Wave transmission across surface interfaces in lattice structures

Abstract

Within the lattice dynamics formulation, we present an exact solution for antiplane surface waves in a square lattice strip with a surface row of material particles of two types separated by a linear interface. The considered problem is a discrete analog of an elastic half-space with surface stresses modelled through the simplified Gurtin-Murdoch model, where we have an interfacial line separating areas with different surface elastic properties. The main attention is paid to the transmittance and the reflectance of a wave across the interface. The presented results shed a light on the influence on surface waves of surface inhomogeneity in surface elastic properties such as grain and subgrain boundaries.

Surface Elasticity for Applications to Material Modelling at Small Scales

“…In [23] we proposed also a scaling law similar to [5] which results in transition from lattice dynamics into the Gurtin-Murdoch surface elasticity. Using this discrete-continuum correspondence in [24] the analysis of wave refraction, transmission and leakage for a surface with linear defect was given.…”

Symmetric-in-Plane Compression of Polyamide Pantographic Fabrics—Modelling, Experiments and Numerical Exploration

“…Those modelling processes may involve extensional and bending elements [17][18][19][20], generalised shells theory [21][22][23], surface elasticity [24,25], or second gradient continua theory [26][27][28]. More specifically, second gradient models raised some mathematical challenges [29,30], and their study needed the interaction between analytical parameters identification [31,32] and numerical simulation [33][34][35][36][37], while taking into account the fibers constituting the pantographic lattice [38][39][40][41][42][43].…”

Transmission of waves across atomic step discontinuities in discrete nanoribbon structures

“…Within this context of surface induced phenomena, the present paper extends the applications of recent framework developed for discrete scattering problems [33,34,43]. In contrast to the recent investigation of the wave transmission of surface localized anti-plane shear wave [42] in lattice structures, motivated by certain discrete counterpart [8] of Gurtin-Murdoch model [11,12,45,46], the present paper applies similar methodology to reveal the transmission characteristic associated with a close-up of discrete form of surface roughness.…”