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Questions tagged [elasticity]

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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Change in Volume of Objects on applying stress

I came across a statement that whenever any stretching or compressing is done on any object, its change in volume is always greater than $0$. This means that density always decreases (mass remaining ...
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1answer
23 views

Description of the stress in an elastic ring

How can one describe in terms of elasticity the stress necessary to stretch an elastic ring of Young Modulus $E$ and rest radius $R_0$, and width $d$ ? My guess is that in the linear regime, the ...
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Elasticity of an object [closed]

I was studying elasticity, and I thought of certain questions that I couldn't find an answer to. I'll will try to explain my queries If in the elastic limit, the strain on say a rectangular block of ...
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31 views

How to determine two elastic tensors are similar?

A elastic tensor is a 3*3 symmetric matrix that determines some material property. I have a elastic tensor A and I want to find the most similar elastic tensor B from a collection of elastic tensors {...
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26 views

Thermo-elastic material & hydrostatic stress

Thermoelastic constitutive equation for linear elastic isotropic material can be written as described in section 3.7, pp 67 (Constitutive Equations, MIT 16.20 Structural Mechanics course). $$\sigma_{...
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1answer
51 views

Why is the law of Hooke valid only for small displacements?

What changes when displacement exceeds a certain limit?
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Springs with some finite mass

Let us consider a spring which is having some finite mass. By the help of some external agent the spring has been extended by some distance $x$. Will the restoring force produced in the spring still ...
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2answers
43 views

Where does the half of Potential energy go? [duplicate]

We have the formula for elastic energy stored in a spring to be 1/2*Force*extension. When we have an object on a vertical spring, then the energy gained should be 1/2*mgh.(h is extension produced) ...
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27 views

Why bulk modulus of air is initial pressure?

So in the definition of bulk modulus the strain part is defined as (∆v/v) where ∆v is change in volume and v is the initial volume and while driving it for air we use the ideal gas law PV= constant ...
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28 views

How to model this problem as a boundary value problem of PDE system [migrated]

I am trying to solve this system of elasticity partial differential equations in 2D in cylindrical coordinates, where the model is axysimmetric, around the $z$ axis. $$\frac{1}{r} \frac{\partial (r\...
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1answer
38 views

How does tension work for a simple pendulum? What force is at play to keep a rigid body from stretching?

Here recently I have been working on programming a physics framework for simulations, but I've ran into a problem... I was testing forces, so I created a simple pendulum like in the photo, and I ...
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2answers
38 views

Spring Constant from a Non-Linear Force-Extension Graph

If you have a linear force-extension graph for say a spring then the spring constant is simply the gradient of the graph. However, how would you calculate the spring constant at a particular point on ...
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What does “substantial changes” in material properties mean in geometric optics?

We know that (I read it from Kip Throne's Modern Classic Physics) if a wave's wavelength is smaller than the length scale over which "substantial changes" of material properties occur, then the wave ...
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24 views

Doubts in understanding the elastic property of matter

Here the graph of potential energy and force produced due to interaction between two atoms are given . And at a particular separation between the atoms, they have their minimum potential energy. And ...
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1answer
33 views

Doubt in the derivation of the relation between Young's modulus and Modulus of rigidity

Please refer to the image attached. My doubt is marked in red. What i don't understand in this part of the derivation is that how and why is the extension and compression is equivalent to a shear ...
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2answers
39 views

Why is the mechanical energy lost whenever an object undergoes plastic deformation?

I have read here that "Mechanical energy is lost whenever an object undergoes plastic deformation." Why is that? I mean the object would be changing its shape, and while it's changing its shape it ...
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1answer
57 views

How can you use tensors in theory of elasticity? [closed]

I am interested in physics and Icame across the usage of tensors in elasticity. How do you do that? How can tensors be useful?
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1answer
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Elastic collision between a circle and a point [duplicate]

In a 2D environment, I have a circle with velocity v, a stationary point (infinite mass), and I am trying to calculate the velocity of the circle after a perfectly elastic collision with the point. ...
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1answer
31 views

Calculating velocities of 2 squares after collision

If I have 2 squares each with random velocities, and both with the same mass, would it be possible to calculate their velocities after a collision, and how would I do so?
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1answer
59 views

Which formula for elastic collision?

When researching a bit about elastic collisions, I've been confused about how many different ways there are to do this. I've seen multiple methods, some of which are extremely complex (using sine and ...
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2answers
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Why does a metal block make a shrill sound but not a wooden block upon hammering?

When hammered, a metal block makes a shrill sound but not a wooden block of identical shape. Is it that the wooden block vibrates with lesser frequency than the metal block? If so, why is that? Also ...
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2answers
44 views

Yi's Bell sound and how it relates to temperature?

Yi's Bell is an ancient chinese musical instrument that plays different sound frequencies when its heated than when its in room temperature. My question is Why does that happen? Why does higher body ...
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2answers
46 views

The relation between the spring constant and its radius [duplicate]

I've observed that the spring constant of a spring with a smaller radius is higher than that of a spring with a larger even though they are made of the same material , their thickness and all other ...
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0answers
43 views

My Elasticity Doubt

I had a question on elasticity which looked something like this. {: .center} We have small beads of mass say $m$ and Mass of rod say $M$. Now we need to find the extension in the rod after the beads ...
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1answer
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What are inelastic elastic-bands?

In the third episode of Julius Sumner Miller's physics series he sets up an experiment with two masses connected by an array of elastic-bands. He comments that the elastic-bands are inelastic. ...
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1answer
43 views

Continuum limit for a bulk of discrete masses coupled by springs

I have a question that has been bothering me for a long time. I know very well how to take the continuum limit for a chain of masses connected by springs. But in my recent project I would like to ...
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3answers
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Hooke's full unapproximated law

It is known that the Hooke's law relating the restoring force of a spring to the distance of retraction from the equilibrium position, is only an approximation. That is, the equation $F=-kx$ is only ...
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1answer
58 views

Why is the partial derivative of strain energy function with respect to strain equal to stress

In Elasticity, we have a strain energy function , $W$, that is a function of strain tensor, $E$. Then the cauchy stress tensor, $T$ can be determined by: $$T_{ij}=\frac{\partial W}{\partial E_{ij}} \...
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Confusion Regarding Hookes law

I am used to seeing Hookes law in the form: $F = kx$ but in another one of my books it gives the equation: $\\ F = \frac{\lambda x}{l}$ where $l$ is the unstretched length, $x$ is the extension and $\...
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4answers
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Stress in a rod clamped between two rigid walls when the temperature is increased

The usual approach to calculate stress is to equate thermal expansion in the unclamped condition to the magnitude of contraction caused by strain produced due to the walls. I have some questions about ...
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0answers
128 views

Elongation of rod in two cases

Case 1: Suppose there is a rod hung vertically from the ceiling. It experiences gravitational force W (its weight).It's Young's Modulus is $Y$. Now I know that the end connected to the ceiling ...
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0answers
25 views

Deformation of a circle ring under tensile force

How will it deform when I apply a tensile force to a circle ring? Can I estimate the force applied on the ring by knowing the major and minor axis of the deformation elliptic ring? For simplicity we ...
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0answers
18 views

How is elastic hysteresis effected by time?

Here's how I understand the phenomenon: let's take the example of weights and rubber band, when a weight is put it does work on the band to stretch it, and heats it up, some of the heat gets ...
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1answer
52 views

When can viscosity be ignored?

I am working on understanding the motion of a solid ball in an infinite elastic (or possibly viscoelastic) medium when subjected to a sinusoidal driving force. The frequency-dependent complex wave ...
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29 views

2D Linear Elastostatics with Displacement Boundary Conditions

I am new to this type of problem and feel as if I am going in circle with regards to boundary conditions. I am interested in finding an analytic solution for: $\mu\nabla^{2}\underline{u}+(\lambda+\mu)...
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How are fluid membranes stretchable?

The Poisson's ratio of fluid lipid membranes is exactly $\nu=0.5$, because fluids can flow. As answered in this question, under the assumption of a finite bulk modulus $K$, this is the value of $\nu$ ...
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Derive Porosity from Stiffness Value

I have the Young's modulus (stiffness) values of a hydro-gel scaffolds, and I need to know the porosity of those scaffolds. I read about Nielsen Equation, which is this: $$ E = \frac{E_0 (1 - P) ^ 2}...
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Surface formed by a heavy elastic material hung from a circular rim

The solution to the problem of a string hung from two points in a uniform gravitational field is well known, its solution is the catenary. A solution can also be found for the problem of a spring of ...
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Work done in circular expansion of a rubberband or an elastic wire

What will be the work done in radially stretching a rubberband it can't be zero as there is potential energy being stored in it All I came up with it that there would be increase in overall length so ...
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2answers
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How does temperature affect the elasticity and spring constant of a rubber band

Rubber bands expand when chilled and contract when heated (no stretching, just when heated/chilled and at rest) to my knowledge. Why are hot rubber bands able to be stretched longer than cold rubber ...
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1answer
123 views

What causes the wave velocity of longitudinal waves in a spring to changes as its length changes?

This video shows the velocity of longitudinal waves changing in a slinky spring as its length changes: https://youtu.be/y7qS6SyyrFU?t=17 Something else responsible for the change in velocity ...
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2answers
132 views

Elastic potential energy and springs

The formula for elastic potential energy(for a spring) has been derived by assuming the following things: 1.Work done by a deforming force on a spring from a relaxed state (state where spring is not ...
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0answers
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Kelvin solid and deformation in transverse direction with Poisson ratio

A Kelvin-Voigt material is a material with such a behavior : I'm wondering if there is a way to model in a similar way the deformation in the transverse directions $y$. Meaning we have for the ...
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1answer
34 views

Statics and dynamics in elasticity : how to add time in elasticity

In elasticity, there is are static relations of the form $R(\sigma,\epsilon)=0$. In fluid dynamics, there is a dynamics relation with the conservation of momentum leading to Navier-Stokes equation. ...
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impossible Poisson's ratio of Lennard-Jones potential type solid (cubic cristal for example), or any potential depending on $r$

We know (for instance : https://en.wikipedia.org/wiki/Poisson%27s_ratio ) that the Poisson ratio is $\nu=1/2-Y/(6B)$, with $Y$ the Young modulus and $B$ the bulk modulus. Let's assume we have a ...
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1answer
59 views

How can Young modulus depend on the geometry of the item & Lennard Jones (question related to an older one)

In the question Young's modulus and geometry of test material, the answer was that it cannot play any role. Nonetheless, for the Lennard-Jones solid, in many places the Young modulus is given as : ...
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1answer
55 views

Relation between strain and velocity

The strain tensor writes $\epsilon_{ij}=\frac{1}{2}\Big(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_i}{\partial x_j}\Big)$ with $u_i$ the displacement in the $i$ direction. Then $\frac{\...
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3answers
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Elongation of rod [closed]

If a force is applied on a unconstrained body lying on a smooth floor ,will it elongate? My thoughts-as force is applied on body ,it moves with some acceleration,but as it is not constrained it will ...
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2answers
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Pressure on a compressible solid, dynamics of the relaxation

I have a sphere made of a solid of bulk compressibility B, and of volumic mass $\rho_0$. The pressure around that sphere is $P_0$. At time $t=0$, we apply a pressure on the sphere $P=P_0+\Delta P$. ...
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1answer
15 views

determine the shear stress and bending moment of the next axis

I have problems to raise the equations. They could recommend me a text to be able to solve it.