Numerical study of nonlinear interaction between a crack and elastic waves under an oblique incidence

A Finite Element (FE) model is proposed to study the interaction between in-plane elastic waves and a crack of different orientations. The crack is modeled by an interface of unilateral contact with Coulombs friction. These contact laws are modified to take into account a pre-stress _σ0${\sigma }_0$ that closes the crack. Using the FE model, it is possible to obtain the contact stresses during wave propagation. These contact stresses provide a better understanding of the coupling between the normal and tangential behavior under oblique incidence, and explain the generation of higher harmonics. This new approach is used to analyze the evolution of the higher harmonics obtained as a function of the angle of incidence, and also as a function of the excitation level. The pre-stress condition is a governing parameter that directly changes the nonlinear phenomenon at work at the interface and therefore the harmonic generation. The diffracted fields obtained by the nonlinear and linear models are also compared.     

On a novel expression of the field scattered by an arbitrary constant impedance plane

The electromagnetic field scattered by an impedance plane is generally given by its plane wave expansion (Fourier representation). Here we derive an alternative expression which is more suitable for point source illumination. For this, we consider an original expression of the Hertz potentials for the incident field and express the scattered potentials in a novel form. A special function then involved can be expressed in an integral which is in turn expanded in a convergent series. The expression presented also permits us to express complete asymptotics. Our development considers an arbitrary impedance, passive or active.     

基于扩展有限元法的裂尖场精度研究

扩展有限元方法基于单元分解的基本思想,通过引入位移加强函数来表征裂纹的不连续性和裂尖的奇异性。在裂尖加强单元与常规单元之间有一层混合单元,当对裂尖特定区域进行加强时,混合单元个数相应增加,混合单元个数与计算精度存在一定联系。本文提出一种正方形裂尖加强区域的选择方式,可得到较单个加强和圆形加强精度更高、更稳定的计算结果。对于不同长度的裂纹,表征裂尖场奇异性所需的裂尖加强范围存在较大差异,以正方形裂尖加强方式进行计算,得到了不同裂纹长度下最优的加强尺寸。     

Effect of scattering of elastic harmonic waves in the far zone by a spatial crack

A three-dimensional wave field formed owing to diffraction of low-frequency waves on a curved crack in an infinite elastic solid at a large distance from the defect is studied by the method of boundary integral equations. Direction diagrams of the scattered field versus the excentricity of the crack surface and wavenumber are obtained for different directions of incidence of planar longitudinal waves onto a gently sloping spheroidal crack. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 115–123, July–August, 2006.     

Numerical simulations of the primary Bjerknes force experienced by bubbles in a standing ultrasonic field: Nonlinear vs. linear

The primary Bjerknes force experienced by a population of multiple bubbles in a liquid set in a nonlinear ultrasonic standing field and their translation are calculated and analyzed by numerical simulations. The force field is evaluated by considering the nonlinear bubble oscillations as well as the nonlinear character of the ultrasonic pressure field (both variables are unknown in the coupled nonlinear differential system). The results at small amplitudes agree with the classical theory on bubble translation, depending on the driving frequency in relation to the bubble resonance. It is shown that, when amplitudes are raised, the force field exhibits important modifications that strongly affect the motion of the bubbles and the way they form agglomerates. An analysis is performed on the importance of the terms in the differential system that provoke (a) the nonlinearity of the bubble oscillations and (b) the nonlinearity of the acoustic wave. This study reveals that both features should be considered to better approximate the primary Bjerknes force field. Simulations of the nonlinear ultrasonic field after the bubbles form agglomerates under the influence of this force are also performed.