# Questions tagged [elasticity]

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.

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### Stretching vs bending of thin membrane

Stretching refers to the deformation of a material when a tensile (pulling) force is applied. The material elongates along the direction of the applied force. Bending involves the deformation of a ...
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### Why is the strain tensor of a rod under uniform torsion the same everywhere along the rod?

I'm currently reading the section on torsion of rods in "Theory of Elasticity" by Landau and Lifshitz (3rd. Ed., Chapter 2). If we suppose that the rod is cylindrical with radius $R$ and the ...
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### "Friction at a contact point", rubber-band experiment

I was working on some practice problems in my book, and the question was to describe all the energy conversions that happens when a person pulls on a rubber band and hits it on a board (any type of ...
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### Why do basketballs with more air in them bounce more than ones with less air?

I thought it this because more air means more pressure, so there will be more pressure when the ball is deformed and it will gain more kinetic energy as it rebounds. However, some sources say that ...
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### Is the shear stiffness of a helical spring for bending negligible?

I want to model a helical spring by beam theory. Lets call $d$ the stock wire diameter and $D=2r$ the the helix radius (see picture below). For example: The axial stretch stiffness is given as here. ...
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1 vote
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### Wrinkling on a fluid foundation [closed]

I have this problem in fluid mechanics/elasticity and honestly don't know how to start. A large elastic sheet of bending modulus A overlies a fluid of density $\rho$. Due to external compression, the ...
1 vote
43 views

### Elasticity theory: homogeneous deformations of a perfect lattice

I want to understand how the macroscopic (linear) elasticity theory emerges from the microscopic properties of matter. My question is about the model of the "perfect lattice", which is used ...
• 208
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### Frame invariance of the conservation of linear momentum at a solid-fluid boundary

The Conservation of Linear Momentum (https://en.wikipedia.org/wiki/Cauchy_momentum_equation) states that $\rho \frac{D \mathbf{u}}{D t} = \nabla \cdot \boldsymbol{\sigma} + \rho \mathbf{f}$ (1) In the ...
1 vote
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### How can I identify a quarter or half wave plate from a used/modified Strainoptics polarimeter?

I'm a glassblower and I need to test glass formulas for compatibility. I'd like to use a polarimeter as it allows not only the detection of strain, but also informs if a glass needs to be softer or ...
1 vote
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### Why don't we see the transverse waves with a phonon lattice dynamic while we see them with linear elasticity theory?

Let's say that we have a lattice with particles sitting on the nodes. Each particle $n$ has neighbors $\bar n$: $$\dfrac{d^2\boldsymbol u_n}{dt^2}=-K\sum_{\bar n}\boldsymbol u_{\bar n}\tag{1}$$ The ...
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### Why lateral strain occurs when volume is not conserved on applying longitudinal stress?

I first thought that lateral strain occurs to conserve volume on applying longitudinal stress but later I realised that I was wrong. But now I have a confusion that why lateral strain occurs if volume ...
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1 vote
280 views

### Why do colliding blocks compute to $\pi$?

If you take two blocks on a frictionless plane (each block is 1kg) with one wall and perfectly elastic collisions, if you collided the block on the right with the one on the left (wall is on the left) ...
223 views

### What is a general definition of bulk modulus?

For a perfectly elastic body, Bulk modulus always remains constant and is defined as, $$B=-V_i \frac{\Delta P}{\Delta V} \tag{1}$$ Which means, $$B \left(\frac{V_f -V_i}{V_i}\right)= -(P_f-P_i)$$ But, ...
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### What happens if a slow train hits you?

It's funny, I used to wonder this at school many years ago. For the purposes of discussion, imagine there is a big (very massive) cube that slides towards you as you're sitting on the floor. It doesn'...
1 vote
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### What is the relation between linear elastic theory and phonon transport?

I am reading about Boltzmann equation and I am having a hard time making a link between elastodynamics and phonon equations. Clearly there should be a limit where both are one and the same, isn't it? ...
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### Elasticity and Hooke's law: who is applying the force?

I am currently studying longitudinal vibrations in an elastic beam. However, I am struggling a bit because it is the first time I have done continuum mechanics. More specifically, when isolating an ...
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### How do you calculate the potential elastic energy in only one of the springs of a series? What about if they were connected in paralel? [duplicate]

Given the elastic constants of 2 springs (k1=125N/m, k2=200N/m), how can you calculate the ratio between the potential elastic energy stored in the first spring (k1) when it is grouped in series with ...
84 views

### What factors does a Spring depend on?

When we consider an ideal spring, the force applied by the spring is proportional to its extension $f_{sp} = kx$. Does the same apply in real life? So I took it into my own hands. I got a spring ...
1 vote
186 views

### Point load distribution inside elastic solid continuum medium in finite elements method

In finite elements method, when point load is applied to a particular node of elastic solid continuum medium (e.g. soil), does it affect nodal forces in the rest of the mesh (i.e. does each node ...
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### Is bouncing ball (100% collision) an oscillatory motion/SHM or both or none?

My teacher told me bouncing ball (100% elastic) is oscillatory motion that does not have a stable equilibrium position and restoring force. It is just to and fro motion and thus called oscillatory ...
1 vote
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### Why do a ring expand radially on rotating it?

The reason told to me is due to centrifugal force. But centrifugal force is a pseudo force so how can we observe its effects like increasing radius of ring in other frame. Also as per me due to ...
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### Why is Volumetric stress change in pressure not final pressure?

While reading about volumetric stress, I found that volumetric stress on a body is equal to restoring force per unit area if force is normal to the surface and is proportional to the area. At ...
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1 vote
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### Rubber band ball and bouncing capacity

My coworker makes rubber band balls by wrapping rubber bands one over another. At the initial stage it was pretty bouncy. Now, as it has become larger and denser, it seems to have lost its bounciness. ...
447 views

### Computing the strain in a cantilever beam under a known deflection

I intend to use a cantilever beam to calibrate a strain gauge, in a setup similar to the picture. My idea is to introduce a small known vertical displacement $\delta$ on one side of the cantilever ...
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### Does a rubber band stretch evenly?

Suppose you have a rubber band, and a point is marked on the rubber band at the 1/3 point. If you now apply force to the two ends of the rubber band to stretch it, will the point maintain its 1/3 ...
1 vote
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### Cross section of a circle of elastic material under a point weight

If I've got a circle of elastic material that's fixed at the circumference, and I drop a point weight on it, what will the cross section look like? For example, if I took some material from a balloon, ...
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### Like force, does the rotational effect of force/torque require some finite time to travel through a real body?

Let's say I am using a long wrench to unscrew a tight bolt because the formulas developed in rigid body statics states that the moment arm should be longer for minimal force application. But how long ...
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### Why does the aggressively bowed string go sharp?

A vibrating string with fixed endpoints, such as on my fiddle, may be bowed (see Helmholtz motion, see stick and slip) with very little to a certain amount of pressure and proximity to the bridge (the ...
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1 vote
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### Proportionality: $I ∝ V$ or $V ∝ I$, are both of them correct?

I have a simple question that's been on my mind for a while. If both current is proportional to voltage ($I \propto V$) and voltage is proportional to current ($V \propto I$), are they actually saying ...
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### Why can you hammer a hole into an underwater ceramic cup?

Hammering a nail into a ceramic cup causes it to shatter when dry but not when submerged in water. Is there an intuitive explanation for this? And does it have anything to do with the Rehbinder effect?...
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### Tension at the ends of an elastic rod being acted by external forces [duplicate]

Consider an elastic rod (mass m, length l) being acted by external forces as shown What would be the tension at the end A and B(marked as green)? And why? My teacher took the tensions at A to be F and ...
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### What's the difference between elastic energy and entropic elasticity?

I was reading up some articles on elasticity theory to make an essay about elastic energy in rubber bands, but in the first paragraph of this article it is said that rubber bands do not show elastic ...
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### Capillary action of water in a sealed vessel

Consider a vessel completely filled with water and a vertically oriented capillary. If the water vessel was open at the top, you would expect capillary action to occur, lowering the water level in the ...
107 views

### What's the difference between constitutive laws and equation of state?

While defining material properties in finite element modeling, when should we opt for constitutive models, such as Linear Elastic or Neohookean (that relate stresses and strains) over Equation of ...
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### Justification for Statements on Beam Deflection

I am teaching students at a high school about bending of a beam (the beam is clamped at one end and then an applied force acts downwards close to the end of the beam to bend it). I thought that it did ...
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### Torque profile with fixed boundary condition

I am trying to find a simple treatment of elasticity theory of a scenario where I have a thin rod attached to a disc (radius $r_0$), and the disc is held fixed at its edge. Now I apply some torque to ...
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### What is the acceleration experienced by a person walking into a tree or pole?

Please go to this website and view videos of people walking into things. I would like to know what is the deceleration their head experiences from this. I have done my research on this already. A ...
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### The displacement for Hertz Contact theory

Hello I just begin to learn Hertz contact theory and have some questions about the geometry of the contact between the sphere and the plate in the figure below. The displacement $w(r)$is w(r) = \...
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### Problem in thermal stress equation

I came across this derivation of thermal stress where the strain is given as $\frac { l_0 \alpha t}{l_0}$. However, I believe it should be $\frac { l_0 \alpha t}{l_0(1+\alpha t)}$ to consider the ...
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I was trying to understand problem regarding finding the adiabatic modulus given the isothermal young's modulus. I'm still an amateur in thermodynamics. I just didn't understand the final step where ...
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### Are the stress and strain tensor covariant or contravariant?

My question is related to this question but I don't find the answer there to be completely satisfactory. The displacement of an elastic medium is a contravariant quantity, which I think is pretty ...
630 views

### What is the result of this Newton's cradle experiment where the initial ball doesn't bounce (exactly as in the regular case) but it has glue on it?

I have a question about a Newton's cradle type collision, but it has a twist to it. First, I will describe two well-known results, and then I'll add my twist. First, consider a cradle with five balls (...
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### Question about the elasticity matrix in metals

The most general anisotropic linear elastic material has 21 elastic constants. I am working with an HCP material and I found that it has 5 independent elastic constants. I am programming a subroutine ...
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### Longitudinal wave in a falling elastic body

Consider an elastic rod hung from a high point with density $\rho$ and Young's modulus $Y$, subject to gravitational acceleration $g$. The coordinate from the hanging point is $x$, while the ...
1 vote
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### Why the total work to move a spring from point A to B equals the integral of all forces needed to hold it balance at every point between A and B?

I'm reading a Calculus book that mentions the Hooke’s Law for Springs that says the force needed to hold a spring at $x$ cm from it normal position is: $F = kx$, where $k$ is a constant. I can ...
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### In-plane stresses on the surface of a cylinder

The three principal stresses on the surface of a cylinder are the hoop, $\sigma_\theta=\frac{pR}{d}$, longitudinal, $\sigma_z=\frac{pR}{2d}$, and radial, $\sigma_r=-p$, stresses. However, what are the ...
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### Identifying the elastic limit? [closed]

Consider this problem I understand that the elastic limit is the point at which the material no longer elastically deforms, that is it doesn't return to its original shape. However, I am struggling ...
1 vote
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### Spring constant of typical flute style champagne glass?

I am a high school student doing a lab report on the relationship between height and resonance frequency of champagne glasses, using the "singing glasses" method where you rub your finger ...
I have a system where two particles $x_1$ and $x_2$ in one dimension are connected by a spring and a dash in parallel. This is analogous to the Kelvin-Voigt model for viscoelastic materials. The two ...