Related papers: Load Capacity of Bodies
We present a complete analytical solution for the stress field inside a homogeneous, inside a homogeneous, linearly elastic solid sphere subjected to a concentrated normal load applied on its surface. Starting from the three-dimensional…
Plasticity of two-dimensional discrete dislocation systems is studied. It is shown, that at some threshold stress level the response becomes stress-rate dependent. Below this stress level the stress-plastic strain relation exhibits…
We advance a quantitative description of the critical shear rate $\dot{\gamma_c}$ needed to dislodge a spherical particle resting on a surface with a model asperity in laminar and turbulent fluid flows. We have built a cone-plane…
We consider a rigid body acted upon by two forces, a constant force and the collective force of interaction with a continuum of particles. We assume that some of the particles that collide with the body reflect elastically (specularly),…
Systems under external confinement and constraints often show interesting properties. In this thesis, we study some systems under external confinement. We begin by finding out the probability distribution of end-to-end separation of a Worm…
We provide a sharp lower bound for the perimeter of the inner parallel sets of a convex body $\Omega$. The bound depends only on the perimeter and inradius $r$ of the original body and states that \[|\partial\Omega_t| \geq…
In this paper we analyze the capacitary potential due to a charged body in order to deduce sharp analytic and geometric inequalities, whose equality cases are saturated by domains with spherical symmetry. In particular, for a regular…
Fatigue caused by cyclic bending of a piece of material, resulting in its mechanical failure, is a phenomenon that had been studied for ages by engineers and physicists alike. In this Letter we study such fatigue in a strip of athermal…
Plasma Physics defines the concept of the Debye length. Given the enormous electrical potential that would develop with no screening, we conjecture that the size of the Universe,as given by the speed of light c and its age t, ct, cannot be…
We prove that the gravitational binding energy {\Omega} of a self gravitating system described by a mass density distribution {\rho}(x) admits an upper bound B[{\rho}(x)] given by a simple function of an appropriate, non-additive Tsallis'…
Let $\Delta$ be the optimal packing density of $\mathbb R^n$ by unit balls. We show the optimal packing density using two sizes of balls approaches $\Delta + (1 - \Delta) \Delta$ as the ratio of the radii tends to infinity. More generally,…
It is stated in the main in essence new approach to mechanics of the stressed state of the solid body from statistically isotropic material and the homogeneous liquid dynamics. The approach essence is in the detected property of the…
The ideal strength is crucial for predicting material behavior under extreme conditions, which can provide insights into material limits, guide design and engineer for enhanced performance and durability. In this work, we present a method…
For $\Omega\subset \mathbb{R}^2$ a smooth and bounded domain, we derive a sharp universal energy estimate for non-negative solutions of free boundary problems on $\Omega$ arising in plasma physics. As a consequence, we are able to deduce…
The ideal shock absorber combines high stiffness with high energy absorption whilst retaining structural integrity after impact and is scalable for industrial production. So far no structure meets all of these criteria. Here, we introduce a…
Given a precompact domain $\Omega \subseteq\mathbb{R}^2$, the electrostatic skeleton of $\Omega$ is defined as a positive measure inside $\Omega$, supported on a set with no simple loops, which generates $\partial \Omega$ as an…
At low temperature, T -> 0, the yield stress of a perfect crystal is equal to its so called theoretical strength. The yield stress of non-perfect crystals is controlled by the stress threshold of dislocation mobility. A non-crystalline…
The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the…
In composite material, the stress may be arbitrarily large in the narrow region between two close-to-touching hard inclusions. The stress is represented by the gradient of a solution to the Lam\'{e} system of linear elasticity. The aim of…
A key feature of mechanical structures ranging from crumple zones in cars to padding in packaging is their ability to provide protection by absorbing mechanical energy. Designing structures to efficiently meet these needs has profound…