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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1answer
17 views

Modeling rubber foams

Are there any good papers/texts on the subject of modeling the dynamics of rubber foams? So far I haven't found any good papers/texts that cover this particular subject and I've done some searching. ...
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1answer
107 views

Mathematical expression of energy storage

I'm trying to develop an idea which is as follows. Put simply, imagine a flat sheet of material which, when distorted (I.e. curved in the third dimension) stores energy. Now, by calculating the ...
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1answer
30 views

Studying dynamic elasticity for finite deformations

this is not a question asking for help with a problem but one asking for help where to begin serious study of elasticity, particularly that applied to dynamic systems. Most textbooks about elasticity ...
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11answers
12k views

Why is filling a balloon from your mouth much harder initially?

Why is it that when you first fill up a balloon, it's hard to get air through, but after inflating it a bit, it becomes much easier to further inflate the balloon?
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0answers
36 views

Give a strain state which describes a purely spatial change of volume [closed]

In a problem, I am asked to provide a strain state (strain tensor) that describes a "purely spatial change of volume". I am unable to understand what is meant by this. Does it mean that there is ...
2
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2answers
295 views

Relationship of the volume of a plumbing system to pressure

How does the volume of water a plumbing system holds vary with water pressure? I know the ratio would include the modulus of elasticity of the plumbing material, the total surface area of the plumbing ...
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1answer
367 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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1answer
46 views

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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1answer
33 views

“Poynting vector” for transverse waves in elastic solid

What is the expression or name for the vector that gives the direction and intensity associated with the energy flux or momentum flux carried by transverse waves in an elastic solid?
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0answers
32 views

derivation of elastic moduli in terms of compliance tensor, and reference textbook

I recently learned that the elastic modulus, namely Young's modulus and shear modulus can be written as in terms of compliance tensor, or elastic constants. The equations for cubic system are $$ \...
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1answer
22 views

Does silicone rubber have a fundamental frequency?

I'm wondering whether impulse excitation techniques may be used to derive the Young's Modulus and Poisson Ratio of Silicone rubber.
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0answers
14 views

Linear elasticity: can “extremal” strain tensors be in the interior of the body?

i am new to elastic theory. I have a question about linear elasticity. In each point $p$ of a body $\Omega$, the strain tensor has three eigenvalues $\lambda_1(p)\geq \lambda_2(p)\geq \lambda_3(p)$. ...
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0answers
28 views

minimum bend radius

How can we calculate the minimum bend radius of a annular cylindrical tube? Intuitively I guess that for two tubes having same wall thickness but different outer diameters, the larger diameter one ...
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1answer
37 views

About elongation produced in a body, when 2 forces of equal magnitude but opp. in direction are applied on a body

When 2 oppositely- directed forces are applied on the same body , they act at the body's center of mass(com). The vector sum of the forces thus becomes 0(zero). How do the forces then bring about ...
3
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1answer
197 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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0answers
11 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
26 views

Young's modulus and geometry of test material

When measuring Young's modulus in a material, does the geometry of the material actually matter? I have seen several references recommend that I use cylindrical pieces. But, wouldn't the tests work ...
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2answers
529 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 ...
0
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1answer
25 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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1answer
44 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 ...
1
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1answer
21 views

Hooke's Law in 3D and in plane stress problems

Using Lame's constants, the Hooke's law of isotropic materials in 3-dimensions can be written as: $$ \begin{aligned} \sigma_{ij}&=\lambda \varepsilon_{kk}\delta_{ij}+2\mu\varepsilon_{ij}=c_{ijk\...
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2answers
34 views

Illustrating the definition of Young's modulus from spring factor

The relationship between Young's modulus $E$ and the spring factor $k$ from Hooke's law is $k=\frac{E A}{L_0}$ where $L_0$ is the initial length of the stretched material and $A$ the cross-...
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2answers
145 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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2answers
46 views

Speed of Sound in matter

So basically when it comes to the speed of sound, it is said that speed of sound in media is based on two main factors - 1)elasticity and 2)density from the formula V= $\sqrt{E/\rho }$ where E is ...
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2answers
562 views

Range of poissons ratio

I know the range of poisson's ratio is -1 to 0.5 but how do you arrive at this expression? I am a 11th grade student and I am not too familiar with advanced physics
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1answer
297 views

A moving brush on a vibrating surface

Hi group, I am a HS student in China preparing for a regional Young Physicist Tournament even. We are very puzzled about why would there be such movement. We would be grateful to see any inspiring ...
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2answers
69 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
82 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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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
17 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
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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0answers
14 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.
0
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1answer
16 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: \begin{...
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0answers
17 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
45 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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2answers
100 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
27 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
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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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 ...
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0answers
37 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
53 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
59 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
23 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
39 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?
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0answers
75 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 ...
1
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1answer
66 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
29 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
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 ...