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
59 views

Deformation of a rubber ball between planes

I want to know the shape of a rubber ball when it is sandwiched between two (not necessary parallel) plane. If two plane is parallel, I think it is possible to approximate the ball as spheroid and ...
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1answer
39 views

pulmonary physics: balloons in closed chambers

Imagine we have an expanded balloon with radius $R_1$ and an internal pressure of $+20$ atm, in an room at $0$ atm of pressure. The system is at equilibrium. Now, I drop the pressure in the room to ...
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2answers
59 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 ...
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0answers
35 views

Strain problem with diferent forces

Good day to everyone. I had a test a couple of weeks ago and just got it back, and I'm getting a little confuse with a certain question that I thought was answered correctly, so here is it: (roughly ...
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1answer
44 views

Calculate water pressure in a elastic material cavity

Imagine there is a ball-shape cavity made of elastic material. The diameter of the cavity is 1 cm so that the capacity of the cavity is $\dfrac{4}{3}\pi\approx4.19 \textrm{cm}^3$. Now we pump ...
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2answers
76 views

Point forces in linear elasticity and small strains

Consider a point force $\boldsymbol{F}=F\boldsymbol{e}_z$ in an infinite elastic material. In a linear approximation, the displacements can be calculated using Green's function for the Laplacian which ...
2
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1answer
82 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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0answers
33 views

Elastic material with exponential behavior?

I know some constitutive models for elastic materials like Neo-Hooke or Mooney-Rivlin, which give a relation between elongation $\lambda=y/y_o$ (where $y$ and $y_o$ are the length of the elastic ...
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2answers
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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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0answers
25 views

Negative Kinetic energy of normal modes in an elastic solid?

So I'm pretty stupid, admittedly, but I'm also pretty confused. I also fully realize this question is probably completely idiotic. The background is normal modes in linear elastic solids. Let the ...
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0answers
34 views

Equilibrium and constitutive relation

The constitutive stress-strain relation, say $\sigma=Y\epsilon$ where $Y$ is the Young's modulus, gives you stresses. At equilibrium, force balancing (say, with respect to a internal pressure $p$) ...
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0answers
31 views

Stress profile of pressurized bent shell

Consider a pressurized cylindrical shell of radius $r$ and pressure $p$, which at equilibrium has a nonvanishing in-plane stress components $pr/2$ and $pr$. This result is generically found by ...
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1answer
121 views

Derivation of elastic energy per unit volume

So I basically asked this question a little while back and didn't get much help, but I really need help, so I'm coming back and asking again. Looking at the section on Continuum Systems on the ...
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0answers
34 views

Mooney-Rivlin coefficients sign

I'm doing a fitting of uniaxial compression data of a isotropic polymer using the Mooney-Rivlin model: $\sigma=\left( 2C_1 + \frac{2C_2}{\lambda} \right )\left( \lambda ^2- \frac{1}{\lambda } ...
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1answer
120 views

9/11 attack: How can a whole building fall even though impact only on the top of building? [closed]

The airplane hit the top of the building. After a few time the whole building collapsed. How is this physically possible?
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0answers
34 views

Strain energy density (potential energy of elastic continua)

This question has to do with writing down the potential energy of an elastic body, which obeys a generalized Hooke's law [; \sigma_{ik} = \sum_{klm} \lambda_{iklm} u_{lm} ;] Where $\sigma$ is the ...
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2answers
40 views

How does my reference point affect the regresion of data about Hooke's law?

A vertical spring is used (subject to a universal support) whose length is $20$ $cm$ when no force is acting on it. We put on a weight of $1$ $N$ and the new length is $22$ $cm$. When writing the data ...
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2answers
155 views

Where does the energy go when you stretch a rubber band?

There is resistance when you stretch a rubber band. That makes sense to me because the energy you exert is turned into potential energy of the rubber band, but if you hold the rubber band in the same ...
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3answers
300 views

gravity delayed by speed of information transfer

A few months ago I had the pleasure of listening to an episode of RadioLab (a very informative podcast I would recommend to everyone) when they had Neil deGrasse Tyson on. He was discussing the very ...
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0answers
76 views

How to calculate the energy in thermoelastic damping?

Note - I'm not 100% sure *thermoelastic damping* is the right term here - so please feel free to correct the question in case I'm wrong! If a force is applied to an elastic rod such that it ...
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1answer
222 views

Fundamental frequency of a material and its Young's modulus

I wonder if there is a connection between fundamental frequency and Young's modulus of a material. For example, how to calculate the Young's modulus of a glass bar by knowing its frequency spectrum?
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3answers
318 views

What does Hooke's law have to do with molecular forces?

In The Feynman Lectures, in the chapter Characteristics of Force, In the section entitled Molecular forces, Feynman talks about the molecular forces, and then he states afterwards: If the ...
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0answers
29 views

Shear flow in J section type beam

What does the distribution of shear flow look like in a J section type beam. I'm only interested in a qualitative picture of it. I'm not interested in the calculations themselves. It is the top of the ...
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1answer
222 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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0answers
35 views

Specific form of Stokes's differential equation

Coming from a chemical background, I have next to no knowledge of the (as it seems to me) complex field of fluid dynamics, so bear with me here. I'm reading a paper written by seismologist Norman ...
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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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1answer
40 views

Origin of a unique stress-strain relation

In a paper by Kees Wapenaar titled, "Retrieving the Elastodynamic Green's Function of an Arbitrary Inhomogeneous Medium by Cross Correlation" (2004), the following is stated: "In the space-frequency ...
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0answers
37 views

When one blows up a latex balloon, why does it get easier to blow once it has a little air in it (after 1 or 2 breaths)? [duplicate]

When one blows up a latex balloon, why does it get easier to blow once it has a little air in it (after 1 or 2 breaths)?
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1answer
657 views

Bending moment of a cantilever beam

The following procedure is here. Consider a cantilever fixed at one end and loaded at the other one. In cartesian coordinates (if $y$ is horizontal and $x$ vertical, meaning that the load acts ...
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1answer
110 views

Coefficient of elasticity of the spring?

I know this might sound a silly question though For a spring that is compressed lets say x meters by a force F N. what is coefficient of elasticity of the spring? We are not given the equilibrium ...
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0answers
58 views

Coefficient Of Restitution of Two Balls With Different Elasticities

In a computer program, I need to simulate the collision of two balls with different elasticity values given between 0.0-1.0. I looked for a formula to derive restitution coefficient from elasticity ...
2
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1answer
251 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 ...
1
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1answer
277 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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2answers
178 views

First-principles derivation of cutting force

I know that the amount of force required to separate a material from itself is linked to the surface energy of that material. However, looking at just the surface energy laughably underestimates the ...
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1answer
914 views

Help calculating work done by stretching a wire [closed]

A wire of length 0.89 m and cross-sectional area 1.7 cm2 is stretched elastically by an amount 1.2 cm. By Hooke’s law, the restoring force is $−k\Delta L$. Calculate the work done in ...
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1answer
535 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
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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0answers
77 views

How to specify boundary conditions as function of curvature in dynamic elastic beam pde?

In this article (already mentioned in this question) the dynamics of a planar elastic beam with "cantilever constrains" (one clamped end and one free end) is modeled. Using the Euler-Bernoulli Beam ...
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1answer
46 views

Can surface waves exist near a fixed surface

(I'll phrase this question in terms of waves in an elastic medium, but this is a more general question.) Surface waves are waves near the surface of a medium whose amplitude decreases as you go away ...
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2answers
51 views

Elastic behaviour of objects

If I strike my car with a wrench with enough force to make a dent in it, then it's obvious that I won't be able to produce any acceleration in the car. But I am applying an external deforming force. ...
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2answers
85 views

Differences between elastic moduli

Is it true that in materials like aluminum and copper, the correct order of elastic moduli, in terms of value are: Bulk < Young's < shear modulii If this is correct, why is this the case?
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2answers
280 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. ...
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1answer
620 views

Diameter of after elongation of a cylinder

This is more Material Science than Physics, but I'm doing a research project right now in computational science that involves some additional information that is outside of my background. I've done ...
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3answers
229 views

origin of the major symmetry property of the elasticity tensor

In linear elasticity theory the stress tensor $\sigma$ is related to the strain tensor $\epsilon$ via the elastic tensor $C$. Specifically $$ \sigma_{ij} = C_{ijkl} \epsilon_{kl} $$ Because $\sigma$ ...
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1answer
48 views

Is an elastic, gravitating object stable?

As I understand, an object can contract under its own gravitantional pull. Then as it does so, different parts of the object must move with some velocity. This in turn means that their relativistic ...
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2answers
189 views

Proof that a traceless strain tensor is pure shear deformation

How can i proove that the traceless part of linear strain tensor $e$ in the Euler description: $$e_{i,j}={ 1 \over 2 } \left({ \partial u_i \over \partial x_j}+{ \partial u_j \over \partial x_i} ...
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1answer
53 views

Relation between area elements in finite deformation theory (continuum mechanics)

There are relations for the line and volume elements in continuum mechanics. For example: \begin{align} \ \ \ \ \ \ \ \ \ \ \ \ \frac{V}{V_0}&={\rm det}(F)\tag{1}\\ \lambda^2&=(F^TFe_1\cdot ...
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0answers
86 views

Deriving general boundary conditions from first principles for elastodynamic scattering

It seems that most of the relevant books only give the linear case and the rest say something along the lines of "here are common examples of boundary conditions." What are the most general boundary ...
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0answers
50 views

What's the relation between the type (Gender) of a balloon and its internal pressure

I'm working on a project about balloons and I need to know the relation between the gender of the balloon and its internal pressure. As far as I know, there are some parameters such as " Elasticity of ...
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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 ...