Questions tagged [stress-strain]

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186
votes
8answers
14k views

Why do we bend a book to keep it straight?

I noticed that I have been bending my book all along, when I was reading it with one hand. This also works for plane flexible sheets of any material. Illustration using an A4 sheet Without bending ...
70
votes
2answers
14k views

Why does dry spaghetti break into three pieces as opposed to only two?

You can try it with your own uncooked spaghetti if you want; it almost always breaks into three when you snap it. I am asking for a good physical theory on why this is along with evidence to back it ...
33
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3answers
8k views

Clarifying the actual definition of elasticity. Is steel really more elastic than rubber?

Yes, I know it's steel. It's everywhere on the web and I did google. But I seek enlightenment. My physics textbook defines elasticity as: Property by virtue of which a material regains its shape. ...
29
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3answers
29k views

Why is stress a tensor quantity?

Why is stress a tensor quantity? Why is pressure not a tensor? According to what I know pressure is an internal force whereas stress is external so how are both quantities not tensors? I am ...
22
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6answers
130k views

What is the difference between stress and pressure?

What is the difference between stress and pressure? Are there any intuitive examples that explain the difference between the two? How about an example of when pressure and stress are not equal?
21
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1answer
933 views

Why does a flat sheet roll back into a cylinder when having rolled it once?

For example, if you were to roll a piece of paper into the shape of a hollow cylinder and then try to return the paper to its original, flat shape, it would naturally roll to the cylinder when you let ...
18
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5answers
4k views

How is potential energy actually stored in a steel spring at the atomic level?

Elasticity is one the most intriguing phenomena, wiki gives a summary explanation of what happens in a steel spring: the atomic lattice changes size and shape when forces are applied (energy is ...
14
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3answers
103k views

Hollow Tube Stronger than Solid bar of same Outside Diameter (O.D.)?

I was listening to some co-workers talking about problems meeting stiffness requirements. Someone said that even with a solid metal rod (instead of the existing tube) we could not meet stiffness ...
14
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2answers
241 views

Dust patterns inside electronic product - what causes this? [duplicate]

(Note: another similar question from a few years ago yielded nought but speculation. I have at provided some detailed observations in the hope that the community can come up with something rigorous as ...
12
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3answers
852 views

Where does the use of tensors to describe orientation dependence of physical phenomena arise from?

In the context of anisotropy, I have often read that the use of a rank 2 tensor is "a model". But what is the idea behind this choice? Can anyone describe in what sense the use of tensor in this ...
12
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1answer
3k views

Why does plastic turn white in the area of stress?

There is a phenomenon with plastic in which it changes color to white in areas where stress is applied. When I bend a plastic rod the area in the centre, it turns white or loses colour. Why does this ...
11
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2answers
2k views

Tearing a piece paper along a crease

Why is it easier to tear paper along a crease? To word it differently: why does a "tear" progress along a crease, if one is present?
10
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7answers
1k views

What's the biggest cube you could have before gravity rounded it?

I took this question from Quora because it seems interesting and this community would have some fun with it. I would assume that one would use the modulus formulas for force to counteract the gravity, ...
9
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3answers
11k views

Why is the (non-relativistic) stress tensor linear and symmetric?

From Wikipedia: "[...] the stress vector $T$ across a surface will always be a linear function of the surface's normal vector $n$, the unit-length vector that is perpendicular to it. [...] The ...
8
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3answers
2k views

Origin of the major symmetry property of the elasticity tensor

In linear elasticity theory the stress tensor $\sigma$ is related to the strain tensor $\epsilon$ via the elastic tensor $C$. Specifically $$ \sigma_{ij} = C_{ijkl} \epsilon_{kl} $$ Because $\sigma$ ...
8
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2answers
6k views

How does the energy in a standing wave travel beyond a node?

In a standing wave, how does energy travel past a node? It should just get reflected. Assume the case of first overtone and you strike the string at a place. How will energy distribute itself? If it ...
7
votes
6answers
3k views

Can any body be uniform in the universe?

If I take any body in the shape of a rod and stretch that, after it reaches breaking stress it breaks at one point. Even though we apply the same the stress on each and every part of the rod it broke ...
7
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4answers
544 views

Why are stresses of continuum systems described via a tensor?

The tittle pretty much says enough. I have always been told so but no one really motivated it. So, I would like to know why do we use a tensor to describe the stresses in continuum mechanics.
7
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3answers
1k views

It would take an elephant, balanced on a pencil, to break through a sheet of graphene the thickness of Cling Film

I'm currently doing some work on a presentation about graphene, and have come across numerous articles which claim something along the lines of It would take an elephant, balanced on a pencil, to ...
7
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4answers
541 views

How wide does a wall of ice need to be to stay in place?

Let us say that we have unlimited manpower to construct a huge wall of water ice e.g. 200 m tall (700 feet). -and that the wall is placed in a climate, where the temperature never (for your purpose) ...
7
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2answers
377 views

Why are springs spiral-shaped? [duplicate]

I've had this question on my mind for quite a while and looking at the web, I couldn't find an answer to this question. I've had a lot of physics experiments involving springs, unintentionally ...
6
votes
4answers
6k views

Does zero strain always imply zero stress?

In solid mechanics, can I always assume that if an object undergoes no strain, then no stress is applied to it? I think it's true only because I can't seem to find a counter-example.
6
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2answers
68k views

Will a diamond break if I hit it with a hammer [closed]

I was having this discussion with my friend about the hardness of diamonds. I would like to know if a diamond will break or not if hit with a hammer. Different sources across the internet mention ...
6
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2answers
2k views

Are Rippled or Wavy Potato Chips Stronger?

I am buying some potato chips. I want to use dip. But half the time I do my chips in the dip, they break apart. Do wavy chips, with the wider bends have a greater strength? Or do the rippled chips, ...
6
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3answers
6k views

What causes stress concentration (aka stress risers/raisers) at corners?

I've read a few explanations about why stress concentration occurs at sharp corners but I don't find the explanations intuitive. Can anyone explain it perhaps using an analogy such as atoms "holding ...
6
votes
1answer
663 views

What is the stiffness of a crushed rod or cylinder?

If you are crushing a uniform rod between two plates with a known force, how do I estimate the deflection (and hence the stiffness) of the rod? I am interested in the overall deflection, including ...
6
votes
2answers
6k views

Why do chocolate bars usually break at the cleavages?

Why do chocolate bars usually break at the cleavages? The chocolate bar is less thick at cleavages. How can we relate thickness and fracture point of chocolate bar?
6
votes
1answer
4k views

Physical meaning of elastic constants of a monoclinic crystal

For the elasticity of a material, Hook's law can be written in tensorial form as: $$\sigma = \mathsf{C}\, \varepsilon$$ where $\sigma$ is the Cauchy stress tensor, $\varepsilon$ is the infinitesimal ...
6
votes
1answer
323 views

Why does a wetted cloth get structurally reinforced while paper doesn't?

In the Hollywood movie, Shanghai Knights (pardon me for the non scientific citation), Jackie Chan states that 'wet cloth' does not break easily. How true a fact is this ? We know from common ...
5
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3answers
1k views

Can we change the volume of a wire by applying force on it in order to stretch it, if yes is there any way to calculate it?

Can we change the volume of a wire by applying force on it in order to stretch it, if yes is there any way to calculate it ??
5
votes
2answers
794 views

What is the purpose of the Maxwell Stress Tensor?

In the calculation of the forces acting on a charge/current distribution, one arrives at the Maxwell stress tensor: $$\sigma_{ij}=\epsilon_0 E_iE_j + \frac{1}{\mu_0} B_iB_j -\frac{1}{2}\left(\...
5
votes
1answer
189 views

Second-order tensors as linear operators

A tensor is formally defined as an object whose components obey some transformation rules. I, however, find it more intuitive to look at (second-order) tensors as a linear operator/function between ...
5
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3answers
2k views

Is it possible that Cauchy stress be asymmetric?

According to conservation of linear momentum and angular momentum, one can derive that Cauchy stress tensor is symmetric and hence has only 6 independent components. Is it possible that, when breaking ...
5
votes
1answer
430 views

What happens when a piezo crystal is exposed to a vacuum?

Application of mechanical stress to a piezo crystal generates a charge. Quoting from wikipedia, a 1 cm3 cube of quartz with 2 kN (500 lbf) of correctly applied force can produce a voltage of 12500 V....
5
votes
1answer
378 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 ...
5
votes
1answer
6k views

Divergence of Cauchy Stress Tensor [closed]

On the wikipedia page for the Cauchy Momementum Equation, it's stated that the equation can be written as $$\rho \frac{D\,\textbf{v}}{D\,t} = \nabla \cdot \sigma + \textbf{f}$$ Where $\sigma$ is ...
5
votes
1answer
634 views

Does a thermally expanding torus experience internal stress?

I'm trying to learn continuum mechanics and thermo-mechanics. As we know, heating an object increases the mean atomic distance $a_0$ of the atoms in a rigid body. Let's assume it is a linear elastic ...
4
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2answers
350 views

Could somebody explain the stress versus strain curve?

I have already read: Stress- Strain curve but this does not answer my question completely. My problem is to understand the decrease of stress ($\sigma$) while the strain ($\epsilon$) is increasing, ...
4
votes
2answers
105 views

What is a coordinate-free formulation of deformation theory?

For example how are stress, strain and shear tensors described invariantly, without any coordinates, purely in a geometric manner? A formulation that avoids indices coordinates and matrices, even in ...
4
votes
2answers
443 views

What is strain? Why does DNA coil upon itself?

I have been reading Lehninger's Principles of Biochemistry to understand DNA supercoiling (pg-930). Supercoiling is the twisting of a DNA upon itself and this happens when the two helically wound ...
4
votes
3answers
877 views

Calculating stress without strain

I am working on an algorithm for a real-time simulation. I would like to calculate to extremely permissive tolerances approximate values for the stress within a 2D geometry. It will not be difficult ...
4
votes
3answers
2k views

Stress tensor in a cube with shear forces

I want to calculate stress matrix in a cube with two faces parallel to x axis and perpendicular to z axis (sorry I don't know how can I put a picture in this post). There are two force uniform ...
4
votes
1answer
117 views

Origin of antisymmetric $\ell=2$ irrep in direct product of two symmetric second-rank tensors

In the excerpt below from Chapter 18 Section 6 of the textbook Group Theory -- Application to the Physics of Condensed Matter by Dresselhaus, Dresselhaus, and Jorio, the irreducible representations of ...
4
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1answer
1k views

Stress calculations in a perforated paper

You have a sheet of paper (torn out of a good quality foolscap notebook) as shown above, and you start pulling it apart with both your hands (forces indicating by the blue arrows). Its difficult to ...
4
votes
1answer
11k views

What is the shear stress of a fluid?

One book defines the shear stress $\tau$ of a (Newtonian) fluid as $$\tau = \eta \frac{\partial v}{\partial r} $$ where $\eta$ is the viscosity. There is not much context, so I've made some guesses. ...
4
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2answers
718 views

Why does stress need to be described with a tensor?

I understand the idea that stress is basically force per unit area. So let's imagine a force on beam as follows: Notice how the force only occurs in one dimension. But when I look up stress, I ...
4
votes
5answers
9k views

What is the difference between traction and stress?

As far as I can tell, stress and traction seem to refer to similar ideas. According to Chapter 8 of Twiss and Moore's Structural Geology, traction is Force per unit area on a surface of a ...
4
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4answers
396 views

Elastic properties of materials at low temperature

It is common knowledge that materials are more brittle at low temperature. But does it apply also on elastic deformations or is it just matter of plastic deformations? Practically: Is it possible to ...
4
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1answer
1k views

Hookes law and objective stress rates

Often, in papers presenting updated Lagrangian simulation methods for solid dynamics, the following procedure for updating the (Cauchy) stress tensor is presented: First, the Cauchy stress tensor is ...
4
votes
2answers
816 views

First-principles derivation of cutting force

I know that the amount of force required to separate a material from itself is linked to the surface energy of that material. However, looking at just the surface energy laughably underestimates the ...

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