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Results for “Elastic bending energy”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records

A novel technique for minimizing energy functional using neural networks

An energy functional describes the equilibrium state of a system. In this work, we present a novel technique, Functional Optimization using Neural Networks (FONN), for minimizing the system’s energy. FONN utilizes neural networks to process information at discrete grid points, considering their interactions with neighboring grid points, to update the state of the system. The training process involves formulating a loss function based on the system’s energy, and with the help of multiple fine-tuning steps, the method employs a progressive energy reduction technique that decreases the energy in multiple steps. FONN’s effectiveness is demonstrated across various problems, including the minimization of the heat and Lyapunov energy. Furthermore, the paper explores the minimization of the elastic bending energy with an area constraint.

97 MATHEMATICS AND COMPUTING↗

Bent DNA Bows as Sensing Amplifiers for Detecting DNA-Interacting Salts and Molecules

Due to the central role of DNA, its interactions with inorganic salts and small organic molecules are important. For example, such interactions play important roles in various fundamental cellular processes in living systems and are involved in many DNA-damage related diseases. Strategies to improve the sensitivity of existing techniques for studying DNA interactions with other molecules would be appreciated in situations where the interactions are too weak. Here we report our development and demonstration of bent DNA bows for amplifying, sensing, and detecting the interactions of 14 inorganic salts and small organic molecules with DNA. With the bent DNA bows, these interactions were easily visualized and quantified in gel electrophoresis, which were difficult to measure without bending. In addition, the strength of the interactions of DNA with the various salts/molecules were quantified using the modified Hill equation. This work highlights the amplification effects of the bending elastic energy stored in the DNA bows and the potential use of the DNA bows for quantitatively measuring DNA interactions with small molecules as simple economic methods; it may also pave the way for exploiting the bent DNA bows for other applications such as screening DNA-interacting molecules and drugs.

59 BASIC BIOLOGICAL SCIENCES↗

Patterning of multicomponent elastic shells by gaussian curvature

Recent findings suggest that shell protein distribution and the morphology of bacterial microcompartments regulate the chemical fluxes facilitating reactions which dictate their biological function. Here, we explore how the morphology and component patterning are coupled through the competition of mean and gaussian bending energies in multicomponent elastic shells that form three-component irregular polyhedra. We observe two softer components with lower bending rigidities allocated on the edges and vertices while the harder component occupies the faces. When subjected to a nonzero interfacial line tension, the two softer components further separate and pattern into subdomains that are mediated by the gaussian curvature. We find that this degree of fractionation is maximized when there is a weaker line tension and when the ratio of bending rigidities between the two softer domains ≈2. Our results reveal a patterning mechanism in multicomponent shells that can capture the observed morphologies of bacterial microcompartments, and moreover, can be realized in synthetic vesicles.

Monte Carlo methods↗

Boundary conditions manipulation of polar vortex domains in BiFeO 3 membranes via phase-field simulations

Polar vortex domains have recently become an emergent research field due to the abundant physical phenomena and potential applications in high-density memories. Here, we explore the mechanisms of creating polar vortex domains in the BiFeO3 (BFO) membranes subjected to different boundary conditions using phase-field simulations. A major difference is that the vortex in membrane can be stabilized even under short-circuit electrical boundary conditions compared to vortex in other systems, such as thin film or superlattice. We found that (a) the formation of polar vortex domains at the membrane interior under bending is mainly driven by the reduction of elastic energy under short-circuit boundary condition, and the vortex chirality (namely, clockwise and counterclockwise) could be identified by n-shape and u-shape bending; (b) in the unbent open-circuit BFO membrane case, exotic trapezoid-shaped vortex nanodomains form at the terminations of 109 degrees domain walls (DWs) and partially charged 71 degrees DWs, which is driven by the local depolarization field and the interplay among electrostatic, elastic, and gradient and Landau energies. We also examine Kittel's law by establishing the dependence of vortex periods on the membrane thickness. Furthermore, these results give further understanding of the effect of boundary conditions on the formation of polar vortex domains, guiding experimental designs of vortex-based high-density memories.

36 MATERIALS SCIENCE↗

Sculpting 2D Crystals via Membrane Contractions before and during Solidification

When phospholipids crystallize within the otherwise fluid membranes of giant unilamellar vesicles, the resulting molecularly thin “2D” solids exhibit great variety in their morphology evolution. For example, within membranes containing moderate amounts of the crystallizing component, crystals grow with a fixed morphology depending on vesicle size. Conversely for membranes containing large amounts of the crystallizing species, we find small compact crystals on vesicles of all sizes. However, on large vesicles, growing crystals sprout flower petals that lengthen progressively. These behaviors result from two combined mechanisms: first, like other 2D solids, the shear rigidity of phospholipid crystals renders them intolerant to morphologies with nonzero Gaussian curvature. As a result and especially at elevated membrane tension, the cost of bending elasticity is reduced at the expense of line energy by the formation of flowers as opposed to compact crystals. Second, the composition-dependent tension rise during cooling relaxes via water permeation of the membrane with a time constant scaling as R2. The amount of crystal formed for a small decrease in temperature determines this composition-dependent increase in stress from thermal contractions versus solidification. Surface Evolver computations were motivated using the predicted tension evolution to develop a processing space that maps to experimental observations for initial and growing crystal morphology. Important variable groups are identified, including a scaled ratio of bending to line energy, a vesicle-size-independent group for membrane contractions, and a time constant for stress relaxation. Though processing stresses ultimately relax, the crystal morphology persists well beyond the processing window.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Strain Gradient Elasticity in SrTiO 3 Membranes: Bending versus Stretching

Young’s modulus determines the mechanical loads required to elastically stretch a material and also the loads required to bend it, given that bending stretches one surface while compressing the opposite one. Flexoelectric materials have the additional property of becoming electrically polarized when bent. The associated energy cost can additionally contribute to elasticity via strain gradients, particularly at small length scales where they are geometrically enhanced. Here, we present nanomechanical measurements of freely suspended SrTiO 3 crystalline membrane drumheads. In this work, we observe an unexpected nonmonotonic thickness dependence of Young’s modulus upon small deflections. Furthermore, the modulus inferred from a predominantly bending deformation is three times larger than that of a predominantly stretching deformation for membranes thinner than 20 nm. In this regime we extract a strain gradient elastic coupling of ~2.2 μN, which could be used in new operational regimes of nanoelectro-mechanics.

36 MATERIALS SCIENCE↗

Range and strength of mechanical interactions of force dipoles in elastic fiber networks

Mechanical forces generated by myosin II molecular motors drive diverse cellular processes, most notably shape change, division and locomotion. These forces may be transmitted over long range through the cytoskeletal medium – a disordered, viscoelastic network of biopolymers. The resulting cell size scale force chains can in principle mediate mechanical interactions between distant actomyosin units, leading to self-organized structural order in the cell cytoskeleton. Inspired by such force transmission through elastic structures in the cytoskeleton, we consider a percolated fiber lattice network, where fibers are represented as linear elastic elements that can both bend and stretch, and the contractile activity of myosin motors is represented by force dipoles. Then, by using a variety of metrics, we show how two such contractile force dipoles interact with each other through their mutual mechanical deformations of the elastic fiber network. As a prelude to two-dipole interactions, we quantify how forces propagate through the network from a single anisotropic force dipole by analyzing clusters of nodes connected by highly strained bonds, as well as through the decay rate of strain energy with distance from a force dipole. We show that predominant fiber bending screens out force propagation, resulting in reduced and strongly network configuration-dependent dipole interactions. On the other hand, stretching-dominated networks support longer-ranged inter-dipole interactions that recapitulate the predictions of linear elasticity theory. By characterizing the differences between tensile and compressive force propagation in the fiber network, we show how inter-dipole interaction depends on the dipoles’ mutual separation and orientation. The resulting elastic interaction energy may mediate a force between multiple distant dipoles, leading to their self-organization into ordered configurations. In conclusion, this provides a potential pathway for active mechanical force-driven structural order in elastic biopolymer networks.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Implementation and Verification of Cable Bending Stiffness in MoorDyn: Preprint

Cable bending stiffness capabilities have been added to MoorDyn to enable modeling of dynamic power cables. The relatively large motions experienced by floating wind turbines and wave energy converters pose a challenge for power cables, whose internal components provide significant bending resistance and are sensitive to deformation. The behavior and associated design considerations of power cables in these highly dynamic applications make coupled analysis relevant for design. MoorDyn is a lumped-mass mooring dynamics model that is used for floating wind energy simulation (often coupled with OpenFAST) and floating wave energy converter simulation (often coupled with WEC-Sim). Its existing line elasticity formulation considers axial stiffness only. To properly capture the dynamics of power cables, a cable bending stiffness model has been added that approximates cable curvature based on the difference in tangent vectors of adjacent line elements. The resulting bending moment is realized by applying forces on adjacent nodes, leaving the underlying lumped-mass formulation unchanged. The bending stiffness implementation is verified in static conditions against analytical solutions and then in a dynamic power cable scenario in comparison with OrcaFlex. The dynamic scenario uses prescribed motions and includes wave loadings on the cable. Results indicate correct implementation of bending stiffness and show close agreement with OrcaFlex.

50 EE - Wind and Water Power Program - Water (EE-4↗

Implementation and Verification of Cable Bending Stiffness in MoorDyn

The relatively large motions experienced by floating wind turbines and wave energy converters pose a challenge for power cables, whose internal components provide significant bending resistance and are sensitive to deformation. The behavior and associated design considerations of power cables in these highly dynamic applications make coupled analysis relevant for design. Bending stiffness capabilities have recently been added to the lumped-mass mooring dynamics model MoorDyn to enable simulation of dynamic power cables. MoorDyn is a common modeling choice for floating wind energy simulation (often coupled with OpenFAST) and floating wave energy converter simulation (often coupled with WEC-Sim) but the model’s previous line elasticity formulation only considered axial stiffness. To properly capture the dynamics of power cables, a bending stiffness model has been added that approximates cable curvature based on the difference in tangent vectors of adjacent elements. The resulting bending moment is realized by applying forces on adjacent nodes, enabling cable modeling while leaving the underlying lumped-mass formulation unchanged. In this paper, the new bending stiffness implementation is verified in static conditions against analytical solutions and then in a dynamic power cable scenario in comparison with the commercial simulator OrcaFlex. The dynamic scenario uses prescribed motions and includes wave loadings on the cable. Results indicate correct implementation of bending stiffness and show close agreement with OrcaFlex.

50 EE - Wind and Water Power Program - Water (EE-4↗

Measuring residual stress in Ti-6Al-4V with HR-EBSD, using reference patterns from annealed material

In this study, elastic strain and residual stress values in an engineering material were determined by high-resolution EBSD (HR-EBSD) using reference patterns from annealed, recrystallized material. Specifically, rolled Ti-6Al-4V sheet was analyzed using HR EBSD in both an as-annealed and a strained state, the latter established via a static two-point bend fixture. The commercial software CrossCourt4 (CC4) was used to evaluate the relative intragranular strain tensor components of the alpha grains mapped by HR-EBSD. The intragranular reference patterns identified in each grain by the software were then replaced with similarly-oriented patterns from scans of the as-annealed, recrystallized material. The CC4 analysis was then repeated to provide calibrated strain and residual stress values. Elastic strains on the order of 10–3 were detected, with corresponding residual stress values on the order of 1 GPa. Subsequent analyses using high energy synchrotron x-ray diffraction showed good correlation with the elastic strains measured by HR-EBSD using the annealed reference patterns. Additionally, the maximum macroscopic stress analytically predicted for two-point bending was in agreement with the residual stress observed. Good repeatability of the methodology and insight into the state of individual grains were also observed. The findings provide encouraging evidence that accurate intragranular and long-range residual stress measurements of engineering significance can be made with HR-EBSD using a physical reference pattern library.

36 MATERIALS SCIENCE↗

Combining four-point bending and corrosion to map stress-dependent corrosion susceptibility of 316H stainless steel in FLiNaK

Understanding the effect of stress on the corrosion of steels in molten salts is important for material screening and safety assessment of molten salt reactors. We present a method that combines four-point bending with corrosion testing, enabling the mapping of corrosion susceptibility as a function of local stress from a single specimen. Guided by finite element analysis, a four-point bending setup was used to bend a 316H stainless-steel bar under controlled elastic stress during a 100-hour exposure in FLiNaK at 700 °C. Post-exposure characterization using scanning electron microscopy and energy-dispersive X-ray spectroscopy revealed a pronounced correlation between stress and corrosion. Regions under tensile stress exhibited significantly deeper attack depths and greater chromium depletion along grain boundaries, whereas compressive zones showed shallower corrosion cracks. The stress effect is attributed to stress concentration under tensile loading, which promotes chromium dissolution and crack propagation. This technique can be readily applied to other structural alloys, enabling quantitative measurement of corrosion susceptibility as a function of local stress.

316H↗

Two–Photon Printing of Shape–Memory Microstructures and Metasurfaces via Radical–Mediated Thiol–Vinyl Hydrothiolation

Shape-memory resists capable of high-resolution curing into arbitrarily designed structures are increasingly demanded for soft robotics, optical sensors, microscale manufacturing, and biomedicine. Amorphous, shape-memory thiol-vinyl networks were printed using two-photon polymerization (2PP) curing of a simple resin formulated with commercially available reagents. The ability to print high-resolution feature sizes down to 200 nm is attributed to the use of radicalmediated, thiol-vinyl step-growth polymerization that quickly crosslinks the resin, limiting diffusive transport. The thermomechanical behavior of the 2PP-cured material analyzed in compression, tension and three-point bending is similar to the behavior of the UV-polymerized samples. To demonstrate the ability to design, field, and test 4D responsive microstructures, an array of nine springs with coil diameters of 330 μm was printed. Following compressive shapefixing, printed arrays can release 11 μJ of stored elastic strain energy when reheated. Further, a new concept of dichroic-memory of a metamaterial device is demonstrated by printing a twisted woodpile structure with circular dichroism as characterized by Mueller Matrix ellipsometry. Furthermore, our results demonstrate how combining high-resolution 2PP curing with stimuli-responsive molecular architectures can further the engineering of responsive microstructures and metamaterials.

36 MATERIALS SCIENCE↗

Nonlinear elasticity and damping govern ultrafast dynamics in click beetles

Many small animals use springs and latches to overcome the mechanical power output limitations of their muscles. Click beetles use springs and latches to bend their bodies at the thoracic hinge and then unbend extremely quickly, resulting in a clicking motion. When unconstrained, this quick clicking motion results in a jump. While the jumping motion has been studied in depth, the physical mechanisms enabling fast unbending have not. Here, we first identify and quantify the phases of the clicking motion: latching, loading, and energy release. We detail the motion kinematics and investigate the governing dynamics (forces) of the energy release. We use high-speed synchrotron X-ray imaging to observe and analyze the motion of the hinge’s internal structures of four Elater abruptus specimens. We show evidence that soft cuticle in the hinge contributes to the spring mechanism through rapid recoil. Using spectral analysis and nonlinear system identification, we determine the equation of motion and model the beetle as a nonlinear single-degree-of-freedom oscillator. Quadratic damping and snap-through buckling are identified to be the dominant damping and elastic forces, respectively, driving the angular position during the energy release phase. The methods used in this study provide experimental and analytical guidelines for the analysis of extreme motion, starting from motion observation to identifying the forces causing the movement. Here, the tools demonstrated here can be applied to other organisms to enhance our understanding of the energy storage and release strategies small animals use to achieve extreme accelerations repeatedly.

59 BASIC BIOLOGICAL SCIENCES↗

OpenFAST Modeling of the T-Omega Wind Floating Offshore Wind Turbine System

To reduce the cost of offshore wind energy through a more efficient design of the floating support structure, T-Omega Wind developed a novel lightweight and shallow-draft platform concept that aims to achieve a wave-following behavior without resonance amplification. The rotor and generator are carried by four tower legs with each leg supported by a shallow-draft float at the base. In preparation for a more detailed analysis, a coupled aero-hydro-elastic model of the proposed concept is developed in OpenFAST. The detailed modeling approach is presented, including a novel application of the SubDyn substructure dynamics module of OpenFAST to approximate the loads on the axle tube at the tower top from the rotor hub bearings. Preliminary results obtained with the OpenFAST model by rigidifying the substructure and blades indicate that the original sizing of the design can lead to large hub acceleration in the axial/surge and pitch directions due to platform-pitch motion. The high axial acceleration also potentially leads to large bending moments in the four tower legs. To address these issues, an updated design is developed with, among other changes, increased float spacing at the tower base and improved shear-transmitting geometry of the tower legs. The new design suggests significantly reduced extreme hub accelerations under the same conditions even with structural flexibility and will be further analyzed in the future through full aero-hydro-servo-elastic simulations.

ENGINEERING,WIND ENERGY↗

OpenFAST Modeling of the T-Omega Wind Floating Offshore Wind Turbine System: Preprint

To reduce the cost of offshore wind energy through a more efficient design of the floating support structure, T-Omega Wind developed a novel lightweight and shallow-draft platform concept that aims to achieve a wave-following behavior without resonance amplification. The rotor and generator are carried by four tower legs with each leg supported by a shallow-draft float at the base. In preparation for a more detailed analysis, a coupled aero-hydro-elastic model of the proposed concept is developed in OpenFAST. The detailed modeling approach is presented, including a novel application of the SubDyn substructure dynamics module of OpenFAST to approximate the loads on the axle tube at the tower top from the rotor hub bearings. Preliminary results obtained with the OpenFAST model by rigidifying the substructure and blades indicate that the original sizing of the design can lead to large hub acceleration in the axial/surge direction and in the pitch direction due to platform-pitch motion. The high hub acceleration also potentially leads to large bending moments in the four tower legs. To address the issue identified, an updated design is developed with, among other changes, increased float spacing at the tower base and improved geometry of the tower legs. The new design suggests significantly reduced extreme platform pitch angles under the same conditions and will be further analyzed in the future through full aero-hydro-servo-elastic simulations.

FOWT↗

OpenFAST Modeling of the T-Omega Wind Floating Offshore Wind Turbine System

To reduce the cost of offshore wind energy through a more efficient design of the floating support structure, T-Omega Wind developed a novel lightweight and shallow-draft platform concept that aims to achieve a wave-following behavior without resonance amplification. The rotor and generator are carried by four tower legs with each leg supported by a shallow-draft float at the base. In preparation for a more detailed analysis, a coupled aero-hydro-elastic model of the proposed concept is developed in OpenFAST. The detailed modeling approach is presented, including a novel application of the SubDyn substructure dynamics module of OpenFAST to approximate the loads on the axle tube at the tower top from the rotor hub bearings. Preliminary results obtained with the OpenFAST model by rigidifying the substructure and blades indicate that the original sizing of the design can lead to large hub acceleration in the axial/surge and pitch directions due to platform-pitch motion. The high axial acceleration also potentially leads to large bending moments in the four tower legs. To address these issues, an updated design is developed with, among other changes, increased float spacing at the tower base and improved shear-transmitting geometry of the tower legs. The new design suggests significantly reduced extreme hub accelerations under the same conditions even with structural flexibility and will be further analyzed in the future through full aero-hydro-servo-elastic simulations.

FOWT↗

Implementation of Creep-Damage Model for Concrete Fracture in MOOSE

Numerical implementation of an isotropic creep-damage model for concrete in multiphysics object-oriented simulation environment (MOOSE) finite element framework is presented in this paper. The constitutive model considers the combined effect of instantaneous and delayed strains on damage propagation. The implementation considers creep using generalized Maxwell or Kelvin-Voigt models. Using strain splitting assumptions, the total mechanical strains are split into elastic and creep components. Damage is considered to evolve as a function of the elastic and creep strains. This work considers damage as a function of fracture energy using the characteristic length of each finite element. This approach preserves the energy release rate of each element and avoids vanishing energy dissipation as the mesh is refined. Further, a creep-damage parameter is used to quantify the effect of creep strain on damage. The model is tested against published results on notched three-point bending specimens involving non-linear creep and predicts that about a third of the creep strain contributes towards damage for the experiments simulated. Results show that the proposed framework has predictive capabilities, and the model can be extended for more complex systems.

36 MATERIALS SCIENCE↗

Flexoelectricity and New Phenomena

It is easy to miss the scientific implications of our recent work on Triboelectricity. Everyone knows that rubbing and contact can produce static electricity; less appreciated is that the thermodynamic driver has been an open question since static electricity was first observed by Thales of Miletus around 585 BC. People think they understand it, for instance one common explanation that can still be found in the current literature is that differences in the work function drives charge transfer, often called the Volta-Helmholtz hypothesis. As summarized in 1967 by Harper, this fails to explain many experimental observations, for instance that charging can occur when two pieces of the same material are rubbed against each other. We are the first to place triboelectricity on a solid foundation rooted in quantum mechanics – the flexoelectric effect. We were able to explain a significant number of previously unexplained phenomena: 1) Bipolar tribocurrents associated with stick-slip, due to the change in sign of the strain gradients. 2) A one-third power scaling of tribocurrents with indentation force. 3) Tribocharging when two identical materials are used, these being due to local variations in the asperities so there are usually local potential differences. 4) Inhomogeneous charging of insulators, related to the statistical nature of asperities. 5) An experimentally observed reversal in the sign of charge transfer for negative and positive curvature, which is related to a change in the sign of the strain gradient. Exploiting our DOE prior funded work on flexoelectricity, we obtained semi-quantitative matching to existing experimental measurements of the surface charge in triboelectric experiments. The work has been well received in the literature. The work has been the focus of a number of popular science press articles, and also formed the basis for a Podcast for children 6-10 “The Rise and Fall of Static Man” posted in December 2019 by NPR as part of their “Wow in the World” series. I was also briefly interviewed by the Chicago PBS station in January 2020. This work are significant for a wide range of energy applications; to quote from an independent source: "Triboelectric power has plenty of potential, says Wenzhuo Wu, an assistant professor of engineering at Purdue. If the basics of static electricity are better understood, we could maximize the efficiency of wind or wave power generators, Wu says. The body's own movement could be used to power internal medical devices. Imagine being able to create a roof shaped to harness the power of a raindrop — the friction of the rain passing over the surface — to generate triboelectricity, powering the building below it." This is the start of new science, some of which we already partially understand such as the role of band bending in charge transfer. We need to understand charge transfer combining elasticity, quantum mechanics, band bending and defect states. These directly involve several of the DOE Grand Challenges: "How do we control material processes at the level of electrons? How do remarkable properties of matter emerge from complex correlations of the atomic or electronic constituents and how can we control these properties? How do we characterize and control matter away—especially very far away— from equilibrium?" I will argue that this work truly falls into the class of disruptive science; it is not just a simple extension, linear science. Not everyone will accept the approach. Since we explain far more about triboelectricity than anyone before, the preponderance of evidence supports the model. The feedback I have received is that many agree with the work, to quote: "The model makes sense, says Michael McAlpine, a professor of engineering at the University of Minnesota. "It's such a simple explanation, I was surprised I didn't put my finger on that," McAlpine says." The proposal received strong reviews. It was also publicized on the Department of Energy Web Site.

16 TIDAL AND WAVE POWER↗