asymptotics

In this paper, we discuss two problems concerning scattering and localisation of flexural waves in structured elastic plates. Firstly, we compare the scattering amplitudes of waves in a thin plate, generated by a point source, due to a single mass and to a large number of smaller masses, having the same equivalent mass and located around a circle. We show that in the second case, the scattering can be reduced, in particular in the medium- and high-frequency regimes.

I hope some of you may find this work interesting. We show, analytically and numerically, that strain gradient plasticity predicts the existence of an inner elastic field adjacent to the crack tip, reminiscent of a dislocation-free zone. The fact that elastic strains dominate plastic strains near the crack tip implies a paradigm-shift with respect to previous crack tip asymptotic studies in plasticity and gradient plasticity, which neglect elastic strains. 

Emilio Martínez-Pañeda, Norman A. Fleck

In this paper, we investigate the formation of band-gaps and localisation phenomena in an elastic strip nearly disintegrated by an array of transverse cracks. We analyse the eigenfrequencies of finite, strongly damaged, elongated solids with reference to the propagation bands of an infinite strip with a periodic damage. Subsequently, we determine analytically the band-gaps of the infinite strip by using a lower-dimensional model, represented by a periodically-damaged beam in which the small ligaments between cracks are modelled as ‘elastic junctions’.