Homogeneous Isotropic Material Research Articles

Damping properties of fibre composite and conventional materials measured by free damped vibration response

The present work contributes to the research on the damping properties of fibre composites through an experimental approach by using the free damped vibration measurement based on impulse-force system response, the developed measurement stand and laser Doppler vibrometry. Moreover, the influence of the material configuration on the damping properties was investigated and was compared with conventional homogeneous isotropic materials. The measurement was based on the analysis of flexural vibrations generated by the Dirac impulse force, as well as on the free decaying-vibrations response; the time- and frequency-domain modal identification was employed. The fibre composites were represented as layered bidirectional long carbon- and glass-fibre composites (laminates) with different material configurations and as short carbon-fibre composites.

Effect of magnetic field and three-phase-lag in a rotating micropolar thermo-viscoelastic half-space homogeneous isotropic material

This paper is devoted to three-phase-lag theory of thermo-elasticity to study the effects of rotation, ramp parameter and magnetic field in a micropolar generalized thermo-viscoelastic medium. By employing normal mode analysis and Lame’s potential theory, the analytical expressions for the displacement components, stresses components, couple stress and temperature field are obtained in the physical domain. Numerical examples are displayed to illustrate the effects of magnetic field, rotation and ramp parameter on the results. When there is no phase-lag effects, the results of the current paper are reduced to exactly the same results available in the literature. However, the magnetic field and rotation have no effect on the non-dimensional temperature. The results indicate that the effect of magnetic field, rotation, ramp parameter, viscous and Phase-lag on the micropolar thermo-viscoelastic medium are very pronounced.

Equilibrium Paths for von Mises Trusses in Finite Elasticity

This paper deals with the equilibrium problem of von Mises trusses in nonlinear elasticity. A general loading condition is considered and the rods are regarded as hyperelastic bodies composed of a homogeneous isotropic material. Under the hypothesis of homogeneous deformations, the finite displacement fields and deformation gradients are derived. Consequently, the Piola-Kirchhoff and Cauchy stress tensors are computed by formulating the boundary-value problem. The equilibrium in the deformed configuration is then written and the stability of the equilibrium paths is assessed through the energy criterion. An application assuming a compressible Mooney-Rivlin material is performed. The equilibrium solutions for the case of vertical load present primary and secondary branches. Although, the stability analysis reveals that the only form of instability is the snap-through phenomenon. Finally, the finite theory is linearized by introducing the hypotheses of small displacement and strain fields. By doing so, the classical solution of the two-bar truss in linear elasticity is recovered.

Analytical Analysis of Distribution of Bending Stresses in Layers of Plywood with Numerical Verification

The study presents methods for accurate estimation of bending stresses in the 3-point flexural bending test of plywood, i.e. a wood-based laminate with an alternate crosswise ply configuration. The characteristic bending strength (MOR) and mean modulus of elasticity (MOE) of standard beech plywood was determined using European Standard bending tests EN 310. Correlations were determined between empirically determined bending moduli of the plywood and material moduli of the veneer layer. Calculations were conducted based on the classical plate theory for thin panels comprising the theory of elasticity including the Kirchhoff-Love hypothesis. Rigidity of individual layer was established theoretically in the axial configuration of transformed rigidity matrix values. Numerical laminate models were developed and simulation tests were conducted. Results of experimental and analytical studies were verified using the Finite Element Method (FEM). Analyses were performed in two plywood cross-band arrangement variants. An analysis of the distribution of stresses in individual layers of plywood used an analytical and numerical method assuming the plywood specimen to be a rhombic-anisotropic material. It was found that the bending load capacity of plywood depends on the configuration of individual layers (veneers). Values of stresses originating from bending do not only depend on the distance of the considered plywood layer from the middle layer but also on stiffness in the direction of operating stresses. Bending strength varies in individual directions of the plywood panel. Therefore, the distribution of stresses in individual layers differs from that resulting from the stress distribution for homogeneous isotropic materials. Results are presented in the form of tables, bitmaps, graphs and photographs. The tests were conducted based on the BFU-BU-18 standard beech plywood thickness of 18 mm.

Simplified beam model of high burnup spent fuel rod under lateral load considering pellet-clad interfacial bonding influence

Abstract An integrated approach of model simplification for high burnup spent nuclear fuel is proposed based on material calibration using optimization. The spent fuel rods are simplified into a beam with a homogenous isotropic material. The proposed approach of model simplification is applied to fuel rods with two kinds of interfacial configurations between the fuel pellets and cladding. The differences among the generated models and the effects of interfacial bonding efficiency are discussed. The strategy of model simplification adopted in this work is to force the simplified beam model of spent fuel rods to possess the same compliance and failure characteristics under critical loads as those that result in the failure of detailed fuel rod models. It is envisioned that the simplified model would enable the assessment of fuel rod failure through an assembly-level analysis, without resorting to a refined model for an individual fuel rod. The effective material properties of the simplified beam model were successfully identified using the integrated optimization process. The feasibility of using the developed simplified beam models in dynamic impact simulations for a horizontal drop condition is examined, and discussions are provided.

Measuring electrical properties of mortar and concrete samples using the spectral induced polarization method: laboratory set-up

Abstract Electrical impedance spectroscopy (EIS), also known as Spectral Induced Polarization (SIP) has proven to be a successful non-destructive technique able to characterize the chemical and physical properties of a complex structure (concrete, rocks, and soil) under various environmental conditions. Because this technique aims to measure small amplitude signals, it can easily be influenced by parasitic effects which are not representative of the intrinsic properties of the investigated material. The purpose of this paper is to validate the resolution of our experimental methodology as a preliminary step to ensure an accurate measurement of the bulk complex resistivity response of concrete samples within a wide frequency range (1.43 mHz–20 kHz). A cement mortar sample is first used as a homogeneous (isotropic) material to improve the sample holder design for reducing the errors and controlling the external parameters (such as coupling effect, geometric factor, contact impedance, electrode polarization) during the laboratory measurements. Also, the performance and installation of the measuring components such as the electrodes (current and potential) and the sample holder design are assessed. The specimen dimensions and designs are selected based on a sample standard size that will be used to determine the physico-mechanical properties of concrete (compressive strength, modulus of elasticity, ultrasonic pulse velocity, length variation). The examinations are performed in parallel with the SIP measurement on the same sample. The accuracy of our measurement setup is then validated using aluminum-bronze plates bonded to the sample using a conductive gel to transmit electric current with a density less than 10 - 3 A m−2. The results showed that by controlling the sponge moisture in the Ag/AgCl non-polarizable voltage electrodes, our SIP measurement system is able to measure the phase lag with an error smaller than 1 mrad over a frequency range from 1.43 mHz to 20 kHz.

On the determination of the third-order elastic constants of homogeneous isotropic materials utilising Rayleigh waves

This paper presents a new method for determining the third-order elastic constants (TOECs) of a homogeneous isotropic material utilising the acoustoelastic effect associated with Rayleigh waves. It is demonstrated that the accuracy of the evaluation of TOECs can be substantially improved by supplementing the classical equations of acoustoelasticity, which describe the effect of applied stress on bulk wave speeds, with the nonlinear characteristic equation for the propagation of Rayleigh waves in pre-stressed media. The developed method can be readily implemented for Structural Health Monitoring applications; for example, the measurement of applied stresses based on the acoustoelastic effect, or the monitoring of near-surface microstructural damage based on the change in magnitude of the TOECs.

Soliton for Nonlinear Rayleigh Surface Waves on Homogeneous Isotropic Materials

We reinvestigate the steady propagation of nonlinear Rayleigh surface waves on homogeneous isotropic materials by the method of multiple scales. We find an explicit form for the steady propagation ...

Caustics investigation of interfacial fracture in orthotropic/isotropic bi-material system

The crack tip stress intensity factor in a homogeneous isotropic material was easily experimentally evaluated via the caustics method. With respect to the bi-material orthotropic/isotropic system, it is not possible to directly evaluate the interfacial crack stress intensity factor via traditional caustics theory. In the study, theoretical caustics and initial curves at interfacial cracks of orthotropic/isotropic bi-material system were simulated based on caustics parametric equations surrounding the interfacial crack tip derived via the principle of the transmission caustics. To verify the theoretical caustics equation, a dynamic caustics experiment and FEM method under an impact load with the orthotropic/isotropic bi-material system were conducted. The KID evaluated by the dynamic caustics equation agreed well with the FEM results. The results provide an integrated theoretical foundation with respect to the application of the caustics equation on the bi-material interfacial crack problem.

До задачі розрахунку релаксації напружень у тонкостінних трубчастих елементах із лінійно- в’язкопружних матеріалів

The relaxation of isotropic homogeneous and non-aging linear-viscoelastic materials under conditions of complex stress state is considered. Thin-walled tubular specimens of High Density Polyethylene (HDPE) for creep under a single-axial stretching, with a pure twist and combined load tension and torsion are considered as base experiments, tests. The solution is obtained by generalizing the initial one-dimensional viscoelasticity model to a complex stressed state, constructed using the hypothesis of the proportionality of deviators. The heredity kernels are given by the Rabotnov’s fractional-exponential function. The dependence between the kernels of intensity and volumetric creep is established, which determine the scalar properties of linear viscoelastic materials in the conditions of a complex stressed state in the defining equations of the type of equations of small elastic-plastic deformations, and the kernels of longitudinal and transverse creep defining the hereditary properties of linear-viscoelastic materials under the conditions of the uniaxial tension. The problems of stress relaxation calculation of thin walled tubes under combined tension with torsion have been solved and experimentally approved.

Coupled Crystal Plasticity-Phase Field Modeling of Multi-Phase Metals

A code has been developed based on image based crystal plasticity modeling of multiphase metals. This model coupled with equilibrium equation and compatibility constraint is solved at each material point of representative volume element. A phenomenological equation for dislocation slip is used. Crystal kinematics couples the boundary conditions to constitutive behavior by integrating evolution equation for elastic deformation gradient obtained using the multiplicative decomposition of deformation. The code is tested for linear homogeneous isotropic elastic material with embedded inclusions. We analyze two types of inclusions namely an elastic inclusion and a void. These two baseline studies have been compared against solutions from currently available commercial and open source packages. In the second example we study the time evolution of residual stresses due to a growing phase. Such models are especially useful for understanding the role of interactions and co-deformation of multiple phases on the overall mechanical response of a multiphase metal. Experimental data set found in the literature is used for calibration of the developed crystal plasticity model.

АНАЛИЗ КРИТИЧЕСКОГО СОСТОЯНИЯ ДИСКРЕТНО-НЕОДНОРОДНОЙ ПОЛОСЫ С НАКЛОННОЙ КОНТАКТНОЙ ГРАНИЦЕЙ И НАРУЖНЫМ МАКРОДЕФЕКТОМ В БОЛЕЕ ПРОЧНОЙ ЧАСТИ

The article considers the stress state of a joint in the form of an elastic-plastic strip with rectilinear parallel edges under conditions of plane deformation. The strip consists of two parts of different strengths made of homogeneous isotropic materials, separated by a straight line which is forming an arbitrary angle with the edge of the strip. The joint is subjected to tensile stress. In its stronger part, there is a surface macrodefect in the form of an external incision or recess. The purpose of the article is to study the critical state of the joint using various geometrical and mechanical parameters and, on this basis, calculate the critical tensile force. The method is based on the study of characteristic fields (slip lines) in the plastic zone, taking into account the presence of a voltage break in the more durable part. A complete analysis of variations of the patterns of characteristic fields leading to different stress diagrams over the net cross section is given, depending on the relative position of the defect and the contact boundary, the size of the defect, the angle of inclination of the contact boundary, and the coefficient of mechanical heterogeneity of the joint. An algorithm has been developed to calculate the critical tensile force in the general case. The average critical stresses in the most characteristic cases have been calculated.

Zero-range potential in the model of the spinor field interacting with a material plane: conditions for transparency of the plane to Dirac particles

In the model of interaction of a spinor field with a homogeneous isotropic material plane, the possibility of the passage of a Dirac particle through it without reflection and a change in polarization isstudied. The model was proposed earlier in the framework of the Symanzik approach to describe the interaction of spinor quantum fields with two-dimensional materials. In its framework the scattering processes of Dirac particles and the properties of their bound states were investigated. In this paper, we study the conditions under which the plane is completely transparent to the particles. A description of the region of model parameters characterizing the properties of the plane material is obtained explicitlyand given in the article, as well as expressions in terms of these parameters for the momentum and polarization of the particle at which interaction with the plane does not affect its movement.

Interface tension-induced stress field around periodic nano-inclusions of arbitrary shape

This paper investigates the plane deformation of periodic nano-inclusions of arbitrary shape embedded in a homogeneous isotropic material. A representative unit cell (RUC) with periodic boundary conditions imposed on its edges is used to represent the periodicity of the structure. Residual interface tension is incorporated into the deformation model so that the normal and tangential stresses have to jump across the matrix–inclusion interface, despite that the displacement can generally be treated as continuous across that interface. The stress field in the entire RUC is obtained by using the complex variable methods with the assistance of conformal mapping, series expansion, and collocation techniques. Numerical examples are presented for three different inclusion shapes. The results show that the interface tension-induced stress field can be greatly influenced by the shape, elastic modulus, and volume fraction of the inclusions.

A uniform Laser Pulse for a Solid Cylinder by using different theories of magneto thermo elasticity

This work is concerned with the study of vibrations induced by a laser beam in the context of different theories of magneto thermoelasticity, coupled thermoelasticity (CTE), thermoelasticity with one relaxation time (L-S) and thermoelasticity without energy dissipation (G-L), of an infinitely long solid conducting circular cylinder. The surface of the cylinder is assumed to be traction free. The temporal profile of the laser beam is considered as non-Gaussian. The cylinder is considered to be made of an isotropic homogeneous thermoelastic material put in a uniform magnetic field in the direction of the axis. This produces an induced magnetic field and an induced electric field. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions. The temperature, displacement, stresses, induced magnetic field and induced electric field are calculated numerically then represent the result by graphs.

Nonlinear rapid heating of shallow arches

The analysis of large amplitude thermally induced vibrations of a shallow curved beam is considered in this article. The beam is made from an isotropic homogeneous material. One surface of the arch is subjected to rapid surface heating while the other surface is kept at reference temperature. The temperature profile is evaluated by means of the 1D heat conduction equation across the thickness of the beam. The thermally induced moments and forces are evaluated from the temperature profile. These resultants are inserted into the equations of motion of the arch. To establish the equations of motion, kinematic assumptions of a shallow arch with considerations of the von Kármán type of geometrical nonlinearity, Euler–Bernoulli beam assumptions, and linear stress–strain–temperature law are employed. The equations of motion are discreted using the conventional polynomial Ritz formulation. The resulting equations are nonlinear and at each time step the Newton–Raphson technique is used to obtain the solution. The equations of motion of the arch are traced in time domain using the Newmark time marching scheme, which results in the temporal evolution of lateral displacement at arbitrary point of the arch. Numerical results are provided to explore the effects of different parameters. It is shown that thermally induced vibrations indeed exist especially for thin arches. As the beam becomes thicker or shorter, the thermally induced vibrations fade up and for sufficiently thick arches, quasi-static and dynamic responses of the arch become identical.

Likely Cavitation in Stochastic Elasticity

We revisit the classic problem of elastic cavitation within the framework of stochastic elasticity. For the deterministic elastic problem, involving homogeneous isotropic incompressible hyperelastic spheres under radially symmetric tension, there is a critical dead-load traction at which cavitation can occur for some materials. In addition to the well-known case of stable cavitation post-bifurcation at the critical dead load, we show the existence of unstable snap cavitation for some isotropic materials satisfying Baker-Ericksen inequalities. For the stochastic problem, we derive the probability distribution of the deformations after bifurcation. In this case, we find that, due to the probabilistic nature of the material parameters, there is always a competition between the stable and unstable states. Therefore, at a critical load, stable or unstable cavitation occurs with a given probability, and there is also a probability that the cavity may form under smaller or greater loads than the expected critical value. We refer to these phenomena as ‘likely cavitation’. Moreover, we provide examples of homogeneous isotropic incompressible materials exhibiting stable or unstable cavitation together with their stochastic equivalent.

The nonlinear elasticity of hyperelastic models for stretch-dominated cellular structures

For stretch-dominated cellular structures with arbitrarily oriented cell walls made from a homogeneous isotropic hyperelastic material, recently, continuum isotropic hyperelastic models were constructed analytically, at a mesoscopic level, from the microstructural architecture and the material properties at the cell level. Here, the nonlinear elastic properties of these models for structures with neo-Hookean cell components are derived explicitly from the strain-energy function and the finite deformation of the cell walls. First, the nonlinear shear modulus is calculated under simple shear superposed on finite uniaxial stretch. Then, the nonlinear Poisson’s ratio is computed under uniaxial stretch and the nonlinear stretch modulus is obtained from a universal relation involving the shear modulus as well. The role of the nonlinear shear and stretch moduli is to quantify stiffening or softening in a material under increasing loads. Volume changes are quantified by the nonlinear bulk modulus under hydrostatic pressure. Numerical examples are presented to illustrate the behaviour of the nonlinear elastic parameters under large strains.

Nonlinear Fracture Resistance Parameters for Elements of Aviation Structures under Biaxial Loading

This study is concerned with practical application of nonlinear deformation and fracture resistance parameters for residual durability estimation of the fuselage elements with operation damage. By means of numerical calculations for the fragment of fuselage skin with central crack the governing parameters of the elastic-plastic crack-tip stress field are determined as a function of biaxial loading. Two variants of modeling of the crack-tip stress field were performed for the panel of homogeneous isotropic material and a set of the special cohesive elements. As a result the assessment of the biaxial loading influence of fracture damage zone state on crack tip stress field in fuselage panel is given.

Modelling of Bound States of Dirac Particles in Singular Background in Framework of Symanzik Approach

The problem of interaction of the fields of quantum electrodynamic with material macro-object is considered by employing the Symanzik approach on modelling the interaction of quantum field with space-time inhomogeneities. Results obtained in the models with Chern–Simons interaction of photon field with 2-dimensional material are briefly reviewed. In the model of interaction of spinor field with homogeneous isotropic material plane constructed in framework of Symanzik approach, the bound states are considered. For localized near plane Dirac particle the dispersion relation and the expressions for current, charge and density are analyzed. The bound states with massless dispersion law is considered. The presented methods of modelling can find application to a wide class of phenomena emerging from the interaction of quantum fields with extended material structures.