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
32 views

Why does a ball eventually stop?

I was wondering, if the force of friction with the ground does not make any work on the ball and just give it the necessary torque to rotate (hence the consideration of static friction coefficient in ...
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2answers
41 views

Difference between stiffness and damping?

I understand stiffness as the extent to which an object (e.g. a mass spring) resists deformation from an applied force, or the rigidity of an object. And I understand damping as the energy ...
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1answer
193 views

What equation predicts at what point a stretched object comes apart?

I am creating a simulation and am interested in pulling stretchy things and when they break, like taffy. I imagine this is a bit tougher then a simple equation like gravity, but I have no idea. Is ...
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2answers
467 views

Determining flexural modulus by performing 3 point bending test using hollow cylindrical tube

I would like to decide the flexural modulus of the material of plastic tube by performing 3 point bending test according to the ASTM D 790 procedure. In ASTM D 790, the form of the specimen is ...
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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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1answer
13 views

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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0answers
32 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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0answers
11 views

Define the term energy density of a body under strain [closed]

How to define energy density of a body in terms of strain? This was my past exam question. But I am unable to solve it.
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1answer
12 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
14 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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1answer
35 views

How to reduce size of bracelets using physics?

My mom has a set of bangles (bracelets) made of gold like the ones shown in the picture. Problem is the size (diameter) of these bangles is a bit more than required. If she goes to a goldsmith he cuts ...
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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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2answers
64 views

Why is the restoring force directly proportional to extension?

When deforming any spring the deforming force is always greater than the restoring force until equilibrium is reached. So, if a constant deforming force caused an extension in any spring the restoring ...
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1answer
18 views

Rubber band elongates like s-curve

A normal rubber band (brownish yellow) with about 1 mm^2 cross section and approximate slack length of 170 mm is suspended vertically and gradually loaded with a number of weights (each weighing 9.36 ...
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0answers
14 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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1answer
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 ...
3
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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
29 views

Why is the Elastic Modulus of concrete smaller than that of steel?

I am trying to get a basic feel for what the Modulus of Elasticity means for different materials. My understanding is that since E = stress / strain, a higher E ...
1
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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 ...
0
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1answer
50 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 ...
0
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0answers
21 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 ...
0
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1answer
31 views

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?
2
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0answers
52 views

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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1answer
44 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 ...
1
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0answers
21 views

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 ...
1
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0answers
31 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 ...
1
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4answers
481 views

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 ...
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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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3answers
35 views

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?
2
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0answers
13 views

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 hole—always. Why does it start there and not anywhere else along ...
0
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0answers
18 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 ...
3
votes
2answers
64 views

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, ...
4
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1answer
2k views

Good books on elasticity

Can someone suggest good books/textbooks/treatises/etc on elasticity?
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0answers
35 views

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 ...
0
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1answer
40 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 ...
1
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1answer
25 views

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 ...
1
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2answers
37 views

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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0answers
15 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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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
20 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, ...
1
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1answer
30 views

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 ...
1
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1answer
43 views

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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0answers
23 views

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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0answers
21 views

The amount of force needed to bend and break a magnesium cylinder? [closed]

I want to determine how much force in Newtons will be need to bend a solid cylinder of magnesium. The cylinder is (x) cm in diameter, and it is (l) cm long. The density of normal magnesium alloy is ...
0
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1answer
23 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 ...
1
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2answers
206 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 = ...
4
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2answers
115 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.
1
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0answers
42 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 ...
0
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2answers
37 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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0answers
33 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 ...