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1answer
430 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 + ...
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2answers
204 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 relation between them? i would really ...
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0answers
19 views

Why is maximum shear stress at 45 degrees instead of near 0?

I think I might havr an immensely stupid question but it's really bothering me so please be patient. I am not physicist smart. Look at this guy's question: ...
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1answer
178 views

Jaumann deviatoric stress rate

Background about terms in this question: Hookes law and objective stress rates From my understading, the Jaumann rate of deviatoric stress is written as: $$dS/dt = \overset{\bigtriangleup}{{S}} = ...
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0answers
8 views

Equation Governing Small Lateral Deflections z of a Uniform Membrane

The equation governing small lateral deflections z of a uniform membrane subjected to a lateral (dimensionless) pressure p is given by $$ \frac{\partial^2 z}{\partial x^2} + \frac{\partial^2 ...
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0answers
25 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 ...
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2answers
568 views

How would one derive the equation to 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 ...
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0answers
23 views

From in-plane strain to Poisson ratio

I have recently been trying to simulate a graphene cantilever and thus I need to know the Poisson ratio, Young's modulus, and density. From literature it is easy to find the Young's modulus and ...
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0answers
45 views

Can a magnetic field weaken aluminum?

I'm wondering if there is any reason to suspect that applying a magnetic field to a piece of solid aluminum would weaken it structurally in any way. The application is that I would like to put a stir ...
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1answer
35 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 ...
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0answers
14 views

The amount of force needed to bend and break a magnesium cylinder? [closed]

I want to determine how much force in Newtons will be need to bend a solid cylinder of magnesium. The cylinder is (x) cm in diameter, and it is (l) cm long. The density of normal magnesium alloy is ...
3
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1answer
64 views

Cauchy stress tensor in different coordinate system

The general form of the cauchy stress tensor is given by the dyadic decomposition $$\boldsymbol \sigma = \sigma_{ij}\,\,\mathbf{e}_i \otimes \mathbf{e}_j$$ I want to know how this can be expanded in ...
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0answers
57 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: ...
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0answers
24 views

Stuck with physics tensile strength problem

So this was a question in my exam. I am not asking for the solution rather some help at a step. A glass spherical shell of radius $R$ has a point source of monochromatic light of wavelength ...
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2answers
56 views

Elongation and tensile strength of rubber

I want to do some experiments on a neoprene rubber sheet (ex. supplier). When I went to order the sheet I was confused because the listed elongation and tensile strength for all sheet sizes (with ...
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3answers
69 views

Why are the x-components of the stress tensor ($\sigma_{xx}, \sigma_{yx}, \text{and } \sigma_{zx}$) different?

I understand the stress tensor at a specific point $P$ as follows. You draw a cube with its center at $P$ and look at its faces. The face with its normal vector in the positive $x$ direction has a ...
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1answer
30 views

Calculate the applied force associated with uniform distortion of an area

I am exploring Hooke's Law and considering how it might apply to an arbitrary area (perhaps as a slice of some volume). Since $$ F = -kx $$ Would it be correct to calculate the force, $F$, ...
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0answers
42 views

How is the Von Mises stress used in 1D or 2D?

The Von Mises Stress is given by: $\sigma_{VM} = \sqrt{\frac{3}{2}\boldsymbol{\sigma}^{'}:\boldsymbol{\sigma}^{'}}$ My understanding is that the $\frac{3}{2}$ is included to ensure that the von mises ...
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0answers
23 views

Plastic deformation energy dissipation due to inelastic collision

I have been attempting to determine an analytical expression for the coefficient of restitution (or any similar collision parameter) for an inelastic collision. So far, I've looked at Hertzian contact ...
2
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1answer
487 views

How to determine plastic strain rate

Equivalent plastic strain rate is defined as $$ \dot{\bar{\epsilon}}=\sqrt{\frac{2}{3}\dot{\epsilon_{ij}}^{p}\dot{\epsilon_{ij}}^{p} } $$ Where, $ \dot{\bar{\epsilon}}$ is equivalent plastic strain ...
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0answers
62 views

What is “Accumulated plastic strain rate” in Current yield Norton law?

I'm doing FEA of steel under high strain rates and using Elasto-ViscoPlastic material model, with Von-mises yield criterion along with Isotropic hardening. The strain rate sensitivity is addressed by ...
0
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1answer
52 views

Deformation of an elliptical ring

How will it deform when I compress an elliptical ring along its long axis? For simplicity we could consider that the ring is homogeneous, elastic, has no internal stress at the beginning, and its ...
3
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2answers
100 views

What will limit the speed at which one can play the piano?

I thought about this as a fun question. Suppose we provide a piano player that is limited only by the typical relativistic rules (i.e., hands and fingers cannot move faster the speed of light), so ...
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0answers
21 views

Bending moment in composite beam with internal “active” stress

I am looking at a problem of a bending composite beam with a symmetric cross -section, $A(s)$. Above the neutral axis $s$ is material $U$ and below the neutral axis is material $L$. $U$ has an ...
5
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1answer
183 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 ...
2
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1answer
35 views

What is the stress on the cube?

In a problem, it is given that a mass of 10.2 Kg is resting on a cube made out of a particular material. Assuming that the x-axis is vertically upwards, what is the stress on the cube. (We can say ...
2
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1answer
93 views

What does it mean for shear modulus to be less than bulk modulus?

It is known that Shear Modulus is generally less than Young's modulus for most materials. What does this mean? Does this mean that it is easier to change shape of a fixed body by applying force than ...
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2answers
81 views

How tall is the tallest Jell-O structure possible?

Given Jell-O with a particular consistency, how tall a structure could be built out of it before it collapses?
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0answers
34 views

Strain problem with diferent forces

Good day to everyone. I had a test a couple of weeks ago and just got it back, and I'm getting a little confuse with a certain question that I thought was answered correctly, so here is it: (roughly ...
0
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1answer
75 views

Confusion between TWO shear stress formulas

There are two formulas that I have encountered so far for shear stress in my Engineering class. Let S be shear stress, F be force, and A be cross sectional area: S = F/A Note: This formula is ...
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1answer
72 views

Physical interpretation of the relative displacement tensor?

I've resolved a relative displacement tensor into a strain tensor and a rotation tensor, where the strain tensor is: $$ \varepsilon_{i,j} =\begin{pmatrix} 0.2 & 0 & 0 \\ 0 & 0.8 ...
3
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1answer
67 views

Perturbations on a fluid thread and hydrodynamic instability

I know that due to fluid instability there are some perturbations ( picture below ) after all of these, my question is the reason of existence of these perturbations. Why exactly they appear? Shear ...
0
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1answer
97 views

Negative Sign in Compression Modulus

I noticed that the bulk modulus often has a negative sign appended to it in order to cancel with a negative change in an object's volume; this allows the bulk modulus to be positive. However, I ...
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1answer
341 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 ...
3
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2answers
96 views

How does stress change through a bar that sharply increases in diameter?

I am looking to analyse the stress through the following bar: The bar is of circular cross section, homogeneous in material, that is of a certain diameter on one half, and a large diameter on the ...
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0answers
21 views

Flamant's use of mass and weight

I apologize for the stupid question, but I've consulted teachers and found their answers unsatisfactory. Professor E.Brune, in the XIX century, delivered a course on l'École des beaux-arts on ...
0
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1answer
167 views

How to calculate Young's modulus from a set of data?

The set of data are force vs deflection. Is Young's modulus constant for a material? If the beam is fixed by one fixed support and one vertical support $E = \frac {F}{δ}\frac{3.5L^3}{384I}$
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1answer
67 views

What diameter is used to calculate stress in an elastomer whose cross sectional area changes continuously when streched?

Consider a cylindrical rope of rubbery elastomer with a radius (in inches) equal to the square root of the inverse of $\pi \rightarrow \sqrt \frac{1}{\pi} $ so that the cross sectional area is $1 \, ...
0
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1answer
50 views

Strain-Displacement relationship symmetrization

In the context of infinitesimal elastic strain theory, one writes the relationship between displacement and strain as $$ \epsilon_{ij} = \frac{1}{2}( \frac{\partial u_i}{\partial x_j} + ...
0
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3answers
104 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 ...
1
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3answers
196 views

Strain and stress tensor

I have problem by definition of strain and stress. From Gockenbach's book that our reference for FEM, we have $$\epsilon=\frac{\nabla u+ \nabla u^T}{2},$$ that $u$ is vector displacement, and ...
4
votes
1answer
329 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 ...
2
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3answers
488 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 ...
0
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1answer
57 views

Drilling a hole into a bone and measuring the force required to break it

I'm currently planning an experiment (high school biology) where I will drill a hole into a bone, then load weights onto it until it breaks. I will be repeating this with holes of different diameters. ...
2
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1answer
50 views

Is stress a property only relevant on surfaces?

I saw that, $$dF=\sigma \cdot dS$$ Where $dF$ is the differential force, $\sigma$ is the stress tensor, and $dS$ is the differential surface. This equation confuses me a bit. I'm under the ...
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2answers
87 views

How does one integrate an equation with a tensor?

I was looking at the equation for the differential force $dF$ caused from a stress tensor $\sigma$ acting on a differential surface $dS$. In mathematical terms, $dF=\sigma \cdot dS$ Taking the ...
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2answers
7k 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 ...
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2answers
279 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 ...
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2answers
1k 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
235 views

How do I calculate the maximum pressure a container can withhold?

Say I have a spherical container with a certain gas inside, heated to a very high temperature, and thus a very high pressure. The gas will exert a force radially outwards onto the container, and at ...