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2
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1answer
279 views

Is there symmetry in 2d stress tensor in linear elastic fracture mechanics?

Assumptions: Cross terms in strain tensor are defined as equal $\varepsilon_{xy} = \varepsilon_{yx}$. pure mode I crack. Far from crack tip, material is purely elastic and we are way below yield ...
2
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0answers
69 views

Heads, Tails… Edge?

No Nobel prizes at stake, but just an idle thought and an idle question. How could one calculate the probability of a flipped coin landing stable on its edge, instead of heads or tails? I assume ...
2
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0answers
39 views

Positivity of Bulk modulus and shear modulus in isotropic materials

I have been searching through many resources, but could not find a proper thermodynamic reasoning for why bulk and shear moduli for isotropic materials should be positive. Some resources like eFunda ...
2
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0answers
14 views

Main differences between elastodynamic and light scattering when using S-matrix to find bound states

What are the main differences (top 5 if question is too broad), for using the S-matrix to find bound states, between elastodynamic and light scattering? (if it facilitates a higher quality ...
2
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0answers
60 views

If I roll an elastic plate into a cylinder, does it shrink?

Suppose I start with a rectangular elastic (to keep things simple, zero Poisson's ratio) sheet of length $2\pi R$, thickness $h$, and (immaterial) width $W$. I roll it up into a cylinder of radius ...
2
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1answer
269 views

Swords, impacts and elasticity for a noob

So I'm a game developer and I'm trying to understand some (extremely) basic facts of impact mechanics. I had read something entitled Dynamics of Hand-Held Impact Weapons, but it was a bit too ...
2
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0answers
205 views

Displacement due to sinusoidal load on a finite strip in an infinite plane

From a paper on tunnel design I've been reading: (http://www.sciencedirect.com/science/article/pii/0886779887900113) In the present application, the solu- tion corresponding to a sinusoidal load ...
1
vote
2answers
920 views

At what point does a projectile leave a slingshot?

Assuming a frictionless / "perfect" environment, and given a ball held in an elastic sling (like a hand-held catapult) where the pocket is lighter than the projectile itself, what is the point at ...
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1answer
56 views

Is shear modulus only applicable to cubical solids?

Do we have any real life/theoretical examples where shear modulus is applicable to non-cubical shapes?
1
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1answer
49 views

Deformation of the cylinder

There is given a cylinder with fixed side surface. On one base is being rendered constant pressure $p$, so cylinder cambers I'm trying to calculate the form of cambering. The problem is that height ...
1
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1answer
120 views

Why elastic materials are discribed by tensors?

I am starting to read about elasticity of thin surfaces and I don't understand why tensors play such a major part? What are the tensors describing about the material? And just to clarify - Is there ...
1
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1answer
476 views

Semi-conductor band-gap and deformation potential

Submitting a semi-conductor to stress leads to a deformation in the energy-bands, roughly described by:$$H_{ij} = {\cal{D}}_{ij}^{\alpha\beta}\;\epsilon_{\alpha\beta}$$ $\epsilon$ being the strain ...
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4answers
547 views

Generic Born stability criteria

The tensorial form of Hooke's law for the strain-stress relationship in a crystal is (in the Voigt notation): where $\sigma$ is the strain, $\epsilon$ is the stress and C is the stiffness tensor: ...
1
vote
1answer
228 views

Modeling linear spring deformation in time

Suppose I had a spring (at equilibrium) and applied a certain force $F$, causing it to undergo elastic deformation. I know that by applying this specific force, hooke's law tells me that the spring ...
1
vote
1answer
540 views

Modulus of Elasticity

Consider a cube of unit dimensions. Let $\alpha$ and $\beta$ be the lateral and longitudinal strains. The expressions for moduli of elasticity on applying unit tension - 1) At one edge: Young's ...
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2answers
4k views

Why does a ball bounce?

If an object is acted on by equal and opposite forces then it will be in equilibrium, and it's acceleration or velocity (and so direction as well) will not be changed. So when a ball bounces, it ...
1
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1answer
127 views

Confusion in Euler-Bernoulli beam theory

Euler-Bernoulli beam equation is given by $$ EI \frac{\mathrm d^2 u}{\mathrm d x^2} = M'(x) \\ EI \frac{\mathrm d u}{\mathrm d x} = xM'(x) + C_1 $$ Where, $E$ is modulus, $I$ is second moment of ...
1
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1answer
77 views

Where does elastic energy come from?

I vaguely remember reading that the elastic potential energy of a spring, $\frac{1}{2} k x^2$ comes from mass which is turned into energy according to the law $E=mc^2$. I also remember hearing that ...
1
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1answer
99 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
1
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1answer
129 views

Coordinate-free derivation of the Lamé-Navier's elasticity equations

Linear static elasticity provides a local equation $-\mathrm{div}\sigma=f$, the constitutive law $\sigma=2\mu\epsilon+\lambda \mathrm{tr}(\epsilon)I$ as well as the strain-displacement relationship ...
1
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1answer
92 views

Modeling elastic moduli as a continuous function in space for a single solid material

I've read a number of solid mechanics papers where a single material is modeled with constant elastic moduli (lame parameters $\lambda$, $\mu$). I've also seen composite materials modeled with ...
1
vote
1answer
256 views

Modellng mechanical behavior of heat shrink film

Consider a heat shrink film (as used in shrink sleeves that decorate plastic or glass bottles). These materials are produced by blow extrusion. When the film is heated (hot steam, hot air or ...
1
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3answers
437 views

2d soft body physics mathematics [duplicate]

Possible Duplicates: Modern references for continuum mechanics Good books on elasticity The definition of rigid body in Box2d is A chunk of matter that is so strong that the distance ...
1
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1answer
135 views

Current Physical Applications of Elastic Fractals

Are there any known uses of modeling with elastic fractals in current physical applications? (Especially uses concerning with self-similarity)
1
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1answer
452 views

Lagrangian density of linear elastic solid

I need the general expression for the lagrangian density of a linear elastic solid. I haven't been able to find this anywhere. Thanks.
1
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0answers
47 views

Proof that a traceless strain tensor is pure shear deformation

How can i proove that the traceless part of linear strain tensor $e$ in the Euler description: $$e_{i,j}={ 1 \over 2 } \left({ \partial u_i \over \partial x_j}+{ \partial u_j \over \partial x_i} ...
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0answers
36 views

Deriving general boundary conditions from first principles for elastodynamic scattering

It seems that most of the relevant books only give the linear case and the rest say something along the lines of "here are common examples of boundary conditions." What are the most general boundary ...
1
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0answers
23 views

LOCAL Temperature Gradient and Stress

I'm investigating the thermo-migration failure mechanism in nanoscale ICs interconnects. Typically, a nano wire under thermal stress suffers from material/mass migration or void nucleation if it ...
1
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0answers
25 views

How much will a round tube deflect under load? [closed]

I'm trying to determine the materials I need to complete a hobby project, and I'm having trouble estimating how much flex a given steel tube would have under different configurations/loads. My setup ...
1
vote
1answer
129 views

Degree of anisotropy of crystal tensors

Does there exist a scalar that can describe how anisotropic the elasticity of a crystal is? What about other tensors such as the permittivity or susceptibility? I found a Wikipedia article that was ...
1
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0answers
34 views

Example of materials with 21 independant coefficients in linear elasticity?

By definition of linear elasticity, the strain et stress tensors are related: \begin{equation} \boldsymbol{\sigma}=\mathbf{C}:\boldsymbol{\varepsilon} \end{equation} and because of minor and major ...
1
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0answers
102 views

Double dot product in Cylindrical polar coordinates - Strain Energy

I'm working with a problem in linear elasticity, and I have to calculate the strain energy function as follows: $$2W=σ_{ij}ε_{ij}$$ Where σ and ε are symmetric rank 2 tensors. For cartesian ...
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0answers
55 views

Energy of a system

I'm considering a ring of mass $m$ sliding along a cardioid with equation $r=a(1+\cos\theta)$. We let the angle between the downward vertical and the radius vector be $\theta$. The ring is attached to ...
1
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0answers
68 views

Finding Tension in an Elastic String?

I know that this is a homework type question and I'm not asking a particular physics question, but I'm really desperate for help. Here's the question: I tried to divide the string to 2 parts with ...
1
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0answers
560 views

What is the relationship between Elasticity and Compliance?

Compliance is like elasticity of hollow tube. Elasticity is less for instance for arteries so they are less compliant. There seems to some sort of relationship between compliance and elasticity. ...
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0answers
141 views

Entropic force in polymers

According to my textbook, the elastic force in a rubber is caused to the tendency of the polymers to return to their initial disordered state of higher entropy. But isn't this looking at entropy on ...
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0answers
1k views

Materials with Zero Poisson Ratio

Poisson's ratio is defined as negative ratio between transverse and axial strain. So, a material with zero poisson ratio must necessarily exhibit no transverse strain. After checking the wikipedia, ...
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vote
0answers
247 views

Explain the Föppl–von Kármán equations

I am a newbe to elasticity. Could someone please explain to me briefly how the Föppl–von Kármán equations work? What are we trying to solve for? Is there some kind of intuition to the way they look? ...
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0answers
36 views

How do I find the force from drop shock using material properties?

I am dropping a cylindrical cast iron bar with a know elastic modulus and poisson's ratio, $E_{1}$ and $v_{1}$, onto a flat beam of elastic modulus, $E_{2}$ and $v_{2}$ so there is tangential drop ...
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0answers
133 views

Decomposition of elastic constants of a crystalline material

I have performed a calculation the tensor of elastic constants (or stiffness tensor) for a given crystalline material. From there, I calculated various elastic properties, such as Young’s modulus, ...
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0answers
316 views

Slackline Jump Tension

So a slackline is basically a bouncy tight rope. I found a site that has a calculator for the tension of a static slackline ...
1
vote
0answers
112 views

Is there analysis library for stress-strain data?

I have three column data that has time-displacement-force from 1D tensile/compression test. Now I would like to get the standard mechanical properties of the material, like Young modulus, yield ...
1
vote
0answers
115 views

Physics for taffy pulling?

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 ...
0
votes
4answers
984 views

Hooke's law limitation question

Let's consider a spring. I am a strong man(well, lets assume) and I am pulling the spring. the work I do is being stored in the spring in the form of its elastic potential energy. Then suddenly, ...
0
votes
1answer
63 views

Will a tug-of-war battle damage my climbing rope

I plan to organize a big tug-of-war with a climbing rope (70m long) with 50-60 adults. I know the climbing rope is elastic. The rope resistance is 9 kN when a chock occurs. Will the rope breaks or ...
0
votes
3answers
70 views

What is the net force experienced (at the lowest point) by a wire being rotated in a vertical circle with a mass 'm' at its free end?

A metallic wire is being rotated in a vertical circle with a mass $m$ fastened to its end. My understanding says that the net force experienced by this mass should be the centripetal force: $T - mg ...
0
votes
1answer
76 views

How must you spin the ball to make it alternate between 2 positions? [closed]

Assume any parameters you may need. Thanks in advance.
0
votes
2answers
54 views

Why don't we consider both the forces while calculating the magnitude of stress in an elastic body?

Consider a wire being stretched from two ends with equal forces. We know that both of these forces collectively participate in elongating the wire; had there been one force the wire would have ...
0
votes
2answers
84 views

Why only vertical component of the stress tensor on vertically suspended bar?

EDIT: I am gonna rephrase the question entirely. Imagine we have a bar which we will analyze in the linear elastic regime. The shape of the cross section is irrelevant. The bar is suspended from a ...
0
votes
2answers
139 views

When a wire is stretched by a load, is there any change in its volume? [closed]

When a wire, or a rod(whose diameter is not negligible) is subjected to a tensile stress, is there any change in its volume? If yes, does the volume increase or decrease? Take into consideration both ...