Analysis of dynamic damage propagation in discrete beam structures

Abstract

In the last decade, significant theoretical advances were obtained for steady-state fracture propagation in spring-mass lattice structures, that also revealed surprising fracture regimes. Very few articles exist, however, on the dynamic fracture processes in lattices composed of beams. In this paper we analyse a failure (feeding) wave propagating in a beam-made lattice strip with periodically placed point masses. The fracture occurs when the strain of the supporting beam reaches the critical value. The problem reduces to a Wiener-Hopf equation, from which the complete solution is obtained. Two cases are considered when the feeding wave transmits into the intact structure as a sinusoidal wave(s) or only as an evanescent wave. For both cases, a complete analysis of the strain inside the structure is presented. We determine the critical level of the feeding wave, below which the steady-state regime does not exist, and its connections to the feeding wave parameters and the failure wave speed. The accompanied dynamic effects are also discussed. Amongst much else, we show that the switch between the two considered regimes introduces a rapid change in the minimum energy required for the failure wave to propagate steadily. The failure wave developing under an incident sinusoidal wave is remarkable due to the fact that there is an upper bound of the domain where the steady-state regime exists. In the present paper, only the latter is examined; the alternative regimes are considered separately.

Alternating Strain Regimes for Failure Propagation in Flexural Systems

“…In terms of applications, it is realistic to consider the case when the supporting links break if a positive or negative critical displacement is reached. As we show here, along with the pure steady-state regimes observed in [45,46], the imposed fracture criterion yields additional regimes, which can be predicted and verified numerically. These regimes correspond to the case when, at each consecutive failure in the system, a change in the sign of the bending moments and shear forces in the supporting beams can be observed.…”

“…The fracture was assumed to be caused by a remote sinusoidal load and the dynamic features of the structure were studied. Further, in [46] the transient failure process was numerically modelled and the results of [45] were verified.…”

“…The influence of lattice vibrations and wave radiation processes on the stability of crack trajectories in Silicon crystals has been investigated experimentally and numerically using molecular dynamics simulations in [42,43,44]. In [45], an analytical model for the failure of a discrete flexural structure, contained within an interface, was studied. The fracture was assumed to be caused by a remote sinusoidal load and the dynamic features of the structure were studied.…”

“…The failure is represented by the sequential removal of transverse links supporting the masses along the central chain, aligned with the horizontal axis. In [45,46], the failure process was investigated under the assumption that the supporting columns of the central chain are removed if the masses achieve a positive critical displacement. The steady-state regimes achieved in this case are referred to here as "pure steady-state regimes" and assumed to be driven by a remote mechanical sinusoidal load.…”

Wave polarization and dynamic degeneracy in a chiral elastic lattice

“…In a continuum, waves where the displacementũ is perpendicular (or parallel) to the wave vectork are denoted as shear (or pressure) waves. Substitutingf = 3k in (8) and (9), we notice that in a continuum shear (or pressure) waves correspond to flux-free (or circulation-free) waves. For intermediate and large values of the modulus of the wave vector, the continuum concepts of shear and pressure waves cannot be applied to the lattice.…”