相关论文: The nonlinearity of helical springs: An energy-bas…

We study the force vs extension behaviour of a helical spring made of a thin torsionally-stiff anisotropic elastic rod. Our focus is on springs of very low helical pitch. For certain parameters of the problem such a spring is found not to…

A sheet of elastic foil rolled into a cylinder and deformed between two parallel plates acts as a non-Hookean spring if deformed normally to the axis. For large deformations the elastic force shows an interesting inverse squares dependence…

We show that when a gradually increasing tensile force is applied to the ends of a helical spring with sufficiently large ratios of radius to pitch and twist to bending rigidity, the end-to-end distance undergoes a sequence of discontinuous…

The elastic response of mechanical, chemical, and biological systems is often modeled using a discrete arrangement of Hookean springs, either representing finite material elements or even the molecular bonds of a system. However, to date,…

Using dynamic simulations and analytic methods, we study the elastic response of a helical filament subject to uniaxial tension over a wide range of bend and twist persistence length. A low-pitch helix at low temperatures exhibits a…

In the present article we determine the exact shape of an ideal spring suspended at both ends. Historically, this goes under the name of Elastica problem. The total energy of the suspended spring is a functional depending on two independent…

Most research papers that exploit conical springs focus only on conical springs with a constant pitch. In order to increase the range of possibilities for designers, this paper proposes a study of conical springs with other types of spirals…

We extend the theory of structured deformations to the setting of linearized elasticity by providing an integral representation for the underlying energy that features bulk and surface contributions. Our derivation is obtained both via a…

The static equilibrium deformation of a heavy spring due to its own weight is calculated for two cases. First for a spring hanging in a constant gravitational field, then for a spring which is at rest in a rotating system where it is…

Hooke's law states that the forces or stresses experienced by an elastic object are proportional to the applied deformations or strains. The number of coefficients of proportionality between stress and strain, i.e., the elastic moduli, is…

In order to clarify common assumptions on the form of energy and momentum in elasticity, a generalized conservation format is proposed for finite elasticity, in which total energy and momentum are not specified a priori. Velocity, stress,…

Elastic wave speeds are fundamental in geomechanics and have historically been described by an analytic formula that assumes linearly elastic solid medium. Empirical relations stemming from this assumption were used to determine nonlinearly…

We derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent…

The Slinky is a well-known example of a highly flexible helical spring, exhibiting large, geometrically nonlinear deformations from minimal applied forces. By considering it as a system of coils that act to resist axial, shearing, and…

Springs are used for a wide range of applications in physics and engineering. Possibly, one of its most common uses is to study the nature of restoring forces in oscillatory systems. While experiments that verify the Hooke's law using…

We consider a thin elastic sheet in the shape of a disk whose reference metric is that of a singular cone. I.e., the reference metric is flat away from the center and has a defect there. We define a geometrically fully nonlinear free…

Most theories and applications of elasticity rely on an energy function that depends on the strains from which the stresses can be derived. This is the traditional setting of Green elasticity, also known as hyper-elasticity. However, in its…

Vibration Energy Harvesting is an emerging technology aimed at turning mechanical energy from vibrations into electricity to power microsystems of the future. Most of present vibration energy harvesters are based on a mass spring structure…

A general expression for the strain energy of a homogeneous, isotropic, plane extensible elastica with an arbitrary undeformed configuration is derived. This energy constitutes the correct expression for one-dimensional models of polymers…

We analyze a simple problem in elasticity: the \emph{initial} motion of an elastic bar that after being hanged from an end is suddenly released. In a second problem a point mass is attached on the top of the bar. The analytical solutions…