Dynamic phenomena and crack propagation in dissimilar elastic lattices

Abstract

Dynamic Mode III interfacial fracture in a dissimilar square-cell lattice, composed of two contrasting mass-spring lattice half-planes joined at an interface, is considered. The fracture, driven by a remotely applied load, is assumed to propagate at a constant speed along the interface. The choice of the load allows the solution of the problem to be matched with the crack tip field for a Mode III interfacial crack propagating between two dissimilar continuous elastic materials. The lattice problem is reduced to a system of functional equations of the Wiener-Hopf type through the Fourier transform. The derived solution of the system fully characterises the process. We demonstrate the existence of trapped vibration modes that propagate ahead of the crack along the interface during the failure process. In addition, we show as the crack propagates several preferential directions for wave radiation can emerge in the structured medium that are determined by the lattice dissimilarity. The energy attributed to the wave radiation as a result of the fracture process is studied and admissible fracture regimes supported by the structure are identified. The results are illustrated by numerical examples that demonstrate the influence of the dissimilarity of the lattice on the existence of the steady failure modes and the lattice dynamics.

Directional Control of Rayleigh Wave Propagation in an Elastic Lattice by Gyroscopic Effects

“…They are of great importance in problems concerning the dynamic propagation of cracks in discrete systems, as discussed by Marder and Gross (1995) and Slepyan (2002) for uniform media and in successive works (Nieves et al, 2013) for non-uniform lattices. Similar localized phenomena may play a substantial role in non-uniform crack propagation as evidenced in (Piccolroaz et al, 2020), where lattice dissimilarity has been shown to promote or diminish localized deformations around the faces of the crack. Trapped modes associated with Rayleigh-Bloch waves in systems incorporating periodic gratings or periodic arrays of resonators were analyzed by Porter and Evans (1999), Porter and Evans (2005), Linton and McIver (2002) and Antonakakis et al (2014) for scalar problems, by Colquitt et al (2015) for vector systems and by Haslinger et al (2017) and Morvaridi et al (2018) for plates.…”

Discrete scattering and meta-arrest of locally resonant elastic wave metamaterials with a semi-infinite crack

“…In fact, many studies have shown that standard microstructures can achieve a reduction in the energy release ratio and even failure [29,37,45,60]. In recent years, elastic wave metamaterials have been extensively studied because of their superior abilities, so it is natural to apply them in practical engineering in which the dynamic fracture should be considered.…”

Tensile material instabilities in elastic beam lattices lead to a bounded stability domain

“…is the composition of elastic structures via periodic lattices [1][2][3][4][5][6][7][8][9]. In these structures, different effects related to out-of-plane or in-plane deformations, the presence of bending moment or prestress have been explored [10][11][12][13].…”