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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Understanding stress-relaxation for viscoelastic materials

I'm studying a viscoelastic material with a cylindrical geometry and I read that for fixed strain(i.e. fixed elongation), I should observe decreasing strain over time. Given that stress $= F/A_0$ ...
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1answer
29 views

Understanding stress-strain calculations

I'm trying to compute the stress-strain curve for an elastic material with cylindrical geometry subject to an increasing uniaxial load. I understand that this requires: stress = $F/A_0$ where $A_0$, ...
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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
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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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 ...
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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
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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1answer
24 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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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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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 ...
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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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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 ...
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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
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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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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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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2answers
71 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
84 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
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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
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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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1answer
28 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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2answers
102 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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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 ...
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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 ...
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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 ...
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1answer
41 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 ...
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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 ...
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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 ...
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0answers
30 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
45 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?
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0answers
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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 hole—always. Why does it start there and not anywhere else along ...
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0answers
25 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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2answers
65 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, ...
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0answers
40 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 ...
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1answer
26 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 ...
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2answers
43 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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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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0answers
17 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
54 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
38 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 ...