Principle Of Minimum Energy Research Articles

An analytical model for micro-cutting considering the cutting tool edge radius effect and material separation

Severe plastic deformation occurs in micro metal cutting process; meanwhile, new surfaces are generated due to the material separation caused by ductile fracture. The energy required for the formation of the new surfaces is of kJ/m2, which should not be neglected in the analysis of micro-cutting. In this work, an analytical model is developed focusing on the analyses of the micro metal cutting process with no stable built-up edge, in which the effects of both edge radius and material separation are taken into account. The cutting tool edge geometry is simplified with the effective rake angle. On the basis of slip-line field theory, the equation of the cutting power is derived. Applying the minimum energy principle, two nonlinear equations are obtained, through which the shear angle and the minimum chip thickness can be estimated simultaneously. The model is examined through the experiments; the investigations show that the calculation results of cutting force and shear angle agreed with the experimental measurements very well. The effects of fracture toughness, shear yield stress, and friction angle to the micro-cutting process are investigated. The numerical results show that the friction angle affects the cutting force and the shear angle greatly.

Verification and application of 2-D DDA-SPH method in solving fluid–structure interaction problems

The study of fluid–structure interaction (FSI) is a challengeable topic, which concerns a coupled system with consideration of not only the behaviors of the fluid and the structure, but also the interaction process between both. In this paper a coupled method is introduced to simulate FSI problems in two-dimensional (2-D) case. In this coupled method (2-D DDA-SPH), the smoothed particle hydrodynamics (SPH) based on kernel approximation and particle approximation is employed to represent the fluid domain governed by Navier–Stokes equations and the discontinuous deformation analysis (DDA) based on the minimum total potential energy principle is used to model the real solid structure (with rigidity or elasticity) through virtual joints. A coupling scheme bridging both methods is used based on a penalty-force method, and an improved contact detection between particle and block is proposed. Several challenging examples, including breaking dam flow through an elastic plate, breaking dam flow on a rigid barrier or an elastic barrier are investigated to demonstrate the capability of the 2-D DDA-SPH method to capture the entire FSI process. Finally, two application examples, failure of gravity dam induced by water pressure, and dynamic response of armor blocks on breakwater under incident wave, are studied by using 2-D DDA-SPH. The simulation results show satisfactory agreements with available experimental, numerical, and analytical results, suggesting the applicability of the 2-D DDA-SPH method to solve FSI problems.

First principle study of the B-site doped double perovskite oxides LaMg0.5M0.5O3 (M=Sc, Ti, Zr)

The stable configuration of double perovskite LaMgO3 was constructed by CASTEP module in Materials Studio. How the B sites doping (Sc3+, Ti4+, Zr4+) affect the structure and physical properties was theoretical investigated. Three configurations of doping are structural geometry and energy optimized by GGA+WC correlation function, according to the principle of minimum energy, the most stable geometry structure is obtained, based on this structure, the physical properties are calculated. The results show that: The energy of LaMg0.5Ti0.5O3 is the lowest and it is deduced as semiconductor according to the band gap. In the vicinity of Fermi level, the interaction between p-electron and d-electron is obvious, which contributes the most to the density of states. By optical properties simulation, the frequency of absorption peaks of the three materials becomes lower and lower in low frequency range, while the absorption peaks of LaMg0.5Sc0.5O3 and LaMg0.5Zr0.5O3 appear earlier than LaMg0.5Ti0.5O3 in high frequency range, but the peak intensity is lower.

Closed-form solution in bi-Helmholtz kernel based two-phase nonlocal integral models for functionally graded Timoshenko beams

Static bending behavior of functionally graded (FG) Timoshenko beams is studied via both strain- and stress-driven two-phase local/nonlocal mixed integral models based on the bi-Helmholtz kernel. The differential governing equations and boundary conditions are derived via the principle of minimum potential energy, the relations between strain and nonlocal stress are expressed as integral equations with the bi-Helmholtz kernel. The Laplace transform technique is utilized to obtain closed-form solutions for the first time. The numerical results are validated by reverting to the local case, and it is concluded that the present model shows well-posedness for exploring bounded beams in contrast to Eringen's pure nonlocal model: for all boundary and loading conditions, the increasing nonlocal length-scale parameter shows consistently softening or stiffening effect on the beam behaviour, according to the strain- or the stress-driven model, respectively. Moreover, the effects of shear-deformation and FG characteristics are also investigated. As the FG parameter increases, the non-dimensional deflection increases, while the softening effect caused by the strain-driven nonlocal phase seems to be more significant.

Modeling and simulation of bonded-type piezoelectric linear motors considering the stress transfer in adhesive layer

This paper provides a general framework for modeling bonded-type piezoelectric linear motors considering the stress transferred by adhesive layer. A three-dimensional static model of stator is first developed by the principle of minimum potential energy and finite element. The stress transferred by adhesive layer could be simulated and analyzed for arbitrary bonding conditions. Basing on the static stress-transfer analysis, a quasi-static stress acted to substrate by piezoelectric elements is assumed and integrated into the substrate dynamic model. A pure mechanical dynamic model is developed for the electromechanical coupling system of stator. Furthermore, the whole-machine dynamic model of motor is presented by incorporating the frictional contact force into the dynamic model of the stator and an analytical model of the mover. Finally, a bonded-type piezoelectric linear motor with V-shaped stator is investigated as an example for simulations and experiments. The methodology presented here for simulating the transferred load of adhesive layer in bonded-type piezoelectric motor as well as for estimating the vibration characteristics of stator and output performances of motor. It is believed that the proposed method would be helpful to design and manufacture the prototypes due to the wider applicability of allowing for irregular geometry and any bonding conditions.

Buckling analysis of nanoplates based on a generic third-order plate theory with shear-dependent non-isotropic surface stresses

In this paper, a general third-order shear deformation plate theory (GTSDPT) is employed to investigate the buckling behaviors of rectangular nanoplates. A new model with non-isotropic surface modulus that depends on in-plane and transverse shear strains, such as that for most crystalline faces, is established to analyze the significance of non-isotropic surface effects on buckling behaviors. The governing equations and the corresponding boundary conditions are established by using the principle of minimum potential energy. The analytical critical buckling load solutions are obtained for nanoplates with different boundary conditions. The proposed model is verified by comparing buckling results against the ones from existing plate theories. Using both Reddy’s third order shear deformation plate theory (TSDPT) and GTSDPT, the influence of plate thickness, length-to-thickness ratio, surface modulus, residual surface stress, bulk modulus and boundary conditions on the buckling behavior of nanoplates with surface stress effects is analyzed in detail. It is observed that the buckling results of the nanoplates from TSDPT and GTSDPT exhibit some differences due to the presence of shear stresses on the interface between surface layers and the bulk of the plates. The TSDPT theory may not be able to capture shear stress effect and the GTSDPT theory may need to be employed in this case. Finally, the influence of surface stresses on the buckling behaviors of nanoplates made of gold, nickel, silver and copper and subjected to uni- and bi-axial compressive loads is investigated using the GTSDPT theory.

Elastic and inelastic stability of a steel arch subjected to a crown point load under an elevated fire environment

This paper focuses on the stability of thin-walled circular arches subjected to a radially-directed concentrated load at the crown point under a temperature increase up to 800℃ induced by fire. A solution is obtained analytically to predict the critical buckling load of the elastic arch based on the principle of minimum potential energy and an admissible displacement function. Subsequently, a planar numerical model is introduced to explore the maximum load (critical buckling load) by drawing the normalized load-displacement equilibrium curves. These curves from the numerical results exhibit close trends with the analytical ones for both fixed-fixed and pinned-pinned arches. In addition, steel arches with inelastic material properties and geometric nonlinearities are considered in the numerical model, indicating that inelastic properties reduce prominently the maximum load. Furthermore, all investigations show the heating process induced by the fire reduces the load capacity (maximum load) dramatically for both elastic and inelastic arches. Finally, parametric analyses are performed to examine the effect of central angle and normalized thickness on the maximum load of the arch.

Dynamic collapse of circular metal foam core sandwich tubes in splitting and curling mode

This paper investigates the dynamic collapse of circular metal foam core sandwich tubes in splitting and curling mode subjected to low-velocity impact. The splitting and curling modes occur along the prefabricated cracks on sandwich tubes. The deformation modes, i.e. crack propagation along the prefabricated crack, new crack initiation, merging old cracks are observed in experiments. It is found that the number of strips in the sandwich tube tends to develop from the number of prefabricated cracks to the number of steady strips. Based on the principle of minimum energy, the method for predicting the number of steady cracks in the inner and outer tubes of the sandwich tubes is established. The quasi-static analytical model is approximately used to predict experimental results, and analytical results capture experimental ones reasonably. It is demonstrated the better energy absorption characteristics can be obtained by the proper thickness of metal foam core.

Viewing buoyant force as an application of principle of minimum potential energy

Principle of minimum potential energy (PMPE) as one of the fundamental concept in physics and engineering will be used in this work to explain the phenomenon of buoyancy, why object with lower mass density can float on fluid with higher mass density, while object with higher mass density can sink in fluid with lower mass density. Before that some examples in mecahnics, e.g. object with different vertical position, object on incline, object with spring moving in vertical direction, and final condition of seesaw-like system, will be discussed to show the consequence of PMPE. Then, in the system of solid object and fluid, including the surrounding fluid with the object and treat them as a whole object or system we can easily show that the floating or sinking phonomena are simply a state where system potential energy is miniumum (both object and fluid). For simplicity, the theoretical demonstration will only use the form of block, where the other form, e.g. cylinder, sphere, cone, irregular form, are the matter of geometry difficulty only. Students engagement to the topic has not been performed but the instrument is proposed for future work.

Meteoritic amino acids as chemical tracers of parent-body chemistries

ABSTRACT The analysis of the organic matter of meteorites made it possible to identify over 70 amino acids (AA), including 8 of those found in living organisms. However, their relative abundances vary drastically with the type of the carbonaceous chondrite, even for isomers of same chemical formula. In this report, we address the question whether this difference may have its origin in the relative stability of these isomers according to the conditions they experienced when they were formed and after. To this end, we rely on the fact that for most of the species observed so far in the interstellar medium (ISM), the most abundant isomer of a given generic chemical formula is the most stable one (minimum energy principle, MEP). Using quantum density functional theory (DFT) simulations, we investigate the relative stability of the lowest energy isomers of alanine (Ala) and amino butyric acid (ABA) in the neutral, protonated, and zwitterionic structures together with corresponding nitrile precursors. It is shown that β-alanine and γ-ABA are the most stable in a protonated form, whereas α-AA are the most stable in the zwitterionic and nitrile structures. The different composition of the carbonaceous chondrites CIs and CMs could be linked to the chemical context of the aqueous alterations of the parent bodies.

Bending analysis of simply-supported sandwich beam using Chebyshev quadrature element method

Based on the higher-order sandwich beam theory, the Chebyshev quadrature sandwich beam element is established for the bending analysis of the simply-supported sandwich beam. Gauss Lobatto sampling is adopted as element nodes. The discrete governing equation of the sandwich beam is obtained by the principle of minimum potential energy. A series of numerical examples are carried out on simply-supported sandwich beams under sinusoidal loading. The results are compared with the finite element method, showing that the proposed method can yield very accurate displacements and stresses. This method is suitable for the static analysis of simply-supported sandwich beams with different materials and different geometric parameters.

Machining process modeling of green alumina ceramics in orthogonal cutting and fragmentation process

Theories on mechanical model and discrete element model (DEM) of machining green ceramics are sought to reveal the material removal mechanisms and cutting force. Theoretical models are based on brittle fracture mechanics, equilibrium, and minimum chipping energy principle etc., and in the model, friction on flank face of tools and material’s rebound deformation are considered. DEM is established based on macro-mechanical properties of green alumina ceramics. Orthogonal cutting experiments were conducted to validate the mechanical model and DEM. Results show that the material removal mechanism of green alumina ceramics contains both crushing failure and chipping failure. The experiments validate good agreement with mechanical model and DEM in regard to chip formation and tangential cutting force. Friction force during machining green alumina ceramics contributes more than 50% of tangential cutting force. It is the reason that there exists more serious flank wear of cutting tool.

Analysis of the Influencing Factors of the Hydroxyl Radical Yield in a Hydrodynamic Cavitation Bubble of a Chitosan Solution Based on a Numerical Simulation.

In this paper, the hydroxyl radical yield of a cavitation bubble and its influencing factors in the process of chitosan degradation with hydrodynamic cavitation in a single-hole orifice plate was investigated by a numerical simulation method. The hydroxyl radical yield of the cavitation bubble was calculated and analyzed by the Gilmore equation as the dynamic equation combined with the mass transfer equation, heat transfer equation, energy balance equation, and the principle of Gibbs free energy minimization. The influence of geometric parameters of the orifice plate and operating parameters on the formation of hydroxyl radicals was investigated. The results showed that the hydroxyl radicals produced at the moment of cavitation bubble collapse increased with the increase of the initial radius (R0), upstream inlet pressure (P1), downstream recovery pressure (P2), downstream pipe diameter (dp), and the ratio of the orifice diameter to the pipe diameter (β). The simulation results provide a certain basis for the regulation of hydrodynamic cavitation degradation of chitosan.

Coupled flexural torsional analysis and buckling optimization of variable stiffness thin-walled composite beams

Present work examines flexural–torsional coupling for static and stability analysis of thin-walled composite beams having variable stiffness. Variable stiffness composites (VSCs), manufactured with curvilinear fibers, are considered in this work. Compared to straight fiber laminates, variable angle tow (VAT) sections may significantly improve structural response as they redistribute the in-plane stresses. A generalized beam kinematic model which considers the effect of flexural, torsional and, warping deformation is adopted and using the principle of minimum potential energy, governing equations are derived. The variable fiber angles can be defined using a general Lagrangian polynomial and as a particular case, the solution is presented for linearly varying fiber angles. Stability analysis considers geometric nonlinearity. The present model neglects transverse shear deformations, and governing equations are numerically solved using a set of C 1 continuous finite elements. Important observations are made on the coupled response of thin-walled VSCs for static and stability analysis, which indicates the necessity of optimization study. An efficient ‘Teaching Learning Based Optimization’ (TLBO) algorithm is applied to obtain the most efficient curvilinear fiber path. The results show that lateral torsional buckling load capacity can be increased by approximately 15% in optimized VSCs compared to unidirectional fiber composites. The present kinematic model and numerical scheme can be easily extended to the optimization studies considering manufacturing constraints, which may be further implemented in commercial designs.

Experimental and Theoretical Studies on Sustainable Synthesis of Gold Sol Displaying Dichroic Effect.

Gold nanoparticles depending on their shape and mixtures of multiple shapes can exhibit peculiar optical properties, including the dichroic effect typical of the Lycurgus cup, which has puzzled scientists for a long time. Such optical properties have been recently exploited in several fields such as paint technology, sensors, dichroic polarizers, display (LCD) devices, laser applications, solar cells and photothermal therapy among others. In this article, we have demonstrated a simple room temperature one-pot synthesis of gold sol displaying a dichroic effect using a slow reduction protocol involving only trisodium citrate as a reducing agent. We found that the dichroic gold sol can be easily formed at room temperature by reducing gold salt by trisodium citrate below a certain critical concentration. The sol displayed an orangish-brown color in scattered/reflected light and violet/blue/indigo/purple/red/pink in transmitted light, depending on the experimental conditions. With minor changes such as the introduction of a third molecule or replacing a small amount of water in the reaction mixture with ethanol, the color of the gold sol under transmitted light changed and a variety of shades of red, pink, cobalt blue, violet, magenta and purple were obtained. The main advantage of the proposed method lies in its simplicity, which involves the identification of the right ratio of the reactants, and simple mixing of reactants at room temperature with no other requirements. TEM micrographs displayed the formation of two main types of particles viz. single crystal gold nanoplates and polycrystalline faceted polyhedron nanoparticles. The mechanism of growth of the nanoplates and faceted polyhedron particles have been described by an enhanced diffusion limited aggregation numerical scheme, where it was assumed that both trisodium citrate and the gold ions in solution undergo a stochastic Brownian motion, and that the evolution of the entire system is regulated by a principle of energy minimization. The predictions of the model matched with the experiments with a good accuracy, indicating that the initial hypothesis is correct.

Curvature-Driven Wrinkling of Thin Elastic Shells

How much energy does it take to stamp a thin elastic shell flat? Motivated by recent experiments on the wrinkling patterns of floating shells, we develop a rigorous method via $\Gamma$-convergence for answering this question to leading order in the shell's thickness and other small parameters. The observed patterns involve "ordered" regions of well-defined wrinkles alongside "disordered" regions whose local features are less robust; as little to no tension is applied, the preference for order is not a priori clear. Rescaling by the energy of a typical pattern, we derive a limiting variational problem for the effective displacement of the shell. It asks, in a linearized way, to cover up a maximum area with a length-shortening map to the plane. Convex analysis yields a boundary value problem characterizing the accompanying patterns via their defect measures. Partial uniqueness and regularity theorems follow from the method of characteristics on the ordered part of the shell. In this way, we can deduce from the principle of minimum energy the leading order features of stamped elastic shells.

Control of Elastic behavior in smart material integrated shallow spherical composite panel using HOSDT kinematics

This work aims to the large bending behaviour of shallow spherical composite reinforced with piezoelectric fibre. This piezocomposite has been modelled by incorporating the Green-Lagrange type of strain in association with the higher-order shear deformation theory, where the displacement field and electric potential field is taken in the function of cubic order and quadratic order of thickness coordinate respectively. The governing equation has been solved using nonlinear finite element method. The large amplitude responses have been obtained by employing the minimum potential energy principle and direct iterative method. The computed responses have been validated with the numerical results available in the existing literature. The actuating ability of the piezoelectric composite panel in order to supress the large amplitude bending responses has been studied using proposed higher order nonlinear mathematical model. Various coupled electromechanical numerical problems have also been solved in order to understand the linear/nonlinear elastic behaviour of spherical piezocomposite panel with the detailed explanation on the actuation response due to the variation in the different geometrical parameters.

Porosity effect on the nonlinear deflection of functionally graded magneto-electro-elastic smart shells under combined loading

This article presents a higher-order nonlinear finite element formulation to evaluate the nonlinear deformation of functionally graded magneto-electro-elastic porous (FG-MEEP) shells under the influence of electro-magnetic and mechanical loads. To derive the equations of motion, Donnell's shell theory with higher-order shear deformation theory and von-Karman's geometric nonlinearity is plugged into the principle of minimum potential energy. The credibility of the formulation is verified against published articles. The even or uneven distribution of porosity is implemented in the analysis. The coupled material properties are functionally graded according to modified power law. Two forms of material gradation such as ‘B’ rich bottom and ‘F’ rich bottom are considered. Several numerical examples are illustrated to demonstrate the influence of parameters such as shell geometry, porosity distribution, gradient index, porosity volume, functionally graded pattern, electro-magnetic loads on the nonlinear central deflection of FG-MEEP shells. Special attention has been paid to distinguish between the structural responses of FG-MEEP shells at fully coupled and uncoupled states.

Self-assembly of superstructures at all scales

Summary Controllable assembly of molecular and nanoscale building blocks into uniform superstructures up to bulk dimensions remains a key challenge in the next phase of nanotechnology development. Here, we report the self-assembly of superstructures at all scales by taking advantage of the partial miscibility of water and 1-butanol to generate transient aqueous emulsion droplets that can encapsulate the target materials and introduce them into template holes. Further diffusion of water into 1-butanol depletes the emulsion droplets, assembling the building blocks into one well-defined superstructure in each hole. Superstructuring of various types and shapes of nanoparticles, biomolecules, and inorganic compounds could be achieved without the need for surfactants and chemical modifications. The versatility, scalability, low-cost, and accurate positioning are crucial advantages for the future development of advanced precision manufacturing.

Toward thermal stimulation of shape memory polymer composite bistable tape springs

Due to their tailored thermomechanical behavior and functionality, shape memory polymer matrix composites (SMPCs) are attractive as deployable structures in aerospace applications. An analytical model based on the classical laminate theory, together with the principle of minimum potential energy is developed to capture the thermo-viscoelastic behavior of a bistable tape spring (BiTS). These tape springs are known to snap between two stable configurations by different stimulus. Here, a shape memory polymer as the matrix of a fiber-reinforced polymer BiTS is introduced to actuate the snap-back. Experimental characterization was performed to obtain the time-temperature dependent properties of a Polyurethane SMPC. The time-temperature superposition principle was employed to convert the thermal effects to a viscoelastic response. Five BiTSs were manufactured and exposed to two different thermo-viscoelastic cycles to verify the model for long-term and high-temperature behaviors. The results show that the model can estimate the coiling radius and the degree of stability of the BiTS in the coiled configuration. Analytical results, supported by experimental results, show that the temperature could initiate the snap-back in BiTS. However, time-temperature history has a significant effect on the bistability and can convert a monostable tape spring to a BiTS and vice versa.