Related papers: Fractal design for efficient brittle plates under …
In this letter we address the fragmentation of thin, brittle layers due to the impact of high-velocity projectiles. Our approach is a geometric statistical one, with lines and circles playing the role of cracks, randomly distributed over…
The principle of hierarchical design is a prominent theme in many natural systems where mechanical efficiency is of importance. Here we establish the properties of a particular hierarchical structure, showing that high mechanical efficiency…
Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of…
Extreme localization of damage in conventional brittle materials is the source of a host of undesirable effects. We show how artificially engineered metamaterials with all brittle constituents can be designed to ensure that every breakable…
Highly-deformable materials, from synthetic hydrogels to biological tissues, are becoming increasingly important from both fundamental and practical perspectives. Their mechanical behaviors, in particular the dynamics of crack propagation…
This paper investigates the optimal distribution of hard and soft material on elastic plates. In the class of isometric deformations stationary points of a Kirchhoff plate functional with incorporated material hardness function are…
A solid slender beam of length $L$, made from a material of Young's modulus $Y$ and subject to a gentle compressive force $F$, requires a volume of material proportional to $L^{3}f^{1/2}$ [where $f\equiv F/(YL^{2})\ll 1$] in order to be…
Fractal geometries, characterized by self-similar patterns and non-integer dimensions, provide an intriguing platform for exploring topological phases of matter. In this work, we introduce a theoretical framework that leverages isospectral…
Cutting mechanics in soft solids have been a subject of study for several decades, an interest fuelled by the multitude of its applications, including material testing, manufacturing, and biomedical technology. Wire cutting is the simplest…
Because of Euler buckling, a simple strut of length $L$ and Young modulus $Y$ requires a volume of material proportional to $L^3 f^{1/2}$ in order to support a compressive force $F$, where $f=F/YL^2$ and $f\ll 1$. By taking into account…
Conforming materials to rigid substrates with Gaussian curvature --- positive for spheres and negative for saddles --- has proven a versatile tool to guide the self-assembly of defects such as scars, pleats, folds, blisters, and liquid…
In this work we derive by Gamma-convergence techniques a model for brittle fracture linearly elastic plates. Precisely, we start from a brittle linearly elastic thin film with positive thickness $\rho$ and study the limit as $\rho$ tends to…
Fractal patterns are observed in computational mechanics of elastic-plastic transitions in two models of linear elastic/perfectly-plastic random heterogeneous materials: (1) a composite made of locally isotropic grains with weak random…
Fracture in a disordered lattice system is studied. In our system, particles are initially arranged on the triangular lattice and each nearest-neighbor pair is connected with a randomly chosen soft or hard Hookean spring. Every spring has…
In many scenarios -- when we bite food or during a crash -- fracture is inevitable. Finding solutions to steer fracture to mitigate its impact or turn it into a purposeful functionality, is therefore crucial. Strategies using composites,…
We introduce a model of fracture which includes the out-of-plane degrees of freedom necessary to describe buckling in a thin-sheet material. The model is a regular square lattice of elastic beams, rigidly connected at the nodes so as to…
A thin flat rectangular plate supported on its edges and subjected to in-plane loading exhibits stable post-buckling behaviour. However, the introduction of a nonlinear (softening) elastic foundation may cause the response to become…
We introduce a lattice model able to describe damage and yielding in heterogeneous materials ranging from brittle to ductile ones. Ductile fracture surfaces, obtained when the system breaks once the strain is completely localized, are shown…
The reliability of processes with moving elastic and isotropic material containing initial cracks is considered in terms of fracture. The material is modelled as a moving plate which is simply supported from two of its sides and subjected…
We study how the loading rate, specimen geometry and microstructural texture select the dynamics of a crack moving through an heterogeneous elastic material in the quasi-static approximation. We find a transition, fully controlled by two…