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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1answer
251 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 ...
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2answers
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 ...
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1answer
578 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 ...
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1answer
584 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 ...
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1answer
576 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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1answer
83 views

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 ...
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1answer
254 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 ...
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2answers
682 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?
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1answer
213 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 ...
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1answer
197 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. ...
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2answers
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 ...
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1answer
285 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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1answer
178 views

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 ...
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1answer
333 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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0answers
53 views

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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0answers
13 views

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 ...
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2answers
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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0answers
94 views

Heads, Tails… Edge?

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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0answers
62 views

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 ...
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0answers
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 ...
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0answers
74 views

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 ...
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1answer
328 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 ...
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0answers
127 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 ...
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0answers
233 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 ...
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2answers
211 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 = ...
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2answers
51 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 ...
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2answers
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 ...
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1answer
25 views

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 ...
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1answer
30 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 ...
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4answers
505 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 ...
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1answer
28 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 ...
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2answers
52 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 ...
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1answer
391 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?
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1answer
104 views

Deformation of the cylinder

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 ...
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1answer
555 views

Explain the Föppl–von Kármán equations

I am a newbe to elasticity. Could someone please explain to me briefly how the Föppl–von Kármán equations work? What are we trying to solve for? Is there some kind of intuition to the way they look? ...
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2answers
138 views

Why elastic materials are discribed by tensors?

I am starting to read about elasticity of thin surfaces and I don't understand why tensors play such a major part? What are the tensors describing about the material? And just to clarify - Is there ...
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1answer
554 views

Semi-conductor band-gap and deformation potential

Submitting a semi-conductor to stress leads to a deformation in the energy-bands, roughly described by:$$H_{ij} = {\cal{D}}_{ij}^{\alpha\beta}\;\epsilon_{\alpha\beta}$$ $\epsilon$ being the strain ...
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4answers
978 views

Generic Born stability criteria

The tensorial form of Hooke's law for the strain-stress relationship in a crystal is (in the Voigt notation): where $\sigma$ is the strain, $\epsilon$ is the stress and C is the stiffness tensor: ...
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1answer
350 views

Modeling linear spring deformation in time

Suppose I had a spring (at equilibrium) and applied a certain force $F$, causing it to undergo elastic deformation. I know that by applying this specific force, hooke's law tells me that the spring ...
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1answer
714 views

Modulus of Elasticity

Consider a cube of unit dimensions. Let $\alpha$ and $\beta$ be the lateral and longitudinal strains. The expressions for moduli of elasticity on applying unit tension - 1) At one edge: Young's ...
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2answers
1k views

At what point does a projectile leave a slingshot?

Assuming a frictionless / "perfect" environment, and given a ball held in an elastic sling (like a hand-held catapult) where the pocket is lighter than the projectile itself, what is the point at ...
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2answers
35 views

Why does a ball eventually stop?

I was wondering, if the force of friction with the ground does not make any work on the ball and just give it the necessary torque to rotate (hence the consideration of static friction coefficient in ...
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3answers
35 views

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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2answers
38 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 ...
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1answer
223 views

Gough-Joule effect in rubber band

When a stretched rubber band is heated, surprisingly, its tension will increase. What is the physics behind this?! Another thing. The Entropic spring model says, for a good specimen, that the ...
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1answer
283 views

A moving brush on a vibrating surface

Hi group, I am a HS student in China preparing for a regional Young Physicist Tournament even. We are very puzzled about why would there be such movement. We would be grateful to see any inspiring ...
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1answer
543 views

Why is elastic modulus greater than shear modulus?

I was looking at data for elastic modulus $E$ and shear modulus $G$, and found that $G$ is always lower than $E$. So I'm wondering what are the underlying principles that may be the cause of this. ...
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1answer
276 views

Confusion in Euler-Bernoulli beam theory

Euler-Bernoulli beam equation is given by $$ EI \frac{\mathrm d^2 u}{\mathrm d x^2} = M'(x) \\ EI \frac{\mathrm d u}{\mathrm d x} = xM'(x) + C_1 $$ Where, $E$ is modulus, $I$ is second moment of ...
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1answer
170 views

Where does elastic energy come from?

I vaguely remember reading that the elastic potential energy of a spring, $\frac{1}{2} k x^2$ comes from mass which is turned into energy according to the law $E=mc^2$. I also remember hearing that ...
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2answers
503 views

Range of poissons ratio

I know the range of poisson's ratio is -1 to 0.5 but how do you arrive at this expression? I am a 11th grade student and I am not too familiar with advanced physics