Connection machine simulation of ultrasonic wave propagation in materials III: The three-dimensional case

A formalism for the simulation by parallel processing of the propagation of ultrasonic pulses of arbitrary shape (i.e. not restricted to continuous waves) in complex media is presented. Recursive relationships yielding the time evolution of the displacement field are derived for both homogeneous and heterogeneous materials. In the latter case, formulas for cross-points at the intersection of up to eight different materials are obtained. A few examples of numerical results obtained with the proposed method are shown to demonstrate its applicability and efficiency. The problem of visualization of the results is also briefly discussed.     

Elastic response to temperature variations in granular media: A phenomenological analysis

The purpose of this work is to discuss a methodology for the interpretation of experimental data and its application, in the context of thermo-elasto-dynamics, to the investigation of the time dependence of variables, such as the resonance frequency of a consolidated granular sample, subjected to various protocols of varying temperature. An analytical equation is deduced, which fits extremely well the experimental curves and has the expected asymptotic behavior of the dependent variable. It also predicts the observed asymmetry in the response to the sign of the temperature variation.     

Modeling the propagation of ultrasonic waves in the interface region between two bonded elements

An important task in nondestructive materials evaluation is the development of techniques to characterize the bond quality of adherent joints. Binding forces are nonlinear and cause a nonlinear modulation of transmitted and reflected ultrasonic waves. As a consequence, the higher harmonics generated by an insonified monochromatic wave give information about the adhesive bonds. The local binding forces in thin bonded interfaces can be obtained by the amplitudes of the ultrasonic waves of the insonified frequency and its higher harmonics as transmitted through the interface. Additional phase measurements may enable one to obtain the evaluation of the full hysteretic cycle of the interaction force. In order to gain a deeper understanding of the interface region and to improve the technique, numerical simulations of the ultrasonic wave propagation through specimens of two bonded elements can be used. A simple model based on the local interaction simulation approach (LISA) is described in this contribution, and a comparison between the results of the simulations and the experimental data is presented. Besides its intrinsic relevance for NDE, the problem considered in this paper may be very useful to analyze and test models for the simulation of ultrasonic wave propagation in nonclassical nonlinear mesoscopic elastic materials.     

A unified treatment of nonclassical nonlinear effects in the propagation of ultrasound in heterogeneous media

Recent experiments on rocks and other materials, such as soil, cement, concrete and damaged elastic materials, have led to the discovery of nonlinear (NL) hysteretic effects in their elastic behaviour. These observations suggest the existence of a NL mesoscopic elasticity universality class, to which all the aforementioned materials belong. The purpose of the present contribution is to search for the basic mathematical roots for nonclassical nonlinearity, in order to explain its universality, classify it and correlate it with the underlying meso- or microscopic interaction mechanisms. In our discussions we explicitly consider two quite different kinds of specimens: a two-bonded-elements structure and a thin multigrained bar. It is remarkable that, although the former includes only one interface and the latter very many interstices, the same "interaction box" formalism can be applied to both. Another important result of the proposed formalism is that the spectral contents of an arbitrary system for any input amplitude may be predicted, under certain assumptions, from the result of a single experiment at a higher amplitude.     

Eigenchannel calculation for a soluble model

We examine the accuracy of the eigenchannel method for treating nuclear reactions by a comparison with the exact solution of a problem of two coupled channels. No crucial deviations between the exact and the eigenchannel cross sections are observed. We also discuss the questions connected with the non-orthogonality of the sets of radial states used in the eigenchannel treatment, and show how to minimize the resulting errors. Our conclusion is that, in principle, the eigenchannel method is capable of producing the correct shape of nuclear cross sections, without introducing spurious wiggles.     

A continuum calculation for the giant dipole resonance in28Si including the effect of collective correlations

Continuum shell model calculations for the giant dipole resonance in²⁸Si based on both the 1p 1h model and the collective correlation model are described and the results compared with experiment. The eigenchannel theory of nuclear reactions has been used to include the effect of the particle continuum.     

Classification scheme for phenomenological universalities in growth problems in physics and other sciences

A classification in universality classes of broad categories of phenomenologies, belonging to physics and other disciplines, may be very useful for a cross fertilization among them and for the purpose of pattern recognition and interpretation of experimental data. We present here a simple scheme for the classification of nonlinear growth problems. The success of the scheme in predicting and characterizing the well known Gompertz, West, and logistic models, suggests to us the study of a hitherto unexplored class of nonlinear growth problems.     

Refraction effects in the generation of helical surface waves on a cylindrical obstacle

We investigate the scattering of compressional waves from an infinite, circular-cylindrical obstacle, and the excitation during the scattering process of surface waves that propagate along helical paths over the cylinder surface. For the case of a rigid or soft obstacle, the surface waves are external, and are obtained via the use of a Watson transformation. For the case of a penetrable cylinder, additional internal, resonant surface waves are generated for which the phase and group velocity dispersion curves can be obtained from the Resonance Scattering Theory. We perform a detailed study of certain refraction effects which take place upon the generation of the surface waves by the incident plane wave.     

Connection machine simulation of ultrasonic wave propagation in materials. II: The two-dimensional case

A local interaction simulation approach (LISA) for the wave propagation in inhomogeneous 2D media is presented. The method is designed to take full advantage of massively parallel computing, such as provided by the Connection Machine. Crosspoints at the intersection of orthogonal interfaces separating media of different physical properties are treated in the framework of a sharp interface model. A comparison with finite difference techniques shows that the proposed method avoids the ambiguities due to the smoothing of the physical quantities, which is necessary in order to transform differential equations into finite difference equations. The smoothing procedure may cause severe numerical errors, when the variations of the physical properties across the interfaces are large.

In order to demonstrate the efficiency and reliability of the approach several examples of simulation of pulse propagation in different media are reported.