Dispersive Rayleigh-Wave Propagation in Microstructured Solids Characterized by Dipolar Gradient Elasticity

Plane-strain crack problems in microstructured solids governed by dipolar gradient elasticity

“…White, 1970). In such situations, dispersion phenomena of Rayleigh waves at high frequencies can only be explained on the basis of a 4 gradient elasticity theory (Georgiadis et al, 2004). In addition, the latter study provides an estimate for a microstructural parameter (i.e.…”

“…The simplest possible linear and isotropic equations result from the following strain-energy density function (Georgiadis et al, 2004;Lazar and Maugin, 2005) …”

“…This approach is appropriate for formulations of both elasticity and plasticity problems and, in general, allows for the emergence of 3 interesting boundary layer effects that can capture corresponding phenomena (see e.g. Shi et al, 2000;Georgiadis, 2003;Georgiadis et al, 2004). In such a formulation, characteristic lengths appear in the mechanical behavior of the material and these lengths can be related with the size of microstructure.…”

“…More recently, this approach and related extensions for microstructured materials have been employed to analyze various problems involving, among other areas, wave propagation (see e.g. Vardoulakis and Georgiadis, 1997;Georgiadis et al, 2000;Georgiadis et al, 2004), fracture (see e.g. Wei and Hutchinson, 1997;Zhang et al, 1998;Chen et al, 1998;Shi et al, 2000;Georgiadis, 2003;Grentzelou and Georgiadis, 2005;2008;Wei, 2006;Karlis et al, 2007;Radi, 2008), and plasticity (see e.g.…”

Ultrasonic evaluation of intact, healing and osteoporotic long bones

“…The examined cases correspond to the three different combinations between the gradient coefficient c and the microinertia term h in the dipolar elasticity examined in (Georgiadis et al 2004 Comparisons were also presented with the velocity of the first-order antisymmetric mode propagating in a dipolar plate in order to investigate the Rayleigh asymptotic behavior . For a transmitter-receiver distance 60 mm, the semi-analytical frequency-group velocity dispersion curves of the Rayleigh wave in both Mindlin's Form II gradient and classical elasticity were converted to t-f curves and were superimposed on the t-f plane of the corresponding signals obtained from the BEM model in (Papacharalampopoulos et al 2011).…”