s ratio. The plastic dissipation per unit strain energy is maximum for materials with vanishing plastic Poisson’s ratio.