A simple beam model for the shear failure of interfaces

We propose a novel model for the shear failure of a glued interface between two solid blocks. We model the interface as an array of elastic beams which experience stretching and bending under shear load and break if the two deformation modes exceed randomly distributed breaking thresholds. The two breaking modes can be independent or combined in the form of a von Mises type breaking criterion. Assuming global load sharing following the beam breaking, we obtain analytically the macroscopic constitutive behavior of the system and describe the microscopic process of the progressive failure of the interface. We work out an efficient simulation technique which allows for the study of large systems. The limiting case of very localized interaction of surface elements is explored by computer simulations.Comment: 11 pages, 13 figure

New universality class for the fragmentation of plastic materials

We present an experimental and theoretical study of the fragmentation of polymeric materials by impacting polypropylene particles of spherical shape against a hard wall. Experiments reveal a power law mass distribution of fragments with an exponent close to 1.2, which is significantly different from the known exponents of three-dimensional bulk materials. A 3D discrete element model is introduced which reproduces both the large permanent deformation of the polymer during impact, and the novel value of the mass distribution exponent. We demonstrate that the dominance of shear in the crack formation and the plastic response of the material are the key features which give rise to the emergence of the novel universality class of fragmentation phenomena.Comment: 4 pages, 4 figures, appearing in Phys. Rev. Let

Computer simulation of fatigue under diametrical compression

We study the fatigue fracture of disordered materials by means of computer simulations of a discrete element model. We extend a two-dimensional fracture model to capture the microscopic mechanisms relevant for fatigue, and we simulate the diametric compression of a disc shape specimen under a constant external force. The model allows to follow the development of the fracture process on the macro- and micro-level varying the relative influence of the mechanisms of damage accumulation over the load history and healing of microcracks. As a specific example we consider recent experimental results on the fatigue fracture of asphalt. Our numerical simulations show that for intermediate applied loads the lifetime of the specimen presents a power law behavior. Under the effect of healing, more prominent for small loads compared to the tensile strength of the material, the lifetime of the sample increases and a fatigue limit emerges below which no macroscopic failure occurs. The numerical results are in a good qualitative agreement with the experimental findings.Comment: 7 pages, 8 figures, RevTex forma

Break-up of shells under explosion and impact

A theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material is presented. Experiments were performed on brown and white hen egg-shells under two different loading conditions: fragmentation due to an impact with a hard wall and explosion by a combustion mixture giving rise to power law fragment size distributions. For the theoretical investigations a three-dimensional discrete element model of shells is constructed. Molecular dynamics simulations of the two loading cases resulted in power law fragment mass distributions in satisfactory agreement with experiments. Based on large scale simulations we give evidence that power law distributions arise due to an underlying phase transition which proved to be abrupt and continuous for explosion and impact, respectively. Our results demonstrate that the fragmentation of closed shells defines a universality class different from that of two- and three-dimensional bulk systems.Comment: 11 pages, 14 figures in eps forma

Phase transition in a spring-block model of surface fracture

A simple and robust spring-block model obeying threshold dynamics is introduced to study surface fracture of an overlayer subject to stress induced by adhesion to a substrate. We find a novel phase transition in the crack morphology and fragment-size statistics when the strain and the substrate coupling are varied. Across the transition, the cracks display in succession short-range, power-law and long-range correlations. The study of stress release prior to cracking yields useful information on the cracking process.Comment: RevTeX, 4 pages, 4 Postscript figures included using epsfi

Structure formation in binary colloids

A theoretical study of the structure formation observed very recently [Phys. Rev. Lett. 90, 128303 (2003)] in binary colloids is presented. In our model solely the dipole-dipole interaction of the particles is considered, electrohidrodynamic effects are excluded. Based on molecular dynamics simulations and analytic calculations we show that the total concentration of the particles, the relative concentration and the relative dipole moment of the components determine the structure of the colloid. At low concentrations the kinetic aggregation of particles results in fractal structures which show a crossover behavior when increasing the concentration. At high concentration various lattice structures are obtained in a good agreement with experiments.Comment: revtex, 4 pages, figures available from authors due to size problem

Dynamic model of fiber bundles

A realistic continuous-time dynamics for fiber bundles is introduced and studied both analytically and numerically. The equation of motion reproduces known stationary-state results in the deterministic limit while the system under non-vanishing stress always breaks down in the presence of noise. Revealed in particular is the characteristic time evolution that the system tends to resist the stress for considerable time, followed by sudden complete rupture. The critical stress beyond which the complete rupture emerges is also obtained