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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What are the assumptions made when analysing a stretched elastic string from a thermodynamic aspect?

Consider a stretched elastic string. Then conducting a thermodynamic analysis of the elastic string. The approach is very similar to that used for $(P, V, T)$ systems, with the pressure and volume ...
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1answer
25 views

Restoring force in circular rod

Can somebody explain how to calculate the restoring force in a uniform circular rod with known Young's modulus and diameter. I would need the restoring force in a specified distance from the origin ...
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90 views

Deformation of an elliptical ring

How will it deform when I compress an elliptical ring along its long axis? For simplicity we could consider that the ring is homogeneous, elastic, has no internal stress at the beginning, and its ...
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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 ...
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1answer
976 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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100 views

Why only vertical component of the stress tensor on vertically suspended bar?

EDIT: I am gonna rephrase the question entirely. Imagine we have a bar which we will analyze in the linear elastic regime. The shape of the cross section is irrelevant. The bar is suspended from a ...
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397 views

When a wire is stretched by a load, is there any change in its volume? [closed]

When a wire, or a rod(whose diameter is not negligible) is subjected to a tensile stress, is there any change in its volume? If yes, does the volume increase or decrease? Take into consideration both ...
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2answers
272 views

How do you make a collision more elastic?

Currently, as described in this question, collisions cannot be elastic. However, is there a way to make a collision more elastic? Background: We're working on a project right now involving high ...
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2answers
1k views

Will larger balls make a Newton's cradle swing more stable?

I got a rather small Netwon's cradle and when I start it, the effect is not very good since all the balls start to swing where the effect we want is obvious. The balls are small and I wonder if larger ...
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3answers
5k views

Young's Modulus and Vibrating String Harmonics

I was wondering how Young's Modulus effects the resonant harmonics of a vibrating (string instrument) string. I know that the string's fundamental frequency is $$\frac{1}2 \times \text{Length} \times ...
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1answer
43 views

Why does a bungee jumper continue to move downwards beyond the equilibrium position of the jumper and cord?

When a bungee jumper jumps, ignoring the mass of the bungee cord, the jumper initially falls in freefall before an inelastic collision occurs between the jumper and cord, and the cord extends as the ...
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26 views

What is the short time limit of Maxwell viscoelastic fluids?

The Maxwell model for viscoelastic fluids writes: $$ \tau\stackrel{\triangledown}{\sigma}+\sigma=2\eta D(v) $$ where $D(v) = \frac{1}{2}(\nabla v +\nabla v^T)$, $v$ velocity and $\sigma$ stress tensor ...
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41 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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1answer
113 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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2answers
86 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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1answer
177 views

On what parameters is breaking stress dependent?

I have recently studied Elasticity in materials. There was a question about breaking stress that if the area along which a linear force is applied is doubled, then what happens to the breaking stress. ...
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1answer
43 views

Tensile stress, is the pressure given indicating just one side?

I'm studying elasticity right now in my chemistry class, and I'm confused as to what exactly tensile stress (and maybe compression stress too) might mean. It's given in N/m^2. And you're stretching ...
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1answer
1k views

Modulus of rigidity inside the water

Transverse wave can't travel inside the water. It travels in solid and on the surface of water because they have modulus of rigidity. What is modulus of rigidity? and why there is no modulus of ...
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1answer
151 views

Why don't we take into account the width contraction of the wire in calculating the stress strain relationship for a stretched wire?

In the stress-strain relationship for a stretched wire, we say that $\frac{F}{A}=Y\frac{β}{l}$; where β is the change in length and the rest have their usual meaning. We also say that there is a ...
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241 views

question about elasticity and tensile strength of wires

To the best of my knowledge, if you double the cross sectional area of a wire you double the maximum weight it can support before breaking. But what if you use two wires of the original cross ...
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1answer
746 views

effect of object mass in coeficient of restitution

I know the coefficient of restitution depends on the velocity before and after the impact of a bouncing ball. How does the mass affect it. Can't figure it out. v ...
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1answer
552 views

Confusion In solving a problem related to Elasticity?

This the question given in my textbook A thin, uniform rod of length $l$ is rotated with constant angular speed $\omega$ about an axis passing through it's one end and perpendicular to one end of ...
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1answer
850 views

Calculation of a bending moment

I'd like to calculate the bending moment of a cantilever, fixed at its base, and submitted to a certain stress on a specific spot, but I can't find the proper definition of this bending moment (first ...
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1answer
242 views

Simplifying some math for an ant-on-rubber-band problem

OK, I've been doing this problem for fun (it's a great problem, BTW!): http://www.physics.harvard.edu/academics/undergrad/probweek/prob76.pdf Here is the solution: ...
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2answers
276 views

Stress and strain

Let us consider a rod having a young's modulus $Y$. Let it be of length $l$, and suppose it is suspended from a point P. Let us pull the rod with a force $F$ at a point Q which is at a distance $2/3l$ ...
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9 views

Standard Minimal Reference Set of Poroelastic Parameters

I am coding a poroelastic reservoir simulator which requires the input of poroelastic parameters of the reservoir rocks. Detournay and Cheng, "Fundamentals of Poroelasticity" (1993) state that: ...
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1answer
23 views

Poisson's ratio and change in volume

The Poisson's ratio $\nu$ is always less than $0.5$. A traction force ($\Delta L >0$) can cause an increase in volume, while a compression force ($\Delta L <0$) can only decrease the volume. ...
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0answers
18 views

Derivation of expression for sagging of a beam [duplicate]

I read in my physics textbook that: A bar of length $l$, breadth $b$ and depth $d$ when loaded at the centre by a load $W$ sags by an amount given by the expression $Wl^3/(4bd^3Y)$ where $Y$ ...
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0answers
34 views

When should gravitational potential energy be included in the law of conservation of energy

I have a problem that says: A block of mass 0.249 kg is placed on top of a light, vertical spring of force constant 4 975 N/m and pushed downward so that the spring is compressed by 0.090 m. ...
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1answer
15 views

Material constraint in anisotropic elasticity

Consider the 2-dimensional (plane strain) case of a linear elastic general anisotropic material. Its elasticity tensor in engineering (Voigt) notation is positive definite, and looks like: ...
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0answers
16 views

Linear viscoelastic differential operators

I am starting with differential operators: $P = \sum_{i=0}^{N}p_i \cfrac{d^i}{dt^i}$ $Q = \sum_{i=0}^{N}q_i \cfrac{d^i}{dt^i}$ $p_i$ and $q_i$ are functions of time only. $K$ is a constant that ...
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0answers
15 views

Pressurizing a circular toroidal shell

Consider a toroidal elastic, isotropic, homogeneous shell with a circular cross-section that is initially not pressurized. Under an internal pressure $p$, the shell might become more straight, but the ...
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0answers
22 views

Tensile strain and extension in wires of different lengths [duplicate]

If we apply a equal force (f) to two ends of two wires (made out of same material) length 'l' and '2l', will the extension be equal ? Since force is directly propotional to the extension, will the two ...
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1answer
54 views

Why a balloon explodes by itself? [duplicate]

I was wondering why a balloon explodes after some time by itself with no specific reason. yesterday I was doing my chores and to my amazement the balloon far in the corner of house pop with no obvious ...
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0answers
29 views

Space/time elasticity and state changing

What happens to a particular section of space/time that has been bent due to a large gravitational force that has passed it by? Does it "snap back" to it's original state. Is it permanently bent? Is ...
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0answers
20 views

Energy losses of a ball, hitting the ground due to elastic and accelerating processes

There is a question about gravitational force and irreversibility. In my answer I pointed towards the phenomenon of photon emission during accelerations and by this of energy loss. My last sentence ...
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0answers
16 views

What is our most complete microscopic theory for the elastic-plastic transition point?

I suppose its all stated in the title. What is our most successful description of the microscopic behavior of material at the elastic-plastic transition point. My condensed matter physics prof was ...
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1answer
48 views

Predicting contact time and COR (coeff of restitution) for a cricket ball and pitch

For real world application, COR --> Bounce produced by pitch, for both spinners & seamers; Contact time --> grip provided by pitch, mainly for spinners Assuming cricket ball to be a sphere and ...
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0answers
36 views

Do stress and strain contradict each other?

According to the book Engineering Physics by R.K Gaur and S.L Gupta Strain: Strain is a fractional deformation produced in the body when it is subjected to set of deforming forces. Stress: The ...
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1answer
25 views

Biot coefficient as function of porosity

Can the Biot poroelasticity coefficient $\alpha$ be approximated as a function solely of porosity $\phi$, and if so then how (and under what conditions)? I've read (e.g. 2.02-3 here) that it can, ...
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2answers
38 views

Realtion of acceleration and deformation [duplicate]

What will happen if I apply 10N force to a body's one end and 11N to it's others end? Which force will accelerate it, which force will deform it? Why?
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35 views

Why don't we consider net force while calculating elongation in an object?

I have been studying elasticity in mechanics . Most of my books while solving problems where we have to calculate the elongation in an object due to an external force don't take into account the net ...
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1answer
83 views

Ball suspended on elastic string (finding tension)

A ball (of mass $m$) is suspended by an elastic string. It accelerates upwards with an acceleration $a$. Find the tension in the string. Taking upwards as positive, we have $$T - mg = ma \iff T = ...
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100 views

Formulae for Elastic Hysteresis of rubber

Being a school student, I'm pretty sure we don't need to explicitly learn any formulae helping us evaluate the energy dissipated by mechanical internal energy in a hysteresis loop. But I was wondering ...
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1answer
61 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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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
47 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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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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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 ...