# 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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### 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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### Does water have shear thinning property? [closed]

I'm working on a project and I need to know if the water is viscoelastic? does water have shear thinning property?
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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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### Pressure vessel analysis of transversely isotropic multilayer material

Suppose I have a transversely isotropic, hyperelastic material with known strain energy that is a fibrous composite. I am interested in an explicit formula for the displacements (so I can get the ...
33 views

### How to predict a flight distance? [closed]

I conducted an experiment by varying the stretch length of a rubber band (angle is always constant) which resulted in different flight distance. My teacher told me to find an equation/law to explain ...
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### 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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### 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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### 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 holeâ€”always. Why does it start there and not anywhere else along ...
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### 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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### shape formed by a stiff string with ends pinched together [closed]

Suppose I have a string of length $L$ with a bending energy given by $$E=\frac{1}{2}\epsilon \int_0^L ds\, (\mathbf{R}''(s))^2$$ Let's say I form a bight with it by pinching the ends together, ...
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### Different ways to calculate the bulk modulus

I am trying to calculate the bulk modulus of unit cells of materials with trigonal or monoclinic structure using two different methods: -The first one is by fitting the changes of volume and energy ...
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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 ...
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### 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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### 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 ...
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### 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 ...
56 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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### 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 ...
72 views

### Infinite elastic half-space with point load (Mindlin's problem)

What is the equilibrium deformation of an infinite half-space (that is, an isotropic and homogeneous linearly-elastic three-dimensional medium, with a single planar surface) produced by a force which ...
31 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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### 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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### 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. ...
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### should transverse and longitudinal phonon velocities be equal for this mass spring system?

Let's say we have a cubic lattice of identical masses $m$, each connected to its 6 nearest neighbors by identical spring constants $k$. Essentially, the problem is I get an eigenvalue problem with ...
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### 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 ...
68 views

### Plastic deformation energy dissipation due to inelastic collision

I have been attempting to determine an analytical expression for the coefficient of restitution (or any similar collision parameter) for an inelastic collision. So far, I've looked at Hertzian contact ...
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### 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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### 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 ...
163 views

### What is the root cause of elasticity of a material?

I know that there exist some interatomic and intermolecular forces in the material but why does stretching a material will enhance attractive force over repulsive force and vice versa.
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### 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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### 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 ...
243 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 ($\delta = \frac{FL}{AE}$)...
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### 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 ...
114 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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### Role of rubber elasticity in the pressure inside a balloon [duplicate]

I'm just wondering if there's a pressure difference between the atmosphere and the air inside the balloon due to the rubber elasticity. A kind of analogous to the Laplace pressure in soap bubbles.
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### 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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### 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 ...
88 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 ...
36 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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### 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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### 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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### 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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### 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 force-...
155 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 ...
I'm doing a fitting of uniaxial compression data of a isotropic polymer using the Mooney-Rivlin model: $\sigma=\left( 2C_1 + \frac{2C_2}{\lambda} \right )\left( \lambda ^2- \frac{1}{\lambda } \right)$...