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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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2answers
30 views

Calculating Elastic Potential Energy of a Stretched Sheet

Essentially, I'm trying to determine the amount of elastic potential energy stored in a thin, elastic sheet that has gone under some type of stretching (ex. A flag of stretchy fabric waving in the ...
1
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2answers
61 views

Conservation of energy when dropping a ball

If we drop a bowling ball from one meter above the earth's surface, we are converting its gravitational potential energy to kinetic energy. When it hits the floor, it transfers its kinetic energy to ...
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0answers
17 views

How can we find the extension and enrgy stored when an elastic rod is stretched by unequal forces applied at its ends [closed]

A uniform rod of cross sectional area A, original length A and young's modulus Y is placed on a smooth horizontal surface. Now two horizontal forces (of magnitudes F and 3F) directed along the length ...
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0answers
21 views

Shearing strain - difference between gamma-xy and epsilon-xy

What is the difference between $\epsilon$$_{xy}$ and $\gamma$$_{xy}$? How does the relation $\epsilon$$_{xy}$ = $\gamma$$_{xy}$/2 comes?
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0answers
40 views

Calculating shear stresses with multiple forces

I have a rigid body where multiple forces (green) of different magnitude are applied. If I sum up the parallel component of the forces and divide it by the surface area, I can get the average shear ...
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1answer
40 views

Landau and Lifshitz argument for symmetry of stress tensor

In Landau and Lifshitz's book on the theory of elasticity (vol 7, theoretical physics series), specifically section 2 of the first chapter, the authors present an argument for justifying the symmetry ...
2
votes
1answer
69 views

Why do materials obey Hooke's law? [duplicate]

Why do materials extend proportionally to the force exerted on them (Hooke's law)? I thought that when materials are compressed or extended under force, their atoms become closer or further apart; ...
2
votes
4answers
171 views

Where is the Elastic Strain Energy per Actual Volume Gone?

I have a probably real stupid question, but I still can not wrap my head around it. The change in inner energy per unit volume $v$ of the actual state of a stressed crystal is given by the well ...
-3
votes
1answer
32 views

How to stack padding materials to pad an edge [closed]

This is about how to combine materials of various elastic and deformation properties as a stack to show different properties as a stack. A cardboard box has two holes punched in the side of the box ...
0
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0answers
13 views

Calculation of Young's modulus for a three-layer stacked material

I am currently working on three-layer stacked material and want to calculate the effective Young's modulus. The spring constant of the three layer material would need the effective Young's modulus ...
0
votes
1answer
40 views

Change of system of coordinates for the stress matrix

I have a stress matrix in cartesian coordinates : $\begin{pmatrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{pmatrix}$. How can I convert it to spherical coordinates ?
1
vote
1answer
50 views

Which Formula for the Internal Elastic Energy is Correct?

I am confused by the internal energy of a crystal. Lets say I have a isotropically stressed crystal. The total differential of the internal energy per unit volume V is defined as $$du = \sigma d\...
1
vote
2answers
126 views

Why a short rope takes more load than a longer rope?

The captain of a ship told me that it should be avoided to put a long rope next to a short one because the short rope takes most of the load and the long becomes relatively inactive, although both ...
0
votes
1answer
77 views

Can a piece of glass get higher than the height the original cup of glass fell from?

If yes, what physics concepts make this possible? This isn't for any class or anything, is just a honest doubt of mine.
0
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0answers
42 views

How to map a (virtual) truss deformation to a surrounding object

I am trying to craft a way of simulating deformable objects without using finite element method (despite it is the goldstar method for such purpose). The goal is to rapidly get an estimate of how a ...
2
votes
2answers
40 views

After elastic collision, where position of center of stationary ball? Does ball stop instantly?

Suppose we have two balls, $A$ and $B$, of radius $1$ with equal mass. Ball $B$ is initially at (center is at) two on the $x$-axis, i.e. $(2,0,0)$, and has velocity $0$. Ball $A$ is initially at (...
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0answers
51 views

Compute stress tensor in finite element simulation

I have implemented a finite element simulation using a tetrahedral mesh that minimizes a linear elasticity potential energy. Among the main quantities I compute for the simulation is the deformation ...
0
votes
2answers
45 views

Making sense of the stress tensor for elastic deformations

I've seen this kind of formula a number of times, in the context of elastic deformations. $$ -\nabla \sigma = f $$ whete $\sigma$ is "the stress tensor" and $f$ is force. I never understood it even ...
3
votes
0answers
77 views

Existence of solid mechanics problems that cannot be solved through Lax-Milgram approaches

Very often, solid mechanicians employ finite-element analyses to solve problems in linear solid mechanics. This approach is guaranteed to work because the Lax-Milgram theorem, along with some ...
0
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0answers
91 views

Hertzian contact between cylinder: calculating the displacement

I'm trying to calculate the total displacement (also known as depth of indentation, total elastic compression and total surface separation in different literature) in a Hertzian model of a contact ...
0
votes
1answer
24 views

Material tangent stiffness matrix for linear elasticity

I am trying to find material stiffness matrix for linear elasticity for finite element code, $$\mathbf{\sigma} = \lambda \hspace{1pt} \operatorname{tr}{\left(\mathbf{\epsilon}\right)}+ 2\mu\mathbf{\...
2
votes
1answer
20 views

Difference between bending elasticity and Stretching elasticity in complex solids

In a solid, elasticity is described by the Young modulus E. Let us consider a thin sheet of material of thickness h. The bending rigidity is usually Eh³. I wanted to know if they are "abnormal" ...
12
votes
1answer
562 views

Can Hooke's law be derived?

Can we derive Hooke's law from the theory of elasticity? I know it is not a fundamental law and therefore can be derived from more basic considerations.
2
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1answer
54 views

Trouble connecting stress and force in continuum mechanics with my concept of force from point mechanics

I'm not very familiar with continuum mechanics and have a hard time combining my knowledge of forces from simple mechanics with what I read about continuum mechanics. Let's suppose we have a metal ...
0
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0answers
17 views

how to calculate the natural frequency of a rounded rubber?

I ought to calculate the natural frequency of a circular Rubber.(Consider the situation that we are disturbing the circle from two points of the circle with 180 degree of difference in the location on ...
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0answers
29 views

How to model falling modelling clay deformation?

I drop a cylindrical piece of modelling clay/plasticine from the height of 15-20 meters. How can I calculate deformation? The cylinder can fall horizontally, vertically and at angle. What is the ...
0
votes
1answer
16 views

What is the unit of bending strain?

In plate theory, there is this equation: $$\epsilon_x=-z\frac{\partial^2 w}{\partial x^2}$$ For example, you can see this equation here. And there is a conflict, which I'd like to resolve. Wikipedia ...
2
votes
1answer
47 views

Spring non-linear behavior for small forces

While writing a report about a classical spring experiment I noticed that, if small forces were applied to our spring, this would stretch much less than expected. Searching on the internet I've kinda ...
0
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1answer
62 views

What is elasticity limit?

Does elasticity limit exist for a perfect gas? Are young's modulus and shear modulus inversely proportional to temperature and what about bulk modulus?
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0answers
15 views

Elastic constants for a 2d lattice (triangular)

Given a 2d lattice (say triangular) with spring interaction, how does one calculate strain tensor for it and hence elastic constants? I am asking this in context of this paper here: Monet et al I ...
0
votes
1answer
25 views

Stopping a spinning object with a flexible gripper

I would like to know how deformation of the contact surface affects friction of a spinning object. In the image below I have a 2D problem of a spinning circle with two elastic "fingers" pinching it ...
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0answers
35 views

Physics of harmfull bungee jumping and hanging

According to the Wikipedia section on long drop hanging, the risk of decapitation increases with length of the rope. By analogy I expect that a long enough bungee rope can tear jumper's leg off. I ...
0
votes
1answer
52 views

Young's modulus in Hooke's law

In the third edition of the book Classical Mechanics, by H. Goldstein et al., on chapter 13 it is stated that: For an elastic rod obeying Hooke’s law, it will be remembered that the extension of ...
1
vote
1answer
64 views

Pulling a Metal Bar in Space [duplicate]

Let's say I have a metal bar (which does not expand or contract at all) that's 1 light-second long which is connected to a block at the end. I am in space holding the other end of the bar. If I pull ...
0
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1answer
30 views

Why are conservative forces responsible for elastic collisions?

In elastic collisions, such as the collisions of two snooker balls, it is stated that conservative forces are responsible for the collision being elastic. (See http://vlab.amrita.edu/?sub=1&brch=...
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0answers
46 views

Is energy stored in velcro considered Elastic Potential Energy in an inelastic Collision?

So just some background for the question, if two pucks with velcro on each side on very slippery ice with close to no friction collide, they stick together. Thus, the collision is inelastic. However,...
0
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1answer
45 views

Dynamic of a bent sheet of paper

Take a standard printer sheet of paper (dimension $L \times H$ say), wrap the sheet of paper around a cylinder of radius $r$ so that the sheet of paper takes its form. Now put the sheet of paper down ...
33
votes
3answers
6k views

Clarifying the actual definition of elasticity. Is steel really more elastic than rubber?

Yes, I know it's steel. It's everywhere on the web and I did google. But I seek enlightenment. My physics textbook defines elasticity as: Property by virtue of which a material regains its shape. ...
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3answers
76 views

Model of an Elastic Rod

For an electrical design, i am having a cable modeled as a perfect elastic static rod, fixed at both ends, as i have depicted how should it be for different given reference lengths. I've studied ...
0
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1answer
52 views

Boltzmann constant times absolute temperature

I came across a research paper with the following paragraph in a research paper. Research Paper section I am trying to fetch fluctuations from Kirchhoff's matrix and that is why I am interested in ...
0
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0answers
35 views

Propagation of acoustic waves into an elastic material

I am trying to understand what happens on the boundary between an elastic material and an acoustic one. I am trying to understand it in two dimensions: Assume that we have a square separated made ...
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0answers
29 views

Potential energy stored by an elastic circular loop on deformation to an ellipse

This question is related to an origami circular loop that I built. This structure is elastic and I intend to find the elastic potential energy stored by it when I deform it to an ellipse. My actual ...
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0answers
19 views

Elasticity of Origami Materials

A few origami structures have elastic properties. Suppose that I have a structure, made from origami techniques, what factors affect the elasticity of the structure apart from the quality of the paper ...
0
votes
2answers
58 views

Force of Body Impact Upon Water

So in 2014 I fell from 70 feet and landed flat on my back on slowly moving water (.5ft/sec) on the Willamette River. I weighed aproximately 190 pounds at the time. I was curious if someone would help ...
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vote
0answers
24 views

Find spring stiffness of a frame structure

I would like to calculate the spring constant of a frame structure. I thought that I could do it like this: I apply a point force on the structure: Then I calculate the displacement at that same ...
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votes
1answer
24 views

Spring Potential energy conversion

Picture this... I take an elastic band, similar to one that people use to work out. Much larger than a rubber band. My friend has lost a bet and I decide that his punishment is for me to put the band ...
0
votes
1answer
46 views

Maxwell material response to step strain - initial condition

A Maxwell material is a model material obtained by connecting a perfectly elastic solid and a Newtonian liquid in series. Let $\sigma$ be the stress, $\gamma$ the shear strain, $G$ the shear modulus ...
2
votes
3answers
58 views

A question based on elasticity

My teacher gave this question as homework while we were learning Elasticity in class. Question description: Objective: To find the total elongation in the frustum as well as the potential ...
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vote
0answers
35 views

Linking elastic moduli to shape fluctuations

I am simulating a polymer network shaped as a sphere. I would like to compute its elastic moduli (bulk and Young's, for example) not by their shear-strain definition but by looking at the fluctuations ...
3
votes
3answers
77 views

Is a mono-molecular spring possible?

I have seen and read a lot of springs being used in the macroscopic world, and I also know that things can behave differently on a much smaller scale. My question is could a single piece of molecules ...