Related papers: Analysis of dynamic failure of the discrete chain …
We consider the scattering of in-plane waves that interact with an edge of a structured {penetrable (inertial)} line defect contained in a triangular lattice, composed of periodically placed masses interconnected by massless elastic rods.…
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…
We address the theory of quasi-static crack propagation in a strip of glass that is pulled from a hot oven towards a cold bath. This problem had been carefully studied in a number of experiments that offer a wealth of data to challenge the…
We address the problem of a front propagation in chains with a bi-stable nondegenerate on-site potential and a nonlinear gradient coupling. For a generic nonlinear coupling, one encounters a special regime of transitions, characterized by…
We model and derive the solution for the problem of a Mode I semi-infinite crack propagating in a discrete triangular lattice with bonds having a contrast in stiffness in the principal lattice directions. The corresponding Green's kernel is…
We have examined a class of cohesive-zone models of dynamic mode-I fracture, looking both at steady-state crack propagation and its stability against out-of-plane perturbations. Our work is an extension of that of Ching, Langer, and…
Scattering of time-harmonic plane wave by two parallel semi-infinite rows, but with staggered edges, is considered on square lattice. The condition imposed on the semi-infinite rows is a discrete analogue of Neumann boundary condition. A…
Scalar wave propagation across a semi-infinite step or step-like discontinuity on any one boundary of the square lattice waveguides is considered within nearest-neighbour interaction approximation. An application of the Wiener-Hopf method…
We extend the Slepyan solution of the problem of a steady-state crack in an infinite ideally brittle lattice model to include dissipation in the form of Kelvin viscosity. As a demonstration of this technique, based on the Wiener-Hopf…
Frictional interfaces exhibits a very rich dynamical behavior due to frictional interactions. This work focuses on the transition between spatially localized and propagating stick-slip motion. To overcome the difficulties related to the…
We consider a propagation of transition fronts in one-dimensional chains with bi-stable nondegenerate on-site potential. If one adopts linear coupling in the chain and piecewise linear on-site force, then it is possible to develop…
A semi-infinite crack in infinite square lattice is subjected to a wave coming from infinity, thereby leading to its scattering by the crack surfaces. A partially damaged zone ahead of the crack-tip is modeled by an arbitrarily distributed…
A class of systems is considered, where immobile species associated to distinct patches, the nodes of a network, interact both locally and at a long-range, as specified by an (interaction) adjacency matrix. Non local interactions are…
We study the evolution of a wave packet in a nonlinear Schr\"odinger lattice equation subject to a dc bias. In the absence of nonlinearity all normal modes are spatially localized giving rise to a Stark ladder with an equidistant eigenvalue…
This paper deals with the theoretical and numerical analysis of dynamic fracture of dissimilar chain consisting of masses lined by springs. Such a structure exhibits quite different dynamic properties in comparison with a symmetrical…
The diffraction of a time-harmonic plane wave on collinear finite defects in a square lattice is studied. This problem is reduced to a matrix Wiener-Hopf equation. This work adapts the recently developed iterative Wiener-Hopf method to this…
Shear cracks propagation is a basic dynamical process that mediates interfacial failure. We develop a general weakly nonlinear elastic theory of shear cracks and show that these experience tensile-mode crack tip deformation, including…
Nonlocal quasistatic fracture evolution for interacting cracks is developed and supporting numerical examples are presented. The approach is implicit and is based on local stationarity and fixed point methods. It is proved that the fracture…
In this Letter we describe a novel class of dynamical excitations -- accelerating oscillatory fronts in a new genre of nonlinear sonic vacua with strongly non-local effects. Indeed, it is surprising that such models naturally arise in…
The dynamics of nonlocally coupled dissipative kicked rotors is rich and complex. In this study, we consider a network of rotors where each interacts equally with a certain range of its neighbors. We focus on the influence of the coupling…