No abstract available

No abstract available

[en] We consider numerically the roughness of a planar crack front within the long-range elastic string model, with a tunable disorder correlation length ξ. The problem is shown to have two important length scales, ξ and the Larkin length L_c. Multiscaling of the crack front is observed for scales below ξ, provided that the disorder is strong enough. The asymptotic scaling with a roughness exponent ζ≈0.39 is recovered for scales larger than both ξ and L_c. If L_c > ξ, these regimes are separated by a third regime characterized by the Larkin exponent ζ_L≈0.5. We discuss the experimental implications of our results

[en] Typically, the plastic yield stress of a sample is determined from a stress–strain curve by defining a yield strain and reading off the stress required to attain it. However, it is not a priori clear that yield strengths of microscale samples measured this way should display the correct finite size scaling. Here we study plastic yield as a depinning transition of a 1 + 1 dimensional interface, and consider how finite size effects depend on the choice of yield strain, as well as the presence of hardening and the strength of elastic coupling. Our results indicate the existence of a crossover length that depends on the yield strain. It is only above this length scale that standard finite size scaling is expected to hold. These results are also expected to be particularly relevant for simulations of single dislocations, such as those used to study strengthening due to included particles. (paper)

[en] Auxetic materials are of great engineering interest not only because of their fascinating negative Poisson’s ratio, but also due to the possibility to increase by design the toughness and indentation resistance. The general understanding of auxetic materials comes often from ordered or periodic structures, while auxetic materials used in applications are typically strongly disordered. Yet, the effect of disorder in auxetics has rarely been investigated. Here, we provide a systematic theoretical and experimental study of the effect of disorder on the mechanical properties of a paradigmatic two-dimensional auxetic lattice with a re-entrant hexagonal geometry. We show that disorder has a marginal effect on the Poisson’s ratio until the point when the lattice topology becomes altered, and in all cases examined disorder preserves the auxetic characteristics. Depending on the direction of loading applied to these disordered auxetic lattices, either brittle or ductile failure is observed. It is found that brittle failure is associated with a disorder-dependent tensile strength, whereas in ductile failure disorder does not affect strength. Our work thus provides general guidelines to design and optimize elasticity and strength of disordered auxetic metamaterials.

[en] Crystalline plasticity is strongly interlinked with dislocation mechanics and nowadays is relatively well understood. Concepts and physical models of plastic deformation in amorphous materials on the other hand—where the concept of linear lattice defects is not applicable—still are lagging behind. We introduce an eigenstrain-based finite element lattice model for simulations of shear band formation and strain avalanches. Our model allows us to study the influence of surfaces and finite size effects on the statistics of avalanches. We find that even with relatively complex loading conditions and open boundary conditions, critical exponents describing avalanche statistics are unchanged, which validates the use of simpler scalar lattice-based models to study these phenomena. (paper)

[en] The fracture stress of materials typically depends on the sample size and is traditionally explained in terms of extreme value statistics. A recent work reported results on the carrying capacity of long polyamide and polyester wires and interpret the results in terms of a probabilistic argument known as the St. Petersburg paradox. Here, we show that the same results can be better explained in terms of extreme value statistics. We also discuss the relevance of rate dependent effects. (paper)

[en] We review statistical theories and numerical methods employed to consider the sample size dependence of the failure strength distribution of disordered materials. We first overview the analytical predictions of extreme value statistics and fibre bundle models and discuss their limitations. Next, we review energetic and geometric approaches to fracture size effects for specimens with a flaw. Finally, we overview the numerical simulations of lattice models and compare with theoretical models.

[en] Magneto-optical methods allow us to observe the dynamics of domain wall motion, but this is intrinsically a very noisy process. We discuss a new method allowing us to reduce the measurement noise, taking advantage of the acquisition of a whole temporal sequence of images. The resulting avalanche distributions give interesting hints as to the magnetization dynamics, but are strongly dependent on the size of the observation windows chosen. We investigate the effects of window size by studying finite-size scaling, and use this to extract the fractal dimension critical exponent 1/σν

[en] A two-dimensional fracture model in which the interaction among elements is modeled by an anisotropic stress-transfer function is presented. The influence of anisotropy on the macroscopic properties of the samples is clarified, by interpolating between several limiting cases of load sharing. Furthermore, the critical stress and the distribution of failure avalanches are obtained numerically for different values of the anisotropy parameter α and as a function of the interaction exponent γ. From numerical results, one can certainly conclude that the anisotropy does not change the crossover point γ_c = 2 in two dimensions. Hence, in the limit of infinite system size, the crossover value γ_c = 2 between local and global load sharing is the same as the one obtained in the isotropic case. In the case of finite systems, however, for γ≤2, the global load sharing behavior is approached very slowly