Related papers: Analytical link between structural strength size e…
A static variational model for shape formation in heteroepitaxial crystal growth is considered. The energy functional takes into account surface energy, elastic misfit-energy and nucleation energy of dislocations. A scaling law for the…
An extensive experimental study of indentation and crack arrest statistics is presented for four different brittle materials (alumina, silicon carbide, silicon nitride, glass). Evidence is given that the crack length statistics can be…
When a thin elastic sheet crumples, the elastic energy condenses into a network of folding lines and point vertices. These folds and vertices have elastic energy densities much greater than the surrounding areas, and most of the work…
The availability of large datasets requires an improved view on statistical laws in complex systems, such as Zipf's law of word frequencies, the Gutenberg-Richter law of earthquake magnitudes, or scale-free degree distribution in networks.…
The dynamics of many socioeconomic systems is determined by the decision making process of agents. The decision process depends on agent's characteristics, such as preferences, risk aversion, behavioral biases, etc.. In addition, in some…
We present an intuitive physical picture for fractures in nacre-type stratified materials via scaling arguments: strain distributions around a fracture are rather different depending on directions and size of fractures. We thus observe that…
The process of crumpling a sheet and compacting it into a ball is dependent on many parameters that are difficult to disentangle. We study the effect of plasticity on the crumpling process, and disentangle the effects of plasticity and…
The main result of this work is a homogenization theorem via variational convergence for elastic materials with stiff checkerboard-type heterogeneities under the assumptions of physical growth and non-self-interpenetration. While the…
We consider a class of real numbers, a subset of irrational numbers and certain mathematical constants, for which the elements in the simple continued fraction appears to be random. As an illustrative example, one can consider $\pi = \{x_0,…
We investigate by numerical simulation the system size dependence of the shear delamination strength of thin elastic films. The films are connected to a rigid substrate by a disordered interface containing a pre-existing crack. The size…
From pasta to biological tissues to contact lenses, gel and gel-like materials inherently soften as they swell with water. In dry, low-relative-humidity environments, these materials stiffen as they de-swell with water. Here, we use…
Predicting the occurrence of landslides is important to prevent or reduce loss of lives and property. The stability of rock slopes is often dominated by one or more locked segments along a potential slip surface; these segments have…
Complex networks grow subject to structural constraints which affect their measurable properties. Assessing the effect that such constraints impose on their observables is thus a crucial aspect to be taken into account in their analysis. To…
We investigate phase-field modeling of brittle fracture in a one-dimensional bar featuring a continuous variation of elastic and/or fracture properties along its axis. Our main goal is to quantitatively assess how the heterogeneity in…
We study how crack buckling affects stress and strain in a thin sheet with random disorder. The sheet is modeled as an elastic lattice of beams where each of the beams have individual thresholds for breaking. A statistical distribution with…
Hydrogels have had a profound impact in the fields of tissue engineering, drug delivery, and materials science as a whole. Due to the network architecture of these materials, imbibement with water often results in uniform swelling and…
This paper investigates the effects of plasticity on the effective fracture toughness. A layered material is considered as a modelling system. An elastic-plastic phase-field model and a surfing boundary condition are used to study how the…
We determine the probability distribution of the breaking strength for chains of N links, which have been produced by repeatedly breaking a very long chain.
Avalanche statistics of various threshold activated dynamical systems are known to depend on the magnitude of the drive, or stress, on the system. Such dependencies exist for earthquake size distributions, in sheared granular avalanches,…
We evaluate the scale at which the multifractal structure of some random Gibbs measures becomes discernible. The value of this scale is obtained through what we call the growth speed in H\"older singularity sets of a Borel measure. This…