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1answer
28 views

Stress in horizontal bars

Imagine we have an horizontal bar. My teacher expresses the tensions along the longitudinal axis by this way $\sigma_{xx}=A(x)y+B(x)$ He doesn't give any motivation behind this. So, is this general? ...
2
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2answers
85 views
+50

what is the static pressure in a yield stress fluid?

Suppose I have a tank filled and there is no slip at the walls. If the tank is filled with a Newtonian fluid and is in static equilibrium, we know that the pressure is defined as $p = \rho g z$. But ...
0
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1answer
87 views

Derivation of normal shear stress

I am self-studying this note and I am stuck in the derivation of the normal shear stress. Specifically I can't see how the relations (23) and (24) come about. Specifically, what I don't understand is ...
7
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3answers
234 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) ...
1
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1answer
38 views

Practical hardware question regarding optical source for an array of fiber bragg gratings [closed]

I have a single 1 meter array of 5 fiber bragg gratings that has FC/APC connectors on both ends. I will be embedding the array in a material and want to be able to do a quick check that the array is ...
1
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2answers
149 views

Strain energy density in index notation

The strain energy density is defined as $$dU = \int_0^{\epsilon_{ij}} \sigma_{ij} d \epsilon_{ij}$$ (see Reddy "Energy Principles and Variational Methods in Applied Mechanics", 2nd Ed, 4.11). Assuming ...
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2answers
83 views

Why are these specific stress invariants chosen?

I've seen these invariants of the Cauchy stress tensor $S$ defined in multiple places: $$J_1 = \lambda_1+\lambda_2+\lambda_3 = Tr(S)$$ $$J_2 = \lambda_1^2+\lambda_2^2+\lambda_3^2$$ $$J_3 = ...
2
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1answer
59 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 ...
2
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0answers
219 views

Stresses on an inclined plane

Background This issue has been bothering me for a few days now. It's actually part of my homework, but I've already finished them and in a sense they're not part of the question here. What I would ...
0
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1answer
570 views

Stress due to the mismatch of thermal expansion coefficients of two different attached materials

I'm simulating the thermo-electro-mechanical behavior of a copper wire which is surrounded by silicon dioxide. In other words, the wire segments is under mechanical and thermal loads and at the same ...
1
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1answer
49 views

How far do atoms move in a wire when whirling it horizontally?

so the question is: I whirl a mass m attached to a wire with length L and diameter d around my head in the horizontal plane. The mass takes t seconds to move around a circle. How far do the ...
0
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1answer
31 views

wall thickness for a very large, low-pressure vessel?

I'm working on a space colony simulation, and I'm at the point where I need to calculate the thickness of the habitat walls, as a function of air pressure and geometry (and assuming some common ...
2
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0answers
31 views

buckling of tube - shell thickness vs. momentum of inertia optimum

is there any simple formula (perhabs semi emperical, or aproximatively derived model) for buckling of tube under axial compression load given its crossection and wall thickness? ( and naturraly ...
5
votes
4answers
411 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.
8
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2answers
530 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?
0
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0answers
26 views

Volumetric and Deviatoric Strain Equation in 2D

Strain is defined as $$\epsilon=\frac{1}{2}\left( \nabla u + \nabla u^T\right).$$ I found a formula for the strain tensor in 3D decomposed into volumetric and deviatoric components: $$\epsilon= v + ...
1
vote
1answer
68 views

why does a thread/rope have more tensile strength when swirled like this as shown in the figure?

Why does a thread/rope swirled like this: become more strong than just the group of single threads without swirling? Is it because of more contact between them and therefore more friction? (I don't ...
1
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1answer
34 views

Are Normal Stress Differences in Newtonian Fluids Equal?

I was reading about normal stress differences in the context of Non-Newtonian fluids. There was a remark that the normal stress differences in Non-Newtonian fluids are not equal whereas the normal ...
0
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0answers
44 views

Can't work out how the following free body diagram was created

I've been asked to draw a free body diagram of the following stepped bar setup: $ P = 10kN \;and\; Q = 30kN$ The one shown in the answer is the following: Could someone explain to me how this ...
2
votes
1answer
70 views

Why does shape of elements matter in finite elements analysis? [closed]

I have used FEA for a couple of years now, but using it and using it correctly are two different things, safety factor is not the solution to everything. I have the feeling I won't be using it right ...
0
votes
1answer
41 views

What is the difference between a linear and non-linear solution in the bending of beams?

I have been working on a simulator for bending of beams and came now to a tricky doubt: What should be the difference between a linear and non linear solution in this case (graphic at bottom)? The ...
1
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2answers
133 views

Electrical analogy for stress and strain

It feels like the relation between stress and strain (and other mechanical properties) is analogous to that of some electrical properties (voltage and current?). I'm comfortable with electrical ...
1
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3answers
2k 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
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2answers
61 views

pure compression or pure traction?

I know that if we are given a stress tensor that is diagonal, the sign on the diagonal entries tell us whether we have traction or compression. Now, imagine that we are given a non diagonal stress ...
0
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2answers
92 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 has ...
2
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2answers
60 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 ...
8
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3answers
15k 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 ...
0
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0answers
40 views

Types of semiconductor relaxation

Ok, so you've basically got tensile and compression strain in a lattice mismatched material right? So as you're epitaxially layering the material, the strained material is deforming more and more ...
0
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1answer
118 views

Maximum Weight Sustained by wire / Breaking limit of wire [closed]

I know that breaking stress depends on material of wire, not on the diameter or the length of wire. and also that Breaking load depends on the area of cross section of wire. But still i have a ...
3
votes
1answer
56 views

in Science materials, what is difference b/w E and G?

I'm studying Science Materials on Callister's Materials Science and Engineering: An Introduction. I've never studied Mechanics (except for basic Physics courses), so I was wandering: when talking ...
2
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0answers
68 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 ...
0
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0answers
117 views

Caculating thermal stresses in a composite rod

The Question Between two rigid walls separated by a distance $l_1+l_2$, two rods of equal cross-section area $A$, and length, coefficient of linear expansion and Young's modulus $l_1, ...
0
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2answers
54 views

Can stress be observed directly?

Strain can be directly observed using e.g. a ruler. Can (internal) stress be directly observed?
0
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1answer
88 views

Why does the pure shear term / strain deviator tensor have non-zero entries on the main diagonal?

In a textbook of mine an operation is performed, of which I think the goal is to get zeros on the main diagonal of a matrix (the matrix represents strain). But im not sure that is the goal and Im also ...
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0answers
21 views

Solid state diffusion as a function of shear stress

I am hoping to get some clarification on the impact of shear stress or shear strain on atomic diffusion in a metallic solid. More specifically, will the kinetics for the dissolution of secondary phase ...
2
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2answers
297 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 ...
0
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0answers
36 views

How do I determine $\phi$ in a hollow circular cross section using torsion equivalence?

I know that the maximum shear stress $$\tau = \frac{T}{J}\rho$$ where $\rho$ is the radial distance from the center of the cross section. I have also determined the torsional constant $J$, which is ...
0
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0answers
68 views

A distributed axial load acting on a bar

Normally, when a distributed force is acting on a bar, if it's 'rectengular' we multiply the length with q, but I have no idea what I'm supposed to do at this situation. I first need to calculate ...
0
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2answers
94 views

Stretching a rod? [closed]

The stress applied on a rod is linearly proportional to its strain. But shouldn't the opposite be true? I mean if you pull particles further apart doesn't the force they apply on each other decrease ...
4
votes
3answers
348 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.
2
votes
2answers
2k 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 ...
2
votes
2answers
290 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 ...
2
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1answer
63 views

stress work of uniformly deforming continuum

I have a volume which is deforming (using explicit time-integration scheme) uniformly with velocity gradient $L$ and stress tensor $\sigma$. I would like to determine work done by the volume ...
1
vote
1answer
2k 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 ...
1
vote
1answer
383 views

Where I can find a torsional stiffness table for different types of stainless steels?

I am trying to comparing the torsional stiffness of different types of stainless steels. I googled the keywords but I could not find any useful information. Would anyone please give me some links ...
2
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0answers
54 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 ...
0
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0answers
61 views

Stress and Mass Density Distribution

I'm simulating electromigration in a copper wire using COMSOL and trying to see the back-stress caused by material transport. However, I do not see any stress growth. In other words, the atomic ...
-1
votes
1answer
100 views

What is the $n$ in the formula in Solid Mechanics? [closed]

The formula is about the critical force for the elastic beam that is supported by its joints: $$ P_{cr} ~=~ n^2 \pi^2 \frac{EI}{ L^2} $$ It should be based on the book Parnes - Solid ...
0
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0answers
34 views

Photoelasticity and existence of stress

Shall we consider photoelasticity a non-mathematical, or purely visual, proof of the existence of stresses in mechanical structures undergoing external loading?
0
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0answers
48 views

What is the relationship between strain and electric current?

Strain or stress can be caused by different sources. I categorized theses sources as mechanical, thermal and electrical loads and formulated the total stress as follows: $$ \epsilon_{total} = ...