Solitary waves in a peridynamic elastic solid

The propagation of large amplitude nonlinear waves in a peridynamic solid is analyzed. With an elastic material model that hardens in compression, sufficiently large wave pulses propagate as solitary waves whose velocity can far exceed the linear wave speed. In spite of their large velocity and amplitude, these waves leave the material they pass through with no net change in velocity and stress. They are nondissipative and nondispersive, and they travel unchanged over large distances. An approximate solution for solitary waves is derived that reproduces the main features of these waves observed in computational simulations. It is demonstrated by numerical studies that the waves interact only weakly with each other when they collide. Wavetrains composed of many non-interacting solitary waves are found to form and propagate under certain boundary and initial conditions.     

Scattering of elastic waves in an elastic matrix containing an inclusion with interfaces

Based on the theory of elastic dynamics, the scattering of elastic waves and dynamic stress concentration in fiber-reinforced composite with interfaces are studied. Analytical expressions of elastic waves in different medium areas are presented and an analytic method of solving this problem is established. The mode coefficients are determined by means of the continuous conditions of displacement and stress on the boundary of the interfaces. The influence of material properties and structural size on the dynamic stress concentration factors near the interfaces is analyzed. It indicates that they have a great influence on the dynamic properties of fiber-reinforced composite. As examples, numerical results of dynamic stress concentration factors near the interfaces are presented and discussed. This paper provides reliable theoretical evidence for the study of dynamic properties in fiber-reinforced composite. Project supported by the National Natural Science Foundation of China (No. 19972018).     

In-plane analysis of a cracked orthotropic half-plane

The stress fields in an orthotropic half-plane containing Volterra type climb and glide edge dislocations under plane stress condition are derived. The dislocation solutions are utilized to formulate integral equations for dislocation density functions on the surface of smooth cracks embedded in the half-plane under in-plane loads. The integral equations are of Cauchy singular type which are solved numerically. The dislocation density functions are employed to evaluate modes I and II stress intensity factors for multiple cracks with different configurations.     

Reflection and transmission of elastic waves by a moving slab

Scattering of elastic waves by a moving slab is considered. Two cases corresponding to strong contact and good lubrication are treated. It is shown that the motion introduces new effective compressional and shear wave velocities in the moving slab. The amplitude of the reflection and transmission coefficients are given for various angles of incidence, frequencies and velocities of motion.     

The axisymmetric Rayleigh waves in a semi-infinite elastic solid

It is well-known that Rayleigh wave, also known as surface acoustic wave(SAW), solutions in semiinfinite solids are plane waves with signatory properties like the distinct velocity and exponentially decaying deformation in the depth. Applications of Rayleigh waves are focused on the deformation and energy in the vicinity of surface of solids and less loss in the propagation. A generalized model of Rayleigh waves in axisymmetric mode is established and solutions are obtained with cylindrical coordinates. It is found that the Rayleigh waves also propagate in the axisymmetric mode with slow decay in radius, confirming the existence of surface acoustic waves is irrelevant to coordinate system. On the other hand, the solutions can be treated as plane waves in regions far away from the source. Furthermore, the particle trajectory of axisymmetric SAW is a line with constant slope rather than the signatory ellipse in Cartesian coordinate case.     

Second harmonic generation in elastic surface waves on an isotropic solid

A procedure for solving the problem of non-linear propagation of elastic surface waves is given. An expression for the particle displacement of the second harmonic is obtained. It is shown that the amplitude of the harmonic increases linearly with distance and time and is proportional to the square of the amplitude of the fundamental frequency wave.     

Reflection and transmission of elastic waves through a couple-stress elastic slab sandwiched between two half-spaces

The reflection and transmission of elastic waves through a couple-stress elastic slab that is sandwiched between two couple-stress elastic half-spaces are studied in this paper. Because of the couple-stress effects, there are three types of elastic waves in the couple-stress elastic solid, two of which are dispersive. The interface conditions between two couple-stress solids involve the surface couple and rotation apart from the surface traction and displacement. The nontraditional interface conditions between the slab and two solid half-spaces are used to obtain the linear algebraic equation sets from which the amplitude ratios of reflection and transmission waves to the incident wave can be determined. Then, the energy fluxes carried by the various reflection and transmission waves are calculated numerically and the normal energy flux conservation is used to validate the numerical results. The special case, couple-stress elastic slab sandwiched by the classical elastic half-spaces, is also studied and compared with the situation that the classical elastic slab sandwiched by the classical elastic half-spaces. Incident longitudinal wave (P wave) and incident transverse wave (SV wave) are both considered. The influences of the couple-stress are mainly discussed based on the numerical results. It is found that the couple-stress mainly influences the transverse modes of elastic waves.     

Magneto-thermo-elastic waves in an infinite perfectly conducting elastic solid with energy dissipation

The generalized thermo-elasticity theory, i.e., Green and Naghdi （G-N） Ⅲ theory, with energy dissipation （TEWED） is employed in the study of time-harmonic plane wave propagation in an unbounded, perfectly electrically conducting elastic medium subject to primary uniform magnetic field. A more general dispersion equation with com- plex coefficients is obtained for coupled magneto-thermo-elastic wave solved in complex domain by using the Leguerre＇s method. It reveals that the coupled magneto-thermoelastic wave corresponds to modified dilatational and thermal wave propagation with finite speeds modified by finite thermal wave speeds, thermo-elastic coupling, thermal diffusivity, and the external magnetic field. Numerical results for a copper-like material are presented.     

Nonlinear surface acoustic waves on an elastic solid of general anisotropy

The effect of elastic nonlinearity on the propagation of Rayleigh waves in an anisotropic elastic solid is considered. A nonlinear integro-differential equation is derived for a quantity which is related to the Fourier transform of the displacement component on the surface. The variation of this quantity along the surface accounts for the slow modulation of the wave through formation and depletion of the different harmonics. Explicit results are given for harmonic generation in an initially sinusoidal wave and for parametric amplification of a weak signal by a pump wave of twice its frequency.     

Compressional waves in fluid-saturated porous solid containing a penny-shaped crack

Diffraction of normal compression waves by a penny-shaped crack in a fluid-saturated porous medium is investigated. Two wave types are considered, namely, compressional wave of the first kind, and the second kind. The former, also known as fast wave, propagates primarily through the solid, whereas the latter or slow wave, propagates mainly in the fluid. Each wave propagates in the medium along with induced wave of the same type in the companion constituent of the material. Application of Biot’s theory in conjunction with integral transform technique reduces the problem to a mixed boundary-value problem whose solution is in turn governed by a Fredholm integral equation of the second kind. Near-field and far-field solutions are obtained in terms of the dynamic stress-intensity factor and the scattering cross section, respectively. They are of particular importance to the linear elastic fracture mechanics (LEFM) and in the scattering theory of elastic waves. The mode I stress-intensity factors are computed numerically for a set of selected material property values, and shown graphically for various mass density and viscosity-to-permeability ratios. The obtained results reveal significant impact of the presence of pore fluid upon the stress-intensity factors, both magnitudes and frequencies at their peak values. The influence of the fluid is also observed from the calculated scattering cross sections of the scattered far-field. Accuracy of the present solution procedure is verified by comparing the numerical results with existing results in the limiting case of dry elastic materials.     

Water waves in an elastic vessel

Linear and nonlinear analyses of water waves in an elastic vessel are carried out to study the dramatic phenomena of Dragon Wash as well as related controllable experiments. It is proposed that the capillary edge waves are generated by parametric resonance, which is shown to be a possible mechanism for both rectangular an circular vessels. For circular vessel, the normal geometric resonance is also operating, thus greatly enhance the dramatic effect. The mechanism of nonlinear mode-mode interaction is proposed for the generation of axisymmetric low-frequency gravity waves by the high- frequency external excitation. A simple model system is studied numerically to demonstrate explicitly this interaction mechanism.     

Reflection and transmission of elastic waves at an elastic/porous solid saturated by two immiscible fluids

Wave propagation in a porous elastic medium saturated by two immiscible fluids is investigated. It is shown that there exist three dilatational waves and one transverse wave propagating with different velocities. It is found that the velocities of all the three longitudinal waves are influenced by the capillary pressure, while the velocity of transverse wave does not at all. The problem of reflection and refraction phenomena due to longitudinal and transverse wave incident obliquely at a plane interface between uniform elastic solid half-space and porous elastic half-space saturated by two immiscible fluids has been analyzed. The amplitude ratios of various reflected and refracted waves are found to be continuous functions of the angle of incidence. Expression of energy ratios of various reflected and refracted waves are derived in closed form. The amplitude ratios and energy ratios have been computed numerically for a particular model and the results obtained are depicted graphically. It is verified that during transmission there is no dissipation of energy at the interface. Some particular cases have also been reduced from the present formulation.     

Anti-plane wave motion in a cylindrically orthotropic elastic solid containing a stress-free crack

A cylindrically orthotropic elastic solid is excited by a point impulsive body force. The solid contains a semi-infinite stress-free crack. The resulting wave motion is anti-plane. An eigenfunction solution to the problem is obtained in the form of an infinite series. The series is summed into two parts. The first part contains the incident and reflected wave pulses while the second part gives the diffraction integral. Wave front patterns are presented with an application to wood.     

Stress intensity factor for transient thermal stresses in an infinite elastic solid containing an annular crack

Summary The present paper treats the transient thermal stress problem in an infinite, isotropic solid containing an annular crack. The elastic medium is cooled by time and position dependent temperature on the annular crack surface. It is very difficult to obtain the analytical expression for the temperature so that we use the finite difference method solely with respect to a time variable. Thus, the analytical solution for the temperature with respect to the spatial variables reduces to a dual integral equation. Results for the stress intensity factors are obtained numerically.

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Spannungsintensitätsfaktor für transiente Wärmespannungen in einem unendlichen elastischen Körper mit ringförmigem Ri\

übersicht Untersucht werden die transienten WÄrmespannungen in einem unendlichen elastischen Körper, der einen ringförmigen Ri\ enthÄlt. Das elastische Medium wird durch eine zeit- und ortsabhÄngige Temperaturverteilung auf der Ri\oberflÄche gekühlt. Da es schwierig ist, eine analytische Lösung für die Temperatur anzugeben, wird bezüglich der Zeit die Finite-Differenzen-Methode angewandt. Dann kann bezüglich der Ortskoordinaten eine analytische Lösung für die Temperatur in Form einer dualen Integralgleichung angegeben werden. Die SpannungsintensitÄtsfaktoren werden numerisch berechnet.

     

Elastic moduli of a cracked solid

Calculations on the basis of the self-consistent method are made for the elastic moduli of bodies containing randomly distributed flat cracks, with or without fluid in their interiors. General concepts are outlined for arbitrary cracks and explicit derivations together with numerical results are given for elliptic cracks. Parameters are identified which adapt the elliptic-crack results to arbitrary convex crack shapes. Finally, some geometrical relations involving randomly distributed cracks and their traces on cross-sections are presented.     

Stress analysis of an elastic cracked layer bonded to a viscoelastic substrate

The effect of a viscoelastic substrate on an elastic cracked layer under an in-plane concentrated load is solved and discussed in this study. Based on a correspondence principle, the viscoelastic solution is directly obtained from the corresponding elastic one. The elastic solution in an anisotropic trimaterial is solved as a rapidly convergent series in terms of complex potentials via the successive iterations of the alternating technique in order to satisfy the continuity condition along the interfaces between dissimilar media. This trimaterial solution is then applied to a problem of a thin layer bonded to a half-plane substrate. Using the standard solid model to formulate the viscoelastic constitutive equation, the real-time stress intensity factors can be directly obtained by performing the numerical calculations. The results obtained in this paper are useful in studying the problem with bone defects where a crack is assumed to exist in an elastic body made of the cortical bone that is bonded to a viscoelastic substrate made of the cancellous bone.