A penny-shaped crack in transversely isotropic magneto-electro-thermo-elastic medium subjected to uniform symmetric heat flux

The problem of a penny-shaped crack subjected to symmetric uniform heat flux in an infinite transversely isotropic magneto-electro-thermo-elastic medium is investigated. The exact solution in the full space is in terms of line integrals and the exact solution in the crack plane also is obtained. Although we start our derivations with magneto-electro-thermo-elastic, the solution presented in this paper is also applicable for linear transversely isotropic thermopiezoelectric, thermomagnetoelastic,thermoelastic materials (see Appendix E). The solution in the crack plane, which shows a great agreement with the solution for a transversely isotropic medium obtained by Tsai (1983), indicates that _σx,_σy,_Dx,_Dy,_Bx${\sigma }_x\text{,}{\sigma }_y\text{,}{D}_x\text{,}{D}_y\text{,}{B}_x$, and _By$B_y$ along the crack rim are of the same singularity of the normal stress or its equivalent quantities. To illustrate how the applied symmetric heat fluxes affect the whole fields, a numerical example is also given.     

Nonlinear interfacial waves in a circular cylindrical container subjected to a vertical excitation

Singular perturbation theory of two-time scale expansions was developed in inviscid fluids to investigate the motion of single interface standing wave in a two-layer liquid-filled circular cylindrical vessel, which is subjected to a vertical periodical oscillation. It is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear amplitude equation including cubic nonlinear and vertically forced terms, was derived by the method of expansion of two-time scales without taking the influence of surface tension into account. By numerical computation, it is shown that different patterns of interface standing wave can be excited for different driving frequency and amplitude. We found that the interface wave mode become more and more complex as increasing of upper to lower layer density ratio γ$\gamma$. The traits of the standing interface wave were proved theoretically. In addition, the dispersion relation and nonlinear amplitude equation obtained in this article can reduce to the known results for a single fluid when γ=0,_h2→_h1$\gamma =0,h_2\to h_1$.     

Molecular modeling of cracks at interfaces in nanoceramic composites

Toughness in Ceramic Matrix Composites (CMCs) is achieved if crack deflection can occur at the fiber/matrix interface, preventing crack penetration into the fiber and enabling energy-dissipating fiber pullout. To investigate toughening in nanoscale CMCs, direct atomistic models are used to study how matrix cracks behave as a function of the degree of interfacial bonding/sliding, as controlled by the density of C interstitial atoms, at the interface between carbon nanotubes (CNTs) and a diamond matrix. Under all interface conditions studied, incident matrix cracks do not penetrate into the nanotube. Under increased loading, weaker interfaces fail in shear while stronger interfaces do not fail and, instead, the CNT fails once the stress on the CNT reaches its tensile strength. An analytic shear lag model captures all of the micromechanical details as a function of loading and material parameters. Interface deflection versus fiber penetration is found to depend on the relative bond strengths of the interface and the CNT, with CNT failure occurring well below the prediction of the toughness-based continuum He–Hutchinson model. The shear lag model, in contrast, predicts the CNT failure point and shows that the nanoscale embrittlement transition occurs at an interface shear strength scaling as _τs~_εf,CNTσCNT${\tau }_s~{\epsilon }_{f,CNT}{\sigma }_{CNT}$ rather than _τs~_σCNT${\tau }_s~{\sigma }_{CNT}$ typically prevailing for micron scale composites, where _εf,CNT${\epsilon }_{f,CNT}$ and _σCNT${\sigma }_{CNT}$ are the CNT failure strain and stress, respectively. Interface bonding also lowers the effective fracture strength in SWCNTs, due to formation of defects, but does not play a role in DWCNTs having interwall coupling, which are weaker than SWCNTs but less prone to damage in the outerwall.     

Spatiotemporal breather in diffraction decreasing media

The similarity transformation between the (3+1$3+1$)-dimensional nonlinear Schrödinger equation with different distributed transverse diffraction and the standard nonlinear Schrödinger equation is found, and a spatiotemporal breather solution is given based on this transformation. The control for the evolutional behaviors of a spatiotemporal breather is discussed. Our results manifest that the relation between the maximum accumulated time _Tm$T_m$ and the accumulated time, _T0$T_0$, with the maximum amplitude, is the basis to realize the control and manipulation of propagation behaviors of breathers, such as fast and slow excitations, sustainment and restraint. These results are potentially useful for future experiments in the optical communications and Bose–Einstein condensations.     

Explicit expression of polarization vector for surface waves,slip waves,Stoneley waves and interfacial slip waves in anisotropic elastic materials

We present explicit expression of the polarization vector for surface waves and slip waves in an anisotropic elastic half-space, and Stoneley waves and interfacial slip waves in two dissimilar anisotropic elastic half-spaces. An unexpected result is that, in the case of interfacial slip waves, the polarization vector for the material in the half-space _x2≥0$x_2\ge 0$ does not depend explicitly on the material property in the half-space _x2≤0$x_2\le 0$. It depends on the material property in the half-space _x2≤0$x_2\le 0$ implicitly through the interfacial slip wave speed υ$\upsilon$. The same is true for the polarization vector for the material in the half-space _x2≤0$x_2\le 0$.     

Lamb wave mode decomposition for structural health monitoring

Lamb waves propagate over large distances in plate-like thin structures and they have received great attention in the structural health monitoring (SHM) field as an efficient means to inspect a large area of a structure by using only a small number of sensors. The times-of-flight of the Lamb wave modes are useful for detecting damage generated in a structure. However, due to the dispersive and multi-mode nature of Lamb waves, it is very challenging to decompose Lamb wave modes into symmetric and anti-symmetric modes for potential applications to structural health monitoring. Thus, we propose an efficient Lamb wave mode decomposition method based on two fundamental rules: the group velocity ratio rule and the mode amplitude ratio rule. The group velocity ratio rule means that the ratio of the group velocities of _A0$A_0$ and _S0$S_0$ modes must be constant. The mode amplitude ratio rule means that the ratio of the magnitudes of _A0$A_0$ and _S0$S_0$ modes in a measured response signal must be always greater than one once the center frequency of the input signal is determined, such that the magnitude of the _A0$A_0$ mode in the excited signal is larger than that of the _S0$S_0$ mode, and vice versa. The proposed method is verified through experiments conducted for a plate specimen.     

The role of shear stresses in brittle fracture

Using the three-dimensional model for brittle fracture developed earlier by S.A.F. Murrell and P.J. Digby (1970,1972) shear stress concentrations are calculated for brittle bodies and the relative roles of tensile and shear stresses in the fracture process are considered. It is found that the maximum shear stress and the maximum tensile stress occur at different places on a crack, and that there is a wide range of stress states for which they do not occur on the same crack. Furthermore, if the theoretical cleavage strength is σ_max and the theoretical shear strength is τ_max, then cleavage precedes inelastic shear and brittle fracture is possible, for suitable stress systems, when $\text{σ}{}_{\max }\text{<}\text{2τ}{}_{\mathrm{<mtext>max</mtext>}}\text{(1 ? ν)}$, where ν is the Poisson's ratio of the solid matrix. This appears to be in accordance with empirical observations.     

Wake response of a stationary finite-sized particle in a turbulent channel flow

Here we consider the effect of a finite-sized stationary particle in a channel flow of modest turbulence at _Reτ=178.12${\mathit{Re}}_{\tau }=178.12$. The size of particle is varied such that the particle Reynolds number ranges from about 40 to 450. The location of the particle is chosen to be either in the buffer layer (_yp+=17.81)$(y_{p+}=17.81)$ or at the channel center. Fully resolved direct numerical simulations of the turbulent channel flow around the particles is performed. Here the ambient turbulence intensity relative to the mean velocity seen by the particle is large (I=23.16%)$(I=23.16\%)$ in the buffer region, while it is substantially lower (I=4.09%)$(I=4.09\%)$ at the channel center. We present results on turbulence modulation due to the particle in terms of wake dynamics and vortex shedding.     

The two-dimensional free-space Green’s function and its derivatives in a tangent-normal system

The two-dimensional free-space Green’s function, G⁽²⁾$G^{\left(2\right)}$, and its derivatives, are used extensively in the formulation of scattering and diffraction problems through its presence in single- and double-layer potentials, and their use in integral equations. The vast majority of the results from elementary classical mathematical physics for G⁽²⁾$G^{\left(2\right)}$ is based on Cartesian coordinate-space, either directly as a Hankel function in coordinate-space or through a transform, such as the Weyl transform, also based on Cartesian coordinate-space. However, if the geometry of the problem is not Cartesian, for example in scattering from a rough surface, there are difficulties in using a transform representation for G⁽²⁾$G^{\left(2\right)}$ which depends on Cartesian geometry, as the standard Weyl transform does. Here we formulate transform-space representations using a tangent-normal coordinate system. The result for G⁽²⁾$G^{\left(2\right)}$ is a new Weyl-type tangent-normal transform representation from which the results for the vector derivatives of the single-layer potential, the double-layer potential, and the vector derivatives of the double-layer potential follow quite simply. The latter three results can be expressed in terms of two new spectral functions in tangent-normal space, _S1$S_1$ and _S2$S_2$. The overall results are new representations for G⁽²⁾$G^{\left(2\right)}$ and its derivatives which may be useful in integral equation formulations of scattering problems for non-Cartesian geometries.     

Influence of grading on the undrained behavior of granular materials

This paper aims at investigating the influence of grading on the undrained behavior of granular materials. Series of undrained triaxial tests were carried out with two different materials, glass balls and Hostun sand. For each material, samples with different gradings and similar relative densities were prepared. Experimental results show that the undrained shear strength decreases when the coefficient of uniformity C_u=d₆₀/d₁₀$C_{\mathrm{u}}=d_{60}/d_{10}$ increases from 1.1 to 20. The conditions of instability for the selected granular materials were also analyzed, based on the sign of the second-order work during undrained triaxial loading. The results demonstrate a significant influence of the grading: increasing the coefficient of uniformity heightens the potential of static liquefaction and the materials become more unstable. Furthermore, numerical tests using the three-dimensional discrete element method (DEM) were conducted on assemblies of spheres. The DEM inter-particle parameters were derived from the experimental test results on glass balls. The DEM simulations showed similar behaviors compared to experimental results and confirmed the influence of the grain size distribution on the stress–strain relationship and instability phenomena.     

Study of the rotational diffusivity coefficient of fibres in planar contracting flows with varying turbulence levels

The Fokker–Planck equation is solved by describing the evolution of a 3D fibre orientation state along a planar contraction. A constant value of the effective rotational diffusion coefficient was determined for four different turbulent flow cases in planar contractions, reported experimentally in the literature. Two hypotheses for the non-dimensional rotational diffusivity are presented, each based on two different turbulent time scales, i.e. the Kolmogorov time scales and the time scale associated with large energy bearing eddies. These hypotheses are dependent on either the Reynolds number, based on the Taylor micro-scale, and/or a non-dimensional fibre length. The hypothesis, based on the assumption of long fibres, _Lf/η?25$L_{\text{f}}/\eta ?25$, compared to the Kolmogorov scale and in the limit of large _Reλ${\mathit{Re}}_{\lambda }$ seems to capture the basic trends presented in the literature. This hypothesis has also the feature of predicting effects of varying fibre length within certain limits. Accordingly, by modeling the variation of turbulent quantities along the contraction in a CFD analysis, local values of rotational diffusivity can be evaluated with the mentioned hypothesis, based on either Kolmogorov time scale or Eulerian integral time scale.     

Rayleigh waves with impedance boundary conditions in anisotropic solids

The paper is concerned with the propagation of Rayleigh waves in an elastic half-space with impedance boundary conditions. The half-space is assumed to be orthotropic and monoclinic with the symmetry plane _x3=0$x_3=0$. The main aim of the paper is to derive explicit secular equations of the wave. For the orthotropic case, the secular equation is obtained by employing the traditional approach. It is an irrational equation. From this equation, a new version of the secular equation for isotropic materials is derived. For the monoclinic case, the method of polarization vector is used for deriving the secular equation and it is an algebraic equation of eighth-order. When the impedance parameters vanish, this equation coincides with the secular equation of Rayleigh waves with traction-free boundary conditions.     

Response of second-harmonic generation of Lamb wave propagation to microdamage thickness in a solid plate

The response features of second-harmonic generation (SHG) of primary Lamb wave propagation to the thickness of microdamage layer (MDL) in a solid plate have been theoretically and numerically investigated in this paper. Here the solid plate with a MDL is regarded as a double-layered plate in analysis of nonlinear Lamb wave propagation. On the basis of a second-order perturbation approximation and modal expansion analysis, the physical process of cumulative SHG by primary Lamb wave propagation in a solid plate with a MDL has been investigated. The influence of variation in the thickness of MDL on the effect of SHG of primary ${\mathit{S}}_0$ mode, which satisfies an approximate phase velocity matching in the low frequency region, has been theoretically analyzed, and then the finite element (FE) simulation has been carried out to validate the results of the theoretical predictions. A close agreement between the theoretical analyses and FE simulations validates the effectiveness of using the effect of SHG of primary ${\mathit{S}}_0$ mode for characterizing changes in the thickness of MDL. Moreover, change mechanism of nonlinear acoustic parameter with the thickness of MDL is revealed It is expected that the results obtained can provide a convenient means for accurately characterizing nonhomogeneous microdamage (MDL thickness) in layered plates.     

The stress concentration factor for slightly roughened random surfaces: Analytical solution

We derive an analytical solution to the stress concentration factor (_kt)$(k_t)$ for slightly roughened random surfaces. Topology is assumed to possess Gaussian distribution of heights and auto correlation length, ACL  . For our development, we combine Gao’s first-order perturbation method, the Hilbert transform, and an energy conservation principal related to the Parseval theorem.The root-mean-square (RMS) value of _kt$k_t$ results in a function of the ratio RMS-roughness to ACL. The derived formula agrees with experimental results previously reported. The results provide insight for more efficient design.     

On the characteristic equations of elasto-plastic flow

Three dimensional characteristic surfaces (slip surfaces) of elasto-plastic Navier's equations and the criteria for their existence are discussed, and the solutions are also applied to two dimensional cases. By making use of isotropic yield function, the following results are proved. If, and only if the plastic/elastic moduli ratio is zero and Det$\text{(φ}{}_{\mathrm{ij}}\text{)=0,(φ}{}_{\mathrm{ij}}\text{=}\text{?φ}\text{?σ}{}_{\mathrm{ij}}$, φ: yield function,σ_ij: stress tensor), characteristic surfaces exist. There are two and only two characteristic surface elements at each point, and they are identical with the surfaces of maximum shearing stress.