Energy Equivalence Principle Research Articles

A constitutive model independent analytical method in determining the tensile properties from incremental spherical indentation tests (ISITs)

In this study, an analytical method based on the simplified expanding cavity model, the equivalent energy principle, and the differential approach was proposed to determine the stress-strain relationship (constitutive behavior) of materials from incremental spherical indentation tests (ISITs). Apart from the load-depth curve obtained from the load cell and displacement sensor, respectively, one measurement of the plastic zone radius rp after the indentation test through digital image correlation (DIC) method was also used to determine the proportional limit σ0. The analytical derivation of this method has a clear physical meaning and does not depend on any specific constitutive models, and thus can be used on a large variety of materials and can be considered as a substitute for destructive uniaxial tensile tests. Experiments were conducted on four materials, 15CrMoR, TC21, SA508, and SA533. Two different models, which took the characteristics of the derived stress-strain data points into consideration, were used to describe the constitutive behavior of the four experimental materials. Experimental results proved that ISITs provided almost identical Young's modulus E (with a maximum error of less than 3%), stress-strain curves, proof strength Rp0.2 (with a maximum error of -5.9% when the strain threshold εth = 0.6%), and tensile strength RT (with a maximum error of -6.7% when εth = 0.6%) as their tensile counterparts. Furthermore, the stress-strain data points derived with the method proposed in this study could even characterize the yield plateau in the stress-strain curves of 15CrMoR, SA508, and SA533.

Nonlinear post-flutter behavior and self-excited force model of a twin-side-girder bridge deck

The nonlinear aeroelastic behavior of a typical bluff bridge section, i.e., open twin-side-girder bridge deck, was investigated through a series of spring-suspended sectional model (SSSM) tests in the post-flutter state. When the reduced wind speed exceeded linear aeroelastic limits, the sectional model underwent significant limit cycle oscillation (LCO) characterized by a quasi-harmonic torsional vibration with slight heave-torsion coupling effect. The stable amplitudes of post-flutter LCOs increased in a roughly linear way with reduced wind speed. The nonlinear self-excited force (NSEF) was measured by a novel force measurement technique and validated by comparing the calculated post-flutter responses with experiments. The measured NSEF contained significant 2nd and 3rd order nonlinear harmonic components. Based on the measured NSEF signals and equivalent energy principle, a NSEF model suitable for large amplitude of vibration was proposed and then verified by comparing its predicted response with experimental results. The identified aerodynamic parameters further indicated that the mechanism of post-flutter LCOs was due to the negative aerodynamic damping provided by the linear term as an energy source to drive the growth of vibration amplitude and the nonlinear positive aerodynamic damping provided by the 3rd order angular velocity term as a stabilizing factor of self-limitation phenomenon.

Educational activities with a tandem accelerator

Selected experiments in fundamental physics have been proposed for many years at the Tandem Accelerator of the University of Napoli ‘Federico II’s Department of Physics as a part of a one-semester laboratory course for graduate students. The aim of this paper is to highlight the educational value of the experimental realization of the nuclear reaction 19F(p,α)16O. With the purpose of verifying the mass–energy equivalence principle, different aspects of both classical and modern physics can be investigated, e.g. conservation laws, atomic models, nuclear physics applications to compositional analysis, nuclear cross-section, Q-value and nuclear spectroscopic analysis.

A new method based on energy principle to predict uniaxial stress–strain relations of ductile materials by small punch testing

Uniaxial stress–strain relations of ductile materials are the most fundamental requirement for the design and safety assessment of structures. In this paper, a novel small punch testing (SPT)-related stress–strain relation (SPT-SR) model is proposed to predict the stress–strain relations of materials on the basis of equivalent energy principle. To examine the validity of the model, numerical simulations by finite element analysis (FEA) with a series of hypothetical materials with different Hollomon's material parameters were carried out. The results demonstrate that the uniaxial stress–strain relations predicted by SPT-SR model from simulated load-displacement curves are in good agreement with the properties of hypothetical materials used in FEA. Furthermore, SPT experiments and tensile tests for four steels (P92, DP600, Q345B, A508-III) at room temperature and 300 °C were conducted. The stress–strain relations predicted by SPT-SR model agree well with the tensile results generated from finite-element-analysis aided testing (FAT) method. Compared with the tensile strengths obtained by uniaxial tensile tests, they can also be well determined based on the strength coefficient and strain hardening exponent predicted by SPT-SR model.

Theoretical Conversions of Different Hardness and Tensile Strength for Ductile Materials Based on Stress–Strain Curves

Based on the power-law stress–strain relation and equivalent energy principle, theoretical equations for converting between Brinell hardness (HB), Rockwell hardness (HR), and Vickers hardness (HV) were established. Combining the pre-existing relation between the tensile strength (σ b ) and Hollomon parameters (K, N), theoretical conversions between hardness (HB/HR/HV) and tensile strength (σ b ) were obtained as well. In addition, to confirm the pre-existing σ b -(K, N) relation, a large number of uniaxial tensile tests were conducted in various ductile materials. Finally, to verify the theoretical conversions, plenty of statistical data listed in ASTM and ISO standards were adopted to test the robustness of the converting equations with various hardness and tensile strength. The results show that both hardness conversions and hardness-strength conversions calculated from the theoretical equations accord well with the standard data.

Unified Model of K Factor and Compliance Based on Energy Equivalence Principle

Unified Model of K Factor and Compliance Based on Energy Equivalence Principle

Design and Dynamic Equivalent Modeling of Double-Layer Hoop Deployable Antenna

This study proposes deployable units driven by elastic hinges and a double-layer hoop deployable antenna composed of these units. A rational modeling method based on the energy equivalence principle is presented to develop an equivalent model of the double-layer hoop antenna in accordance with the structural characteristics of the antenna. The equivalent beam models of the rods with elastic hinges are proposed. The relationship of geometrical and material parameters is established considering the strain energy and the kinetic energy of the periodic unit, which are the same as those of the equivalent beam in the same displacement field. The equivalent model of the antenna is obtained by assembling several equivalent beam models in the circumferential direction. The precision of the equivalent model of the antenna is acceptable as found by comparing the modal analysis results obtained through equivalent model calculation, finite element simulation, and modal test.

Comparative study on damping models of linear system subjected to arbitrary dynamic loading

Linear and nonlinear damping models, correlated through equivalent damping coefficient, have been developed for discrete vibrating system employing energy equivalence principle at steady state response of the system. Application of, so developed, damping models to derive response of discrete vibrating system subjected to arbitrary dynamic loading is not obvious due to transient nature of the system. Thus, the equivalent damping coefficient of damping models needs to be redefined to derive realistic transient response of the system. In the present study, first cycle damping coefficient (FCDC) approach is proposed that uses the first cycle transient response of the system to derive equivalent damping coefficient for linear and nonlinear damping models through genetic algorithm propelled energy equivalence with that of linear viscous damping model. A single degree of freedom (SDOF) system with linear and nonlinear damping models subjected to arbitrary dynamic loading are solved. Efficacy of proposed FCDC approach is established through the experimental study on a lightly damped single storey building model. Velocity squared damping model yields higher peak displacement response for the system vis-a-vis system with linear viscous damping model. Proposed FCDC approach can be effectively utilised if the transient response of the system is available experimentally.

Численный метод оценки эффективных упругих характеристик горной породы по двумерным и трехмерным цифровым изображениям керна

Представлен численный алгоритм оценки упругих свойств образцов горной породы по дву- и трехмерным компьютерным томограммам. Метод основан на принципе эквивалентности энергии деформаций, вызываемых однородными граничными статическими условиями, имитирующими физический эксперимент. На этой основе определяется эффективный тензор податливости представительного объема неоднородной среды. Особенностью алгоритма является новая схема расчета статического напряженно-деформированного состояния образца методом установления решения соответствующей задачи динамической теории упругости. Приводятся результаты численных расчетов. Предложенный метод верифицировался на однородных образцах с заданными свойствами, а также для слоистых материалов, для которых доказана справедливость построения эффективных параметров по методу Шенберга. В заключение приведены эффективные параметры для трехмерного образца кернового материала. A numerical method to estimate the effective elastic moduli of rocks from two- and three-dimensional digital images of rock core samples is proposed. The method is based on the energy equivalence principle for deformations caused by the homogeneous boundary static conditions that simulate a physical experiment. On this basis, the effective compliance tensor of a representative volume of an inhomogeneous medium is determined. A specific feature of the proposed algorithm is a new scheme for calculating the stress-strain static state of a sample by solving the corresponding problem of dynamic elasticity theory using the relaxation method. The obtained numerical results are discussed. The proposed method is verified using homogeneous samples with specified properties as well as for layered materials with effective parameters obtained according to the Schoenberg method. In conclusion, the effective parameters for a three-dimensional core sample are presented.

Application of Principles of Theory of Damage Accumulation to Calculation of Asphalt-Concrete Coatings

It was found that, when exposed to the repeated loads, the asphalt concrete pavement of roads accumulates damage which must be considered in their calculation. By entering the damage measuring theory (L.M. Kachanova continuity, damage Rabotnova Y.N.) and applying the principle of equivalence of a continuous state of stress and damage caused by media the authors modified the criteria proposed by Pisarenko-Lebedev and Drucker-Prager. Such modified criteria take into account the effect of damage accumulation in the calculation of asphalt concrete pavement on the tensile strength in bending and shear. To determine the functional dependence of damage and continuity on the number of applied loads, the authors used the principle of energy equivalence for continuous and damaged media.

Unified ring-compression model for determining tensile properties of tubular materials

The stress-strain relation is the key mechanical properties in safety design and evaluation for tubular structures. However, conventional uniaxial tension and compression tests have some drawbacks and limitations for these structures. In the current investigation, a unified ring-compression model to acquire the stress–strain relation of tubular material is introduced based on the equivalent energy principle. In the model, a unified relation among strain energy, load, deflection, geometric parameters and material property parameters is proposed to depict the elastoplastic response during ring compression test. The model has only four undetermined parameters which can be calibrated by a few FEA (finite element analysis) calculations. The accuracy of the model has been verified within a wide range of imaginary materials by using FEA. Results show that both the forward-predicted load-deflection relation and the reverse-predicted stress-strain relations from the model are in excellent accord with the results from FEA. In addition, the model is verified with three homogeneous ductile materials by conducting ring compression and standard tensile tests. And it is applied in obtaining the hoop stress-strain relation of tubular zirconium alloy in the nuclear power engineering.

Unified elastoplastic model based on a strain energy equivalence principle

A unified elastoplastic model was proposed to describe the relation among load, displacement, and uniaxial constitutive parameters of ductile materials according to the von Mises energy equivalence principle at a special location or energy center in the deformed region of a structural component (SC). Two pairs of parameters were considered in the model: one was related to the volume of deformed region and the other to the Mises equivalent strain at the energy center. In addition, they are easily determined by finite element analysis (FEA). For eight kinds of SCs under proportional loading, the load–displacement behaviors of various materials predicted by the unified model were highly consistent with the results of FEA.

Coupling microplane-based damage and continuum plasticity models for analysis of damage-induced anisotropy in plain concrete

A novel plastic-damage constitutive model for plain concrete is developed in this paper. For this purpose, the microplane theory is proposed for overcoming the deficiency of available anisotropic continuum plastic-damage models in reproducing the true anisotropic nature of damage in multidimensional loadings. Based on the microplane theory, the degeneration process in concrete is considered along with plastic deformations. Using the principle of strain energy equivalence, a transformation between the nominal and effective states of material is achieved, that results in a decoupled formulation for damage and plasticity. A yield function with multiple internal variables and a non-associative flow function are employed to describe the plastic behavior of concrete. In order to discriminate between the behavior of concrete in tension and compression, stress tensor is decomposed into tensile and compressive parts, and two sets of microplanes are defined for each material point, leading to corresponding independent anisotropic damage tensors in tension and compression. Several numerical examples are analyzed using the proposed model and robustness and accuracy of the formulation are assessed using the available experimental tests. In addition, superiority of the proposed model over the available isotropic and anisotropic formulations is demonstrated by comparisons between the different approaches. The effects of three different cubature schemes on the response of concrete specimens are also analyzed.

Investigation for plastic damage constitutive models of the concrete material

In this paper, some simple stress-strain relationships of the concrete material recommended in relevant Codes are appropriately simplified, then the damage factors of the simplified plastic damage constitutive model is determined based on Sidiroff’s energy equivalence principle. Mechanical characteristics of the concrete material under the simple tension or compression are analyzed by Finite element method. Through the comparison of numerical analysis results and Code constitutive relations, the damage factors of the simplified plastic damage constitutive model is verified. The unreinforced concrete beam static tests by Petersson is simulation analyzed by the nonlinear finite element method and plastic damage constitutive model. The effect of the unit size and the different linear softening constitutive relation on the analysis results are considered. The results show that there is no obvious size effect on the plastic damage analysis results based on fracture cracking criterion, the results of the bilinear softening constitutive analysis have good accuracy, and the form of softening constitutive relation has a great influence on the result.

A Definition of Equivalent Inhomogeneity Applicable to Various Interphase Models and Various Shapes of Inhomogeneity

The concept of equivalent inhomogeneity has been introduced to analyze the effective properties of composites with interphases using techniques devised for problems without interphases. The basic idea is to replace the inhomogeneity and the surrounding it interphase by a single equivalent inhomogeneity with constant stiffness tensor, combining properties of both, which is then perfectly boned to the matrix. In this presentation a new definition of equivalent inhomogeneity is discussed. It is based on Hill's energy equivalence principle, applied to the problem consisting only of the original inhomogeneity and its interphase. It is more general than the definitions proposed in the past in that, conceptually and practically, it allows to consider inhomogeneities of various shapes and various models of interphases. This is illustrated considering spherical and cylindrical particles with two models of interphases, Gurtin-Murdoch material surface model and spring layer model. The resulting equivalent inhomogeneities are subsequently used to determine effective properties of randomly distributed unidirectional particulate composites. Properties of the equivalent cylindrical inhomogeneities are transversely isotropic, thus the method of conditional moments, which is a statistical method capable of handling anisotropy and randomness, has been employed for that purpose. Closed-form formulas for the effective stiffness tensor have been developed in all cases considered here. Comparisons with solutions available in the literature are made and other possible applications are discussed.

Mechatronic modeling of a parallel kinematics multi-axial simulation table based on decoupling the actuators and manipulator dynamics

In this work a mechatronic model was developed for a parallel Multi-Axial Simulation Table (MAST) mechanism. The dynamics of the mechanism was obtained using the principle of energy equivalence and Boltzmann–Hamel equations. In this way, the procedure to obtain the explicit dynamic equations is simplified and has the advantage of being systematic. Also, the actuators and the control were modeled and integrated to simulate and study the system’s positioning and torque.A remarkable contribution of this work is that the mechatronic model developed considers the mechanism as a disturbance to the actuators in a decoupled manner, allowing to easily evaluate alternative designs of whether the actuators, the mechanism or both. Additionally, the procedure taken has been validated with experimental data from an actual MAST prototype.

Theoretical model for predicting uniaxial stress-strain relation by dual conical indentation based on equivalent energy principle

For conical indentation, the strain energy is a function of the semi-vertical cone angle, the indentation depth and the stress-strain relation. According to equivalent energy principle of representative volume elements (RVE) and the classical cavity assumption for material deformation region, the function with dual-parameters about volume and deformation is theoretically derived in the present study. This original equivalent-energy indentation model (EIM) is capable of forward-predicting load-depth relation and reverse-predicting uniaxial stress-strain relation for ductile materials only based on loading part of indentation. Further analyses show that the forward and reverse predicted results from EIM method are in excellent agreement with those by finite element analyses (FEA). Macro conical indentation experiments on five types of metals have been conducted using conventional indenters which are similar to Rockwell sclerometer. Consequently, the stress-strain relations predicted by EIM are quite close to those from standard tensile tests.

Distorted wave response of ultrasonic annular stator incorporating non-uniform geometry

The traveling wave ultrasonic stator is normally fabricated with teeth. The tooth geometry improves the driving speed, but it creates natural frequency splitting and mode contamination, especially a distorted traveling wave. A dynamic model of a stepped-plate periodic stator is developed to examine the distortion. The stator is treated as an annular supported by a thin mid plate, and the support stiffness is formulated by using equivalent energy principle. The effects of the tooth and mid plate on the natural frequency and vibration mode are examined by using the perturbation method. The rules governing the frequency splitting, frequency perturbation as well as mode contamination are also identified. The traveling wave response and elliptical trace on stator surface are obtained by using the mode superposition method and they are proved to be distorted due to the tooth geometry. The response at the repeated doublets becomes coupled forward and backward traveling waves, but that at the split doublets becomes coupled forward traveling, standing and backward traveling waves. The results indicate that the tooth mass instead of the stiffness decreases the vibration amplitude and driving speed of the dominant wave, but their effects are different at the repeated and split doublets. Inspection of the model implies that the distortion can be suppressed by using a suitable combination of the wavenumber, tooth count, tooth height and occupying fraction. Numerical calculations are carried out to demonstrate the tooth geometry effect on the transient waveform, driving speed and elliptical trace. The optimization of the tooth geometry that can help achieve a purer traveling wave is discussed.

Effective properties of short-fiber composites with Gurtin-Murdoch model of interphase

A mathematical model employing the concept of the energy-equivalent inhomogeneity combined with the method of conditional moments has been applied to analyze short-fiber composites. The fibers are parallel, randomly distributed, and their interphase is assumed to be adequately described by the Gurtin-Murdoch material surface model. The properties of the energy-equivalent fiber, incorporating properties of the original fiber and its interphase, are determined on the basis of Hill's energy equivalence principle assuming its cylindrical shape. To describe random distribution of fibers a statistical method, the method of conditional moments, has been employed. Closed-form formulas for the components of the effective stiffness tensor of short-fiber reinforced composites have been developed which, in the limit, compare well with the results available in the literature for infinite parallel fibers with Gurtin-Murdoch interphase model. Influence of fiber length on contribution of the surface effects to the effective properties of the material containing cylindrical cavities has been analyzed for all five independent components of its stiffness tensor, and for two sets of surface properties in the Gurtin-Murdoch model.

Effect of the equivalent stiffness of flexible supports on the MEMS cantilever-based sensors

Small deflections and moments exist on the boundaries of the flexible supports of MEMS cantilever-based sensors. The qualitative dynamical behavior is significantly affected by the non-ideal boundary conditions. Based on the Boussinesq’s and Cerruti’s displacement equations and the principle of energy equivalence, rigorous theoretical solutions of the normal, tangential and rotational equivalent stiffness are presented in this paper. The proposed model is validated by the fact that the theoretical results remained a good situation consistency with the reported experimental data. The variations of the equivalent stiffness with the geometric dimensions of the cross section of the flexible supports are investigated. It is observed that when the “Hard material” is used as the supports’ materials, e.g. Silicon carbide, the equivalent stiffness is large. Yet the equivalent stiffness is small for the “Soft material”, e.g. Silicon and Poly-silicon. In addition, by employing the method of multiple time scales, the non-dimensional differential partial equation of the motion as well as coupled boundary conditions are analytically solved. The results indicate that the resonance frequencies decrease with the flexible supports, however, increase due to the nonlinearity mechanical spring.