Questions tagged [stress-strain]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
9
votes
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 ...
29
votes
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 ...
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 ...
10
votes
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, ...
18
votes
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 ...
7
votes
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) ...
22
votes
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?
2
votes
3answers
1k views

Potential energy of an infinitesimal length of elastic rod

I am having an embarrassingly hard time with the derivation for the potential energy of an infinitesimal element of an elastic rod of area $A$. The picture shown below is an element of the rod that ...
3
votes
1answer
770 views

Showing symmetry of the stress tensor by applying divergence theorem to $\int\int_{\delta V(t)} \vec{x}\times \vec{t} dS$ [duplicate]

I'm currently working through the symmetry of the stress tensor, in relation to viscous flow. I am looking at this by examining the conservation of angular momentum equation for a material volume $V(t)...
0
votes
2answers
5k views

What factors affect the Young's modulus of elasticity?

Is Young's modulus of a material different for various diameters of that material? I would assume it does, but I cannot find a reference. Is the Young's modulus of a $1~\rm mm$ thick steel wire the ...
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 ...
6
votes
1answer
659 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 ...
14
votes
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 ...
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. ...
3
votes
1answer
4k views

Formulas for compressibility of solids

I am taking a course in mechanics this semester, as well as a course in reservoir physics. Both courses have sections devoted to pressure/compressibility of solids, but the formulas look slightly ...
4
votes
2answers
441 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 ...
2
votes
1answer
591 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 ...
2
votes
1answer
3k views

Does resistivity of material change under strain

As I am reading the document on physics of strain gauge, I encounter the following paragraph that I do not understand. How could resistivity change (delta rho) under strain/elongation? I always ...
1
vote
1answer
321 views

Question concerning the diagram for stress tensor

I have a couple of questions related to the diagram in the answer by Kyle Kanos to this question, Why is stress a tensor quantity?. Q1. If the box shown is of finite size why are there not three ...
1
vote
1answer
300 views

Why is 3D stress tensor acting only on three surfaces?

I'm trying to learn about the stress tensor (in 3D) The tensors are said to have directions (the first subindex $i$ in $\sigma_{ij}$) and specify the surface upon which they act (the second subindex $...
33
votes
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. ...
14
votes
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 ...
3
votes
2answers
34k views

What is the difference between “Elastic limit” and “Yield point”?

Elastic limit - the point till which the wire retains its original length after the force is withdrawn. Yield point - the point where there is a large permanent change in length with no extra load ...
7
votes
4answers
543 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.
5
votes
2answers
793 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(\...
4
votes
1answer
192 views

Nonsensical dispersion relations for elastic wave propagation

In an earlier question about Einstein notation, a link was provided to a medical paper which used acoustic propagation to noninvasively detect the orientation of muscle fibers. In short, muscle fibers ...
2
votes
3answers
1k views

What is the motivation for Mohr's circle?

I am very puzzled by the motivation for Mohr's circle in Wikipedia here. Please, explain why we need something called "Mohr's circle". Use as little words as possible and be precise. Helper questions ...
8
votes
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 ...
4
votes
2answers
707 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
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 ...
3
votes
1answer
23k views

Calculating force absorbed by compression of a material (i.e. rubber)

Say I was trying to design padding to absorb impacts using polymers or similar materials, such as rubber. I have a good understanding of any relevant physics, most likely, but I wouldn't know where to ...
2
votes
1answer
813 views

What is the difference of engineering and true stress?

What is the difference of engineering and true stress? Also, why does the engineering stress decrease after the ultimate tensile strength point?
2
votes
2answers
237 views

True strain, engineering strain, strain gauges

I've been somewhat confused over the concepts of true and engineering strain, and I just want to see if I am understanding this correctly. Let us denote true and engineering strain as $\epsilon_t$ ...
1
vote
2answers
454 views

Horizontal Beam Bending Due to Gravity

I just thought about this problem recently but am not sure where to find a solution. I am not certain which parameters are important in this problem, so please bear with me. Assume that a beam of ...
1
vote
4answers
33k views

How would one derive the equation of thermal stress?

The equation of thermal stress is: Stress =$\frac{F}{A}$ = -$E$ $a$ $dT$, where $E$ is Young's Modulus, $a$ is the coefficient of linear thermal expansion, and $dT$ is the change in temperature. I ...
1
vote
3answers
2k views

Ideal, isotropic fluid and stress tensor

An ideal fluid is the one which cannot support any shearing stress. It also doesn't have viscosity. My question is what does it mean by a fluid to be isotropic? Is an ideal fluid necessarily isotropic ...
11
votes
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?
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 ...
4
votes
0answers
232 views

Cauchy stress tensor for a spherically symmetric problem [closed]

Given a sperically symmetric problem, I am asked to show that its Cauchy stress tensor, in spherical coordinates will assume the form: $${\overline{\overline{\sigma}}}=\sigma_{RR}(r)\overline{e_r}\...
3
votes
2answers
333 views

Is Young's modulus a measure of stiffness or elasticity?

Young's modulus seems like a modulus of stiffness. It tells us how difficult is it (how much stress is required) to produce longitudinal strain in a solid. It does not tell anything about how an ...
3
votes
1answer
2k views

Why does glass break at the line where you score it?

Why does it take such a small incision for the glass to break at that spot? Why is the structural strength of the material influenced by such a small imperfection?
2
votes
2answers
798 views

Why traction vector depends on surface(section) orientration?

Need help with stress tensors. Every book says that traction vector at a point P depends on orientation of surface cutting this point. But as far as I know traction is defined in this way: Traction is ...
2
votes
1answer
116 views

Trouble connecting stress and force in continuum mechanics with my concept of force from point mechanics

I'm not very familiar with continuum mechanics and have a hard time combining my knowledge of forces from simple mechanics with what I read about continuum mechanics. Let's suppose we have a metal ...
1
vote
2answers
1k views

Why are stress forces considered as acting on a cross-sectional area through a solid?

I'm trying to understand the Cauchy-Stress tensor, in which the stress acting on a body at a point is analyzed by considering the cross-sectional area through which a force passes. And my question is -...
0
votes
2answers
5k views

Does the thickness of a rubber sheet affect the tensile strength?

I'm really confused which thickness of rubber sheet I should choose. Does the thickness affect the tensile strength and elongation in any way? Is there any relationship between them?
0
votes
1answer
272 views

Is the coefficient of thermal expansion a symmetric tensor?

Is the coefficient of thermal expansion (CTE) a symmetric tensor? For thermal stresses, CTE has to be symmetric otherwise the stress tensor would not be symmetric. So does this mean that CTE tensor is ...
0
votes
1answer
412 views

Calculating the pressure between a housing and a shaft in an interference fit

I'm trying to calculate the pressure between a journal/shaft and a housing bore in a case of interference fit. Considere a 2D axisymmetric (effectively 1D) journal bearing with interference fit: ...
0
votes
6answers
1k views

Does large acceleration have to cause damage to the human body?

My whole life, I've heard that large accelerations cause damage to humans (e.g. g-forces in space movies). However, after reading about general relativity, it seems to me that a strong force which ...