Interaction between many parallel screw dislocations and a semi-infinite crack in a magnetoelectroelastic solid

Based on the fundamental equations of magnetoelectroelastic material and the analytic theory, and using the Muskhelishvili-introduced well-known elastic techniques combined with the superposition principle, the closed form solution of the generalized stress field of the interaction between many parallel screw dislocations and a semi-infinite crack in an infinite magnetoelectroelastic solid is obtained, on the assumption that the surface of the crack is impermeable electrically and magnetically. Besides, the Peach-Koehler formula of n parallel screw dislocations is given. Numerical examples show that the generalized stress varies with the position of point z and is related to the material constants. The results indicate that the stress concentration occurs at the dislocation core and the tip of the crack. The result of interaction makes the system stay in a lower energy state.

Comparative study of nudged elastic band and molecular dynamics methods for diffusion kinetics in solid-state electrolytes

Considerable efforts are being made to transition current lithium-ion and sodium-ion batteries towards the use of solid-state electrolytes.Computational methods,specifically nudged elastic band(NEB)and molecular dynamics(MD)methods,provide powerful tools for the design of solid-state electrolytes.The MD method is usually the choice for studying the materials involving complex multiple diffusion paths or having disordered structures.However,it relies on simulations at temperatures much higher than working temperature.This paper studies the reliability of the MD method using the system of Na diffusion in MgO as a benchmark.We carefully study the convergence behavior of the MD method and demonstrate that total effective simulation time of 12 ns can converge the calculated diffusion barrier to about 0.01 eV.The calculated diffusion barrier is 0.31 eV from both methods.The diffusion coefficients at room temperature are 4.3×10^(-9) cm^(2)⋅s^(−1) and 2.2×10^(-9) cm^(2)⋅s^(−1),respectively,from the NEB and MD methods.Our results justify the reliability of the MD method,even though high temperature simulations have to be employed to overcome the limitation on simulation time.

Tensile Shock Physics in Compressible Thermoviscoelastic Solid Medium

This paper addresses tensile shock physics in thermoviscoelastic (TVE) solids without memory. The mathematical model is derived using conservation and balance laws (CBL) of classical continuum mechanics (CCM), incorporating the contravariant second Piola-Kirchhoff stress tensor, the covariant Green’s strain tensor, and its rates up to order n. This mathematical model permits the study of finite deformation and finite strain compressible deformation physics with an ordered rate dissipation mechanism. Constitutive theories are derived using conjugate pairs in entropy inequality and the representation theorem. The resulting mathematical model is both thermodynamically and mathematically consistent and has closure. The solution of the initial value problems (IVPs) describing evolutions is obtained using a variationally consistent space-time coupled finite element method, derived using space-time residual functional in which the local approximations are in hpk higher-order scalar product spaces. This permits accurate description problem physics over the discretization and also permits precise a posteriori computation of the space-time residual functional, an accurate measure of the accuracy of the computed solution. Model problem studies are presented to demonstrate tensile shock formation, propagation, reflection, and interaction. A unique feature of this research is that tensile shocks can only exist in solid matter, as their existence requires a medium to be elastic (presence of strain), which is only possible in a solid medium. In tensile shock physics, a decrease in the density of the medium caused by tensile waves leads to shock formation ahead of the wave. In contrast, in compressive shocks, an increase in density and the corresponding compressive waves result in the formation of compression shocks behind of the wave. Although these are two similar phenomena, they are inherently different in nature. To our knowledge, this work has not been reported in the published literature.

Analytical solutions of steady vibration of free rectangular plate on semi-infinite elastic foundation

The method of double Fourier transform Was employed in the analysis of the semi-infinite elastic foundation with vertical load. And an integral representations for the displacements of the semi-infinite elastic foundation was presented. The analytical solution of steady vibration of an elastic rectangle plate with four free edges on the semi-infinite elastic foundation was also given by combining the analytical solution of the elastic rectangle plate with the integral representation for displacements of the semiinfinite elastic foundation. Some computational results and the analysis on the influence of parameters were presented.

APPLICATION OF A NEW FAST MULTIPOLE BEM FOR SIMULATION OF 2D ELASTIC SOLID WITH LARGE NUMBER OF INCLUSIONS

A fast multipole method(FMM)is applied for BEM to reduce both the operation and memory requirement in dealing with very large scale problems.In this paper,a new version of fast multipole BEM for 2D elastostatics is presented and used for simulation of 2D elastic solid with a large number of randomly distributed inclusions combined with a similar subregion approach.Generalized minimum residual method(GMRES)is used as an iterative solver to solve the equation system formed by BEM iteratively.The numerical results show that the scheme presented is applicable to certain large scale problems.

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids. The propagation of three longitudinal waves is represented through three scalar potential functions. The lone transverse wave is presented by a vector potential function. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. It is shown that there exist three longitudinal waves and one transverse wave. The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated. For the presence of viscosity in pore-fluids, the waves refracted to the porous medium attenuate in the direction normal to the interface. The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a non- singular system of linear algebraic equations. These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave. The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model. The conservation of the energy across the interface is verified. The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed,

Reflection and refraction of plane waves at the boundary of an elastic solid and double-porosity dual-permeability materials

Phenomena of reflection and refraction of plane harmonic waves at a plane interface between an elastic solid and doubleporosity dual-permeability material are investigated. The elastic solid behaves non-dissipatively, while double-porosity dual-permeability materials behave dissipatively to wave propagation due to the presence of viscosity in pore fluids. All the waves(i.e., incident and reflected) in an elastic medium are considered as homogeneous(i.e., having the same directions of propagation and attenuation), while all the refracted waves in double-porosity dual-permeability materials are inhomogeneous(i.e., having different directions of propagation and attenuation). The coefficients of reflection and refraction for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected and refracted waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy among various reflected and refracted waves. The effect of incident direction on the partition of the incident energy is analyzed with a change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure.It has been confirmed from numerical interpretation that during the reflection/refraction process, conservation of incident energy is obtained at each angle of incidence.

Eigen theory of elastic mechanics for anisotropic solids

Eigen characters of the fundamental equations, equilibrium equation of stress and harmony equation of deformation, of the traditional elastic mechanics under geometrical space were testified by means of the concept of standard space, and the modal equilibrium equation and the modal harmony equation under mechanical space were obtained. Based on them and the modal Hooke’s law, a new system of the fundamental equation of elastic mechanics is given. The advantages of the theory given here are as following: the form of the fundamental equation is in common for both isotropy and anisotropy, both force method and displacement method, both force boundary and displacement boundary; the number of stress functions is equal to that of the anisotropic subspaces, which avoids the man made mistakes; the solution of stress field or strain field is given in form of the modal superimposition, which makes calculation simplified greatly; no matter how complicated the anisotropy of solids may be, the complete solutions can be obtained.

THEORY OF NONLOCAL ASYMMETRIC ELASTIC SOLIDS

In this paper, a nonlinear theory of nonlocal asymmetric, elastic solids is developed on the basis of basic theories of nonlocal continuum field theory and nonlinear continuum mechanics. It perfects and expands the nonlocal elastic field theory developed by Eringen and others. The linear theory of nonlocal asymmetric elasticity developed in [1] expands to the finite deformation. We show that there is the nonlocal body moment in the nonlocal elastic solids. The nonlocal body moment causes the stress asymmetric and itself is caused by the covalent bond formed by the reaction between atoms. The theory developed in this paper is applied to explain reasonably that curves of dispersion relation of one-dimensional plane longitudinal waves are not similar with those of transverse waves.

RESTUDY OF THEORIES FOR ELASTIC SOLIDS WITH MICROSTRUCTURE

The dynamical theories of elastic solids with microstructure are restudied and the reason why so many notations have been introduced for derivation of basic equations for such theories is given. In view of the existing problems in those theories the rather general principle of power and energy rate is postulated and the equations of motion, the balance equations of energy rate and energy and the boundary conditions for local and nonlocal theories are naturally derived with help of that principle and the generalized Piola's theorem. These basic equations and the boundary conditions together with the initial conditions may be. used to solve the mixed problems of the dynamical theory of elastic solids with microstructure.

Elastic Modulus,Hardness,and Fracture Toughness of Li_(6.4)La_(3)Zr_(1.4)Ta_(0.6)O_(12) Solid Electrolyte

Li_(6.4)La_(3)Zr_(1.4)Ta_(0.6)O_(12)(LLZTO) is a promising inorganic solid electrolyte due to its high Li+conductivity and electrochemical stability for all-solid-state batteries.Mechanical characterization of LLZTO is limited by the synthesis of the condensed phase.Here we systematically measure the elastic modules,hardness,and fracture toughness of LLZTO poly crystalline pellets of different densities using the customized environmental nanoindentation.The LLZTO samples are sintered using the hot-pressing method with different amounts of Li2CO3 additives,resulting in the relative density of the pellets varying from 83% to 98% and the largest grain size of 13.21 ± 5.22 μm.The mechanical properties show a monotonic increase as the sintered sample densifies,elastic modulus and hardness reach 158.47± 10.10 GPa and 11.27± 1.38 GPa,respectively,for LLZTO of 98% density.Similarly,fracture toughness increases from 0.44 to 1.51 MPa·m^(1/2),showing a transition from the intergranular to transgranular fracture behavior as the pellet density increases.The ionic conductivity reaches 4.54 × 10^(-4 )S/cm in the condensed LLZTO which enables a stable Li plating/stripping in a symmetric solid-state cell for over 100 cycles.This study puts forward a quantitative study of the mechanical behavior of LLZTO of different microstructures that is relevant to the mechanical stability and electrochemical performance of all-solid-state batteries.

TWO-DIMENSIONAL STRESS WAVE ANALYSIS IN INCOMPRESSIBLE ELASTIC SOLIDS

Two-dimensional stress wares in n general incompressible elastic solid are investigated. First, baxic equations for simple wares and shock waves are presented for a general strain energy junction. Then the characteristic ware speeds and the associated characteristic vectors are deduced. It is shown that there usually exist two simple waves and two shock wares. Finally, two examples are given for the case of plane strain deformation and antiplane strain deformation, respectively. It is proved that, in the case of plane strain deformation, the oblique reflection problem of a plane shock is not solvable in general.

Forward modeling of ocean-bottom cable data and wave-mode separation in fluid–solid elastic media with irregular seabed

In marine seismic exploration, ocean-bottom cable techniques accurately record the multicomponent seismic wavefield; however, the seismic wave propagation in fluid–solid media cannot be simulated by a single wave equation. In addition, when the seabed interface is irregular, traditional finite-difference schemes cannot simulate the seismic wave propagation across the irregular seabed interface. Therefore, an acoustic–elastic forward modeling and vector-based P-and S-wave separation method is proposed. In this method, we divide the fluid–solid elastic media with irregular interface into orthogonal grids and map the irregular interface in the Cartesian coordinates system into a horizontal interface in the curvilinear coordinates system of the computational domain using coordinates transformation. The acoustic and elastic wave equations in the curvilinear coordinates system are applied to the fluid and solid medium, respectively. At the irregular interface, the two equations are combined into an acoustic–elastic equation in the curvilinear coordinates system. We next introduce a full staggered-grid scheme to improve the stability of the numerical simulation. Thus, separate P-and S-wave equations in the curvilinear coordinates system are derived to realize the P-and S-wave separation method.

PATH-INDEPENDENT J-INTEGRAL AND ITS DUAL FORM IN ELASTIC-PLASTIC SOLIDS WITH FINITE DISPLACEMENTS

In this paper, based on energy variational principles of elastic-plastic solids, the path-independent J-integral and its dual form in elastic-plastic solids with finite displacements are presented. Whose testification is given there after.

VARIATIONAL PRINCIPLES OF FLUID FULLFILLED ELASTIC SOLIDS

The generalized variational principles of isothermal quasi-static fluid full-filled elastic solids are established by using Variational Integral Method. Then by introducing constraints, several kinds of variational principles are worked out, including five-field variable, four-field variable, three-field variable and two-field variable formulations. Some new variational principles are presented besides the principles noted in the previous works. Based on variational principles, finite element models can be set up.

Mathematical modeling for coupled solid elastic-deformation and gas leak flow in multi-coal-seams

Based on the new viewpoint of solid and gas interaction mechanics, gas leakage in a double deformable coal seam can be understood. That is, under the action of geophysical fields, the methane flow in a double deformable coal seam can be essentially considered to be compressible with time dependent and mixed permeation and diffusion through a pore cleat deformable heterogeneous and anisotropy medium. Based on this new viewpoint, a coupled mathematical model for coal seam deformation and gas leakage in a double coal seam was formulated and numerical simulations for gas emission from the coal seam are presented. It is found that coupled models might be closer to reality.

COUPLED FIELDS OF TWO-DIMENSIONAL ANISOTROPIC MAGNETO-ELECTRO-ELASTIC SOLIDS WITH AN ELLIPTICAL INCLUSION

The two-dimensional elliptical inclusion problems in infinite anisotropic magnetoelectro-elastic solids are considered. Based on the extended Stroh formalism, the technique of conformal mapping and the concept of perturbation, the magneta-electro-elastic fields in both the matrix: and the inclusion are obtained explicitly. The results are of very importance for studying the effective properties of piezoelectric-piezomagnetic composite materials.

Space Elastic Modal Modeling and Control of A New Generation Solid Bundled Rocket

In this paper,based upon the characteristics of elastic modal combination of large solid bundled launch vehicles,the finite element theory is used to describe the complex elastic vibration of a solid bundled launch vehicle,and a new three-channel unified elastic vibration equation was established.The elastic vibration equation can reflect the coupling between channels and between boosters and core stage.Some issues need consideration in the theoretical derivation,an engineering application was proposed,and the elastic vibration model was verified.The results of the theoretical derivation and simulation show that the elastic vibration equation of a solid bundled launch vehicle established in the paper is correct and can meet the needs for the engineering application.

Application of Real-time Ultrasound Elastography in Diagnosing Benign and Malignant Thyroid Solid Nodules

Objective Real-time ultrasound elastography(US-E) is a helpful tool in diagnosing thyroid nodules.This study aims to evaluate thyroid solid nodules,to establish the accuracy of US-E in providing information on the nature of these nodules,and to assess the clinical value of elasticity scores(ES) and strain ratio(SR) in differentiating thyroid solid nodules and to explore its distribution characteristics using pathological analysis as reference. Methods Traditional ultrasonography and US-E were performed on 131 thyroid solid nodules(99 benign ones and 32 malignant ones) in 120 patients(78 females and 41 males).Three radiologists evaluated the nodules based on a four-degree elasticity scoring system.The nodules were classified according to the ES as soft(ES 1-2) or hard(ES 3-4).The SR was calculated online. Results The sensitivity and specificity of the ES for thyroid cancer diagnosis were 78%and 80%,respectively.SR values > 2.9 used as a standard to distinguish benign from malignant nodules had a sensitivity of 87%and a specificity of 92%.The SR of the benign lesions was 1.64±1.37,which was significantly different from that of malignant lesions,which was 4.96±2.13(P<0.01). Conclusions Both the ES and SR were higher in malignant nodules than those in benign ones.Real-time US-E was a useful index in the differential diagnosis of thyroid solid nodules.It can provide quantitative information on thyroid nodule characterization and improve diagnostic confidence.

Operationalized principle of elastic mechanics

The fundamental mechanical equations were studied under the mechanical space. The differential stress operator and strain operator were obtained. There were strain energy operator and Hamilton operator for elastic body in same way, and the following results were testified. 1) The equilibrium equation of force is equivalent to the harmony equation of deformation under the mechanical space. They are all the basic mode of eigen equation of stress or strain operator. 2) The eigen value of stress or strain operator is corresponding to the order of kinetic energy of elastic body, and the elastic wave represents the non basic mode. 3) The eigen functions of stress operator or strain operator corresponding to some kinetic energy order are fields of modal stress or modal strain in same order. 4) The eigen equations of strain energy operator are the fundamental equations of elastic mechanics which are expressed with the potential functions. [