# Tagged Questions

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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### A question regarding collisions

Let us consider a system of 2 identical spherical bodies connected by a massless string that is taut. If one body is placed at the origin then the other is placed at some coordinate $(x,y)$. The ...
46 views

### Why do materials show plastic behaviour for large stress?

As the stress is increased, the strain increases proportionally up to elastic limit and the material regains its original dimension within elastic limit. When the stress is increased further the ...
63 views

### physical meaning of major symmetry of the stiffness tensor

What happens if a stiffness tensor does not have the "major symmetry" $C_{ijkl}=C_{klij}$? Background: In linear elasticity (generalising Hooke's law from a spring to a continuous medium), the ...
61 views

### What is the mechanism of heat exchange of a bouncing ball?

Imagine a falling ball on a perfectly hard ground. The kinetic energy will be first converted into a deformation of the ball, then the ball will restore it into kinetic and heat energy and recover ...
308 views

### Relationship of the volume of a plumbing system to pressure

How does the volume of water a plumbing system holds vary with water pressure? I know the ratio would include the modulus of elasticity of the plumbing material, the total surface area of the plumbing ...
332 views

### Where does this formula for sagging of a beam come from?

In one of my physics textbooks there is a chapter on the elasticity of materials which contains pretty basic outline about Young's modulus, stress-strain, elastic potential energy and related stuff. ...
167 views

### Elasticity of a body on which variable force is applied

Let us consider a rod of some cross sectional area $A$ and length $L$. At one end a longitudinal foce of 5x acts on the rod. At a distance of $\frac{L}{2}$ from that point longitudinal force of 5x ...
290 views

### Physics of Wrinkling: Understanding inextensibility condition

I'm reading this very cool paper on the formation of wrinkles in elastic materials. The key result of the paper is a set of scaling laws for the amplitude and wavelength of wrinkles based on the ...
1k views

### Mass Effect on Slingshot Motion?

For my physics class (I'm a high school student), we created slingshots. Our task is to predict the distance a projectile, launched from a slingshot using surgical tubing, would land. We aren't given ...
585 views

### A differential equation of Buckling Rod

I tried to solve a differential equation, but unfortunately got stuck at some point. The problem is to solve the diff. eq. of hard clamped on both ends rod. And the force compresses the rod at both ...
606 views

### Boundary conditions of Navier-Cauchy equation

I'm having difficulties with Neumann boundary conditions in Navier-Cauchy equations (a.k.a. the elastostatic equations). The trouble is that if I rotate a body then Neumann boundary condition should ...
601 views

### Lagrangian density of linear elastic solid

I need the general expression for the lagrangian density of a linear elastic solid. I haven't been able to find this anywhere. Thanks.
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### What determines the rate of vibration decay of a metal?

Suppose we have a tuning fork in a vacuum and strike it. Is there anything in the theory of metals that would predict that the tuning fork's vibration amplitude would decrease with time. Put another ...
836 views

### How does a fabric containing 10% stretch material make it stretchy?

Why should adding a small amount of a stretchy material make an otherwise non-stretchy fabric stretch? Shouldn't the non-stretch fibres still constrain the maximum stretch of the fabric?
225 views

### Calculating elastic energy constant [closed]

I ran into a kinetic physics problem: "A spring is hanging on the ceiling. Let's place an object 'M' at the end of the spring. Yet hold 'M' so the spring doesn't stretch. The distance between the ...
204 views

### Meaning of Lagrange Multiplier in Ou-Yang and Helfrich's Shape equation for Membrane

Dear people in Physics Stackexchange, My question is mostly related to the following papers: U. Seifert, Z. Phys. B 97, 299 (1995). "The concept of effective tension for fluctuating vesicles". U. ...
1k views

### Guitar strings and temperature

I am investigating Mersenne's law with a guitar by varying tension (hanging weights) and string length. Will temperature change (room temperature to ~4°C) effect the frequency noticeably? If so, is ...
293 views

### Is shear elasticity the same as shear modulus?

I've encountered both the terms "shear elasticity" and "shear modulus". Are these the same?
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### Why does elastic energy only depend on first derivatives?

Say we have an elastic material that is deformed with displacement function $u : \mathbb{R}^n \rightarrow \mathbb{R}^n$. It is reasonable to assume that the energy required for such a displacement is ...
338 views

### Is there symmetry in 2d stress tensor in linear elastic fracture mechanics?

Assumptions: Cross terms in strain tensor are defined as equal $\varepsilon_{xy} = \varepsilon_{yx}$. pure mode I crack. Far from crack tip, material is purely elastic and we are way below yield ...
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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 $\lambda_1(p)\geq \lambda_2(p)\geq \lambda_3(p)$. ...
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### Deriving the formula for energy stored in a spring without using geometry (determining the area under a curve)?

Using Hooke's Law, we know that the force applied is proportional to the extension of the spring. Therefore by plotting a graph of force against extension, through the area under the curve we are able ...
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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 ...
50 views

### Are hardness, strength and toughness of materials not the same thing in a way?

I had to look through several videos and re-read Wikipedia statements about these material properties several times before I could even begin to differentiate them. However, now that I have found out ...
46 views

### Deformation of an elastic bar

We know that if we fix a bar at one of its ends, then the other one will descend by $s = A \cdot F l^3, A = const.$ (we can assume that $F$ is the gravitational force. ...
109 views

### Mathematical expression of energy storage

I'm trying to develop an idea which is as follows. Put simply, imagine a flat sheet of material which, when distorted (I.e. curved in the third dimension) stores energy. Now, by calculating the ...
65 views

### Is strain always relative to some initial state?

Let us say I am given a material with no knowledge about its history. Can I somehow calculate its strain ? Or a strain is always relative to some initial state (change in length/initial length) ?
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No Nobel prizes at stake, but just an idle thought and an idle question. How could one calculate the probability of a flipped coin landing stable on its edge, instead of heads or tails? I assume ...
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### Positivity of Bulk modulus and shear modulus in isotropic materials

I have been searching through many resources, but could not find a proper thermodynamic reasoning for why bulk and shear moduli for isotropic materials should be positive. Some resources like eFunda ...
22 views

### Main differences between elastodynamic and light scattering when using S-matrix to find bound states

What are the main differences (top 5 if question is too broad), for using the S-matrix to find bound states, between elastodynamic and light scattering? (if it facilitates a higher quality question/...
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### If I roll an elastic plate into a cylinder, does it shrink?

Suppose I start with a rectangular elastic (to keep things simple, zero Poisson's ratio) sheet of length $2\pi R$, thickness $h$, and (immaterial) width $W$. I roll it up into a cylinder of radius $R$,...
331 views

### Swords, impacts and elasticity for a noob

So I'm a game developer and I'm trying to understand some (extremely) basic facts of impact mechanics. I had read something entitled Dynamics of Hand-Held Impact Weapons, but it was a bit too ...
129 views

### Is there analysis library for stress-strain data?

I have three column data that has time-displacement-force from 1D tensile/compression test. Now I would like to get the standard mechanical properties of the material, like Young modulus, yield stress/...
236 views

### Displacement due to sinusoidal load on a finite strip in an infinite plane

From a paper on tunnel design I've been reading: (http://www.sciencedirect.com/science/article/pii/0886779887900113) In the present application, the solu- tion corresponding to a sinusoidal load ...
117 views

### Why is the restoring force directly proportional to extension?

When deforming any spring the deforming force is always greater than the restoring force until equilibrium is reached. So, if a constant deforming force caused an extension in any spring the restoring ...
241 views

### Elongation in bar with unequal applied forces

How is elongation in a uniform rod with unequal forces acting on opposite sides calculated? If applied forces are equal and opposite, the elongation is defined by the formula ($\delta = \frac{FL}{AE}$)...
52 views

### Bending + Contact Force

When we have 2 bodies in contact with each other, for example a book lying on the surface of a table. The table's molecules bend a little bit because of the weight of the book thus producing the ...
6k views

### Why does a ball bounce?

If an object is acted on by equal and opposite forces then it will be in equilibrium, and it's acceleration or velocity (and so direction as well) will not be changed. So when a ball bounces, it ...
28 views

### Understanding stress-relaxation for viscoelastic materials

I'm studying a viscoelastic material with a cylindrical geometry and I read that for fixed strain(i.e. fixed elongation), I should observe decreasing strain over time. Given that stress $= F/A_0$ ...
35 views

### Young's modulus and geometry of test material

When measuring Young's modulus in a material, does the geometry of the material actually matter? I have seen several references recommend that I use cylindrical pieces. But, wouldn't the tests work ...
46 views

### Speed of Sound in matter

So basically when it comes to the speed of sound, it is said that speed of sound in media is based on two main factors - 1)elasticity and 2)density from the formula V= $\sqrt{E/\rho }$ where E is ...
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### Does every force applied to a rigid body results in strain (in molecular level)?

If force is applied to a rigid body and the body moves/remains still/vibrate or anything. But even if we can't see any strain in the naked eye, isn't there some sort of strain in the molecular level?
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### Reason for lateral contraction when tensile stress is applied to string

I have read that a wire contracts side ways on stretching it . But why? What happens at the atomic level when a string is stretched? When there is no force applied in the side ways direction, why does ...
45 views

### Young's Modulus and resonance frequency

While trying to find an idea for a simple undergraduate level lab project (using PASCO sensors), I stumbled upon this equation: $$Y = \frac{38.3*f_0^2*\rho*\ell^4 }{ d^2}$$ where: $Y$ = Young's ...
953 views

### Hooke's Law is valid upto what limit?

My textbook states: " the extension produced in the wire is directly proportional to the load applied,within elastic limit." But my Physics professor said that it is valid upto only proportionality ...
29 views

### How can I learn about elastic bodies?

I'm writing a program that needs to be able to simulate a system of elastic bodies, that can collide with each other and with other rigid bodies, and deform accordingly. I think it would be an ...
53 views

### On the isotropy of materials

I am working on honeycomb structures and first of all I would like to understand whether it is isotropic or not, and, if the latter holds, which kind of anisotropy does it have? How to do it? I don't ...
403 views

### Is shear modulus only applicable to cubical solids?

Do we have any real life/theoretical examples where shear modulus is applicable to non-cubical shapes?
There is given a cylinder with fixed side surface. On one base is being rendered constant pressure $p$, so cylinder cambers I'm trying to calculate the form of cambering. The problem is that height ...