Related papers: A buckling question
The preference of thin flat sheets to bend rather than stretch, combined with results from Geometry, mean that changes in a thin sheet's Gaussian curvature are prohibitively expensive. As a result, an imposed curvature in one principal…
Continuum elasticity is a powerful tool applicable in a broad range of physical systems and phenomena. Yet, understanding how and on what scales material disorder may lead to the breakdown of continuum elasticity is not fully understood. We…
Mechanical instability in a pre-tensioned finite hyperelastic tube subjected to a slowly increasing internal pressure produces a spatially localized bulge at a critical pressure. The subsequent fate of the bulge, under continued inflation,…
All systems are expected to be designed to fulfil their functions over their requested lifetime. Nevertheless, failure of a system may occur, and this is unfortunately, true also for vacuum systems. From a mechanical point of view,…
Biological soft tissues exhibit elastic properties which can be dramatically different from rubber-type materials (elastomers). To gain a better understanding of the role of constitutive relationships in determining material responses under…
Advances in manufacturing techniques may now realize virtually any imaginable microstructures, paving the way for architected materials with properties beyond those found in nature. This has lead to a quest for closing gaps in…
The subject of this paper is the rigorous derivation of lower dimensional models for a nonlinearly elastic thin-walled beam whose cross-section is given by a thin tubular neighbourhood of a smooth curve. Denoting by h and {\delta}_h,…
Starting from three-dimensional nonlinear elasticity under the restriction of incompressibility, we derive reduced models to capture the behavior of strings in response to external forces. Our $\Gamma$-convergence analysis of the…
Dynamic buckling of an elastic column under compression at constant speed is investigated assuming the first-mode buckling. Two cases are considered: (i) an imperfect column (Hoff's statement), and (ii) a perfect column having an initial…
The idea that a material can exhibit negative compressibility is highly consequential for research and applications. As new forms for this effect are discovered, it is important to examine the range of possible mechanisms and ways to design…
The buckling of elastic bodies is a common phenomenon in the mechanics of solids. Wrinkling of membranes can often be interpreted as buckling under constraints that prohibit large amplitude deformation. We present a combination of analytic…
Buckling and barrelling instabilities in the uniaxial compressions of an elastic rectangle have been studied by many authors under lubricated end conditions. However, in practice it is very difficult to realize such conditions due to…
We show that the slow viscoelastic response of a foam is that of a power-law fluid with a terminal relaxation. Investigations of the foam mechanics in creep and recovery tests reveal that the power-law contribution is fully reversible,…
Essentially new approach to analysis of internal forces, arising in cylindrical rod under action of an axial tension force, has allowed to detect the three-dimensional axisymmetric stress state. According to the new conceptual model the…
Crumpled sheets have a surprisingly large resistance to further compression. We have studied the crumpling of thin sheets of Mylar under different loading conditions. When placed under a fixed compressive force, the size of a crumpled…
We develop a geometric approach to understand the mechanics of perforated thin elastic sheets, using the method of strain-dependent image elastic charges. This technique recognizes the buckling response of a hole under external load as a…
We investigate with experiments the twist induced transverse buckling instabilities of an elastic sheet of length $L$, width $W$, and thickness $t$, that is clamped at two opposite ends while held under a tension $T$. Above a critical…
We derive geometrically linearized theories for incompressible materials from nonlinear elasticity theory in the small displacement regime. Our nonlinear stored energy densities may vary on the same (small) length scale as the typical…
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…
A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam's inextensibility---local arc length preservation---rather than traditional extensible effects attributed to fully restricted…