Reflection of Bounded Acoustic Beams from a Layered Solid

It is well known that when a bounded beam of acoustic waves is incident on a fluid-solid interface at certain critical angles, the reflected beam is significantly distorted and displaced due to the interference between specularly and nonspecularly reflected waves. Measurement and analysis of the reflected field can be used to estimate certain near surface elastic properties of the solid by means of several alternative nondestructive experimental arrangements [1,2]. In most of these experiments the interface generated leaky waves play a significant role. Thus a good understanding of the interface phenomena is a prerequisite to the design of experiments for their practical applications

The problem of sharp notch in microstructured solids governed by dipolar gradient elasticity

In this paper, we deal with the asymptotic problem of a body of infinite extent with a notch (re-entrant corner) under remotely applied plane-strain or anti-plane shear loadings. The problem is formulated within the framework of the Toupin-Mindlin theory of dipolar gradient elasticity. This generalized continuum theory is appropriate to model the response of materials with microstructure. A linear version of the theory results by considering a linear isotropic expression for the strain-energy density that depends on strain-gradient terms, in addition to the standard strain terms appearing in classical elasticity. Through this formulation, a microstructural material constant is introduced, in addition to the standard Lamé constants . The faces of the notch are considered to be traction-free and a boundary-layer approach is followed. The boundary value problem is attacked with the asymptotic Knein-Williams technique. Our analysis leads to an eigenvalue problem, which, along with the restriction of a bounded strain energy, provides the asymptotic fields. The cases of a crack and a half-space are analyzed in detail as limit cases of the general notch (infinite wedge) problem. The results show significant departure from the predictions of the standard fracture mechanics

A Decomposition Theorem For Maximum Weight Bipartite Matchings with Applications To Evolutionary Trees

Many structures, both man-made and of natural origin, are composed of different elastic materials formed in layers. Often the layers are bonded together along common faces, but it can happen that the bonding is not perfect and flaws occur as cracks or regions of poor bonding in the interface. It is of importance to be able to detect these interface cracks, and one of the most practical methods for accomplishing this, in the cases of engineering interest, utilizes the scattering of elastic waves and the subsequent detection of these scattered waves by appropriate transducers. The goal of this work is to contribute to the theoretical basis for detecting the interface flaw by these means