In this paper, a discrete analogue of Sommerfeld half plane diffraction is investigated. The two-dimensional problem of diffraction on a square lattice, of a plane (transverse) wave by a semi-infinite crack, is solved. The discrete Wiener–Hopf method has been used to obtain the exact solution of discrete Helmholtz equation, with input data prescribed on the crack boundary sites due to a time ha...

*Correspondence: Bjørn Skjetne, Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway e-mail: [email protected] Crack morphology obtained in the fracture of materials with a disordered micro-structure is studied using numerical simulations. Physical properties are embedded on a regular three dimensional lattice as discrete stochastic elements which confo...

The paper addresses a problem of partial fracture of a lattice by a propagating fault modelling a crack bridged by elastic fibres. It is assumed that the strength of bonds within the lattice alternates periodically, so that during the dynamic crack propagation only weaker bonds break, whereas the stronger bonds remain intact. The mathematical problem is reduced to the functional equation of the...

Kachanov’s simplifiedmodel ofmicrocrack interaction is applied to an investigationof the behaviour of a cracked body under predominantly compressive periodic loading, so that the cracks experience periods of closure and slip, with frictional dissipation. The model is shown to be equivalent to a discrete elastic frictional systemwith each crack representing one node. Theorems and algorithms from...

Abstract. Public Key Cryptosystems assure privacy as well as integrity of the transactions between two parties. The sizes of the keys play an important role. The larger the key the harder is to crack a block of encrypted data. We propose a new public key cryptosystem and a Key Exchange Protocol based on the generalization of discrete logarithm problem using Non-abelian group of block upper tria...

Recent ideas on the mechanisms controlling the initial stages of plastic flow at cracks in intrinsically brittle materials, at the ductile-brittle transition, are reviewed. New experiments on precracked specimens of Si are reported, which confirm earlier work that the ductile-brittle transition is controlled by dislocation velocity. A model has been developed in which at the ductile-brittle tra...

We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo in [9]. The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute minimizers of the energy, but, in a sense, we look for local minimizers which are sufficiently close to the approximate solution obtained in the prev...

In this paper we propose a spatial model for the initiation of cracks in the bone cement of hip replacement specimens. The failure of hip replacements can be attributed mainly to damage accumulation, consisting of crack initiation and growth, occurring in the cement mantle that interlocks the hip prosthesis and the femur bone. Since crack initiation is an important factor in determining the lif...

Multiple length-scale effects are demonstrated in indentation-strength measurements of a range of ceramic materials under inert and reactive conditions. Meso-scale effects associated with flaw disruption by lateral cracking at large indentation loads are shown to increase strengths above the ideal indentation response. Micro-scale effects associated with toughening by microstructural restraints...