Related papers: A model for the fragmentation kinetics of crumpled…
The fragmentation of a two-dimensional circular disc by lateral impact is investigated using a cell model of brittle solid. The disc is composed of numerous unbreakable randomly shaped convex polygons connected together by simple elastic…
A variational framework is introduced to describe how a surface bends when it is subject to local constraints on its geometry. This framework is applied to describe the patterns of a folded sheet of paper. The unstretchability of paper…
In recent paper (Goloveshkin and Myagkov 2014) we proposed a two-dimensional energy-based model of fragmentation of rapidly expanding cylinder under plane strain conditions. The model allowed one to estimate the average fragment length and…
Mechanical metamaterials are usually designed to show desired responses to prescribed forces. In some applications, the desired force-response relationship might be hard to specify exactly, although examples of forces and corresponding…
We examine the focusing of kinetic energy and the amplification of various quantities during the snapping motion of the free end of a flexible structure. This brief but violent event appears to be a regularized finite-time singularity, with…
We study the interaction between two cracks propagating quasistatically during the tearing of a thin brittle sheet. We show that the cracks attract each other following a path described by a power law resulting from the competition between…
Processes of coalescence and fragmentation are used to understand the time-evolution of the mass distribution of various systems and may result in a steady state or in stable deterministic or stochastic cycles. Motivated by applications in…
Homogeneous fragmentations describe the evolution of a unit mass that breaks down randomly into pieces as time passes. They can be thought of as continuous time analogs of a certain type of branching random walks, which suggests the use of…
We propose a stochastic model of a fragmentation process, developed by taking into account fragment lifetime as a function of their size based on the Gibrat process. If lifetime is determined by a power function of fragment size, numerical…
To go beyond the simple model for the fold as two flexible surfaces or faces linked by a crease that behaves as an elastic hinge, we carefully shape and anneal a crease within a polymer sheet and study its mechanical response. First, we…
Wrinkling instabilities of thin elastic sheets can be used to generate periodic structures over a wide range of length scales. Viscosity of the thin elastic sheet or its surrounding medium has been shown to be responsible for dynamic…
Using numerical simulations, we study the dynamical evolution of particles interacting via competing long-range repulsion and short-range attraction in two dimensions. The particles are compressed using a time-dependent quasi-one…
We reproduce patterns of drying paste by means of smoothed particle hydrodynamics which is the one of methods for solving the equations of continuum in the Lagrangian description. In addition to reproduce a realistic pattern, we find that…
We present a theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material. Experiments were performed on brown and white hen egg-shells under two different loading conditions: impact…
We present a numerical model for a two dimensional (2D) granular assembly, falling in a rectangular container when the bottom is removed. We observe the occurrence of cracks splitting the initial pile into pieces, like in experiments. We…
The compression of soft elastic matter and biological tissue can lead to creasing, an instability where a surface folds sharply into periodic self-contacts. Intriguingly, the unfolding of the surface upon releasing the strain is usually not…
Models of folding of a triangular lattice embedded in a discrete space are studied as simple models of the crumpling transition of fixed-connectivity membranes. Both the case of planar folding and three-dimensional folding on a…
Thin elastic sheets appear in systems ranging from graphene to biological membranes, where phenomena such as wrinkling, folding, and thermal fluctuations originate from geometric nonlinearities. These effects are treated within weakly…
The problem of crack pattern formation due to thermal shock loading at the surface of half-space is solved numerically using two-dimensional boundary element method. The results of numerical simulations with 100-200 random simultaneously…
Brittle materials under impact loading exhibit a transition from a cracked solid to a granular medium. Appropriate representation of this transition to granular mechanics and the resulting initial fragment size and shape distribution in…