Questions related to the Continuum Mechanics Division of Elasticity. The bending of beams, deflection of rods, or in general, applications of Hooke's Law generalized to three dimensions.
Questions tagged [elasticity]
864 questions
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Elastic band around a cylinder
An elastic band is stretched using a known force and then placed around a cylinder. How are the forces or tensions distributed? I assume there will be two components: firstly, a tangential or circumferential component, and secondly, a radial or…
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What does it mean that "two independent scalars of the second degree can be formed from the components of the strain tensor?"
The following is from Theory of Elasticity by Landau and Lifshitz.
Why can only two independent scalars of second order be formed from the symmetric strain tensor $u_{i k}$, which for infinitesimal strain is defined as
$$ u_{i k} = \frac12 \left(…
Kappie001
- 205
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Fracture because of high-speed rotation
I was watching a rerun of an early MythBusters episode, where they look at whether CDs in high-speed drives can explode / fail simply because of being rotated too fast. The following are some calculations I did:
Let the thickness of the CD be $t$,…
Anonymous
- 347
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What is the root cause of elasticity of a material?
I know that there exist some interatomic and intermolecular forces in the material but why does stretching a material will enhance attractive force over repulsive force and vice versa.
Mohammad Abid
- 291
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What shape does an elastic rod take when both ends are dragged to the same point?
Suppose we have an ideal elastic rod of some kind, where the energy at a point along the rod is proportional to the square of the curvature, and we drag the ends of this rod so that they touch, and the rest of the rod is now making some kind of…
zucculent
- 1,395
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Why is there a difference between work done and elastic potential energy above the elastic limit?
When a spring is inelastically deformed, the work done is no longer equal to the elastic potential energy stored in the spring – what accounts for this disparity?
Put another way, the spring is no longer storing all of the energy from mechanical…
Josh
- 37
3
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To deform a solid body even negligably is external force of any magnitude sufficient?
Is it necessary that when an external force is applied on a solid body, it always gets deformed however small the deformation may be?
If the material is highly elastic like steel, even then there will be a deformation of the body for negligibly…
Matt
- 644
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Young modulus and Sound Velocity in a continuus medium
In elasticity theory, general equations of motion are:
$$\rho \partial^2_t \overline{u} = \mu \nabla^2 \overline{u} + (\mu+\lambda) \nabla(\nabla \cdot \overline{u})$$
where $\overline u$ are displacements.
In a thin homogeneus rod with tractions…
Boy S
- 1,424
3
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Rubber band elongates like s-curve
A normal rubber band (brownish yellow) with about 1 mm^2 cross section and approximate slack length of 170 mm is suspended vertically and gradually loaded with a number of weights (each weighing 9.36 grams) and the resulting elongation of the…
Jens
- 1,282
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Energy of local rotation in elasticity theory
In the theory of elasticity there is an important object, the displacement increment vector $u_i$. The derivative of such an object can be decomposed into symmetric and antisymmetric parts:
$$
\partial_i u_j = \underbrace{\frac{1}{2} (\partial_i u_j…
Nikita
- 5,657
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Continuum limit for a bulk of discrete masses coupled by springs
I have a question that has been bothering me for a long time. I know very well how to take the continuum limit for a chain of masses connected by springs. But in my recent project I would like to extend this to a bulk of masses (3D) connected by…
LLanadas
- 31
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2 answers
Why is chewing gum only elastic for a brief period when pulling it out of your mouth?
Assume you are chewing some gum and pull it out of your mouth like so:
If you release the gum quickly it will spring back to your mouth as if it is elastic, but if you leave it for a few seconds then release it will just fall down like a piece of…
DannyH
- 423
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votes
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Properties relevant to impact absorption?
Assuming you are creating or evaluating a material used as padding. An approximation of the padding's use would be wrapping a lightweight bat so as to make it as close to harmless on a person as possible, with the minimal layer possible.
The…
Thanos Maravel
- 123
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Linear elasticity: can "extremal" strain tensors be in the interior of the body?
i am new to elastic theory. I have a question about linear elasticity. In each point $p$ of a body $\Omega$, the strain tensor has three eigenvalues $\lambda_1(p)\geq \lambda_2(p)\geq \lambda_3(p)$. Let $\partial\Omega$ be the boundary of $\Omega$…
Chevallier
- 163
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Why do tube balloons inflate first from the side with the hole?
When I inflate tube balloons (like you'd use for making balloon animals), the bulge always starts close to the end of the tube with the hole—always. Why does it start there and not anywhere else along the length of the balloon? Why doesn't it…
adam.baker
- 205