Questions tagged [stress-strain]

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Relation between stress and resistance in a block of metal

I opened up my broken electronic weighing balance to understand how the machine actually calculates the weight of things. To my surprise, instead of a pressure sensor I found a setup with a metal ...
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29 views

Determine throwing angle from fractured glass

Our neigbours glass windows has allegedly been shattered by neibouring kids. The question is whether the stone came from below the window thrown by someone standing on the ground or above the window ...
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The concept of stress and pressure [closed]

Definition of stress and strain Stress and strain are among the most basic and important concepts in the strength of materials. When a force is applied to a structure or a member of it, tension and ...
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23 views

How can the equation of force for a spring and damper in series simplify to just the equation for a spring if the damper is set to “zero”?

I have been working extensively on modeling physical objects using the stress/strain relationships of springs and dampers as described here: https://en.wikipedia.org/wiki/Viscoelasticity#...
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22 views

Is the force $F$ in formula of longitudinal stress applied on both sides of a rod?

Suppose a force $F$ is applied on one face of a rod (with cross-sectional area $A$) and one end is fixed. And now suppose another situation with the same rod, force $F$ is applied on both faces of the ...
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Strain rate and deformation in non-Cartesian coordinates

I have a question regarding the connection between deformation, strain, and strain rate: The deformation tensor $\textbf{F}$ is defined by $F_{ij} = \partial X_i / \partial x_j$ and its determinant ...
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29 views

Stress to make concrete stronger

In reinforced concrete steel rods are embedded in wet cement and held in tension while the mixture dries. Once fully dry the tension is removed, and the concrete should be stronger as a result of this ...
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Why doesn't the Stress Power in the theorem of the expended mechanical power contribute to the kinetic energy?

The following is the formula of the expended mechanical power: $P(t)$ $=$ $\frac{d}{dt}$ $\int \frac{1}{2} \rho\ v^2 dV$ $+$ $\int \sigma \colon d\ dV$ where $P(t)$ is the mechanical power entering ...
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Cauchy's Postulate

According to the Cauchy Postulate, the stress vector (T)^(n) remains unchanged for all surfaces passing through the point P and having the same normal vector n at P i.e., having a common tangent at P. ...
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46 views

Why is the number of independent elements of a stiffness tensor 21?

I think that the dilatation of an elastic material is proportional to the hydrostatic pressure. That is, ${\rm{tr}}(\boldsymbol\sigma)=3k\ {\rm{tr}}(\boldsymbol\epsilon)$ for small strains. If so, ...
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Why is it that the yield shear is half of the yield stress?

Why is it that $\tau_{yield} = \frac{\sigma_{yield}}{2}$ ? I know this question is already asked. I can't comment (otherwise I would ask there) but I was wondering if someone wouldn't mind giving a ...
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2answers
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Elastic Modulus of Elastomers

For an elastomer, what could be the modulus of elasticity. My thought process is that the modulus of elasticity is the tangent of a point of the stress-strain graph. And therefore looking at the graph ...
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Chinese finger-trap and other nets which assume different 3D shapes under different positions and loads

Please allow a question for general orientation of a newbie lay-person. I just came from a different stack exchange site seeing with curiosity a link to this question: Is the surface of a sphere and a ...
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Vertical shear force changing to horizontal shear force

first time here, hope it goes well! This is NOT a homework question, I am just doing it as a practice. I cant seem to find the solution/logic anywhere, but if the question is asking to determine ...
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51 views

What is the unit for modulus of elasticity?

I've previously asked a question regarding the modulus of elasticity which I am still unsure about. I've been told various formulae to calculate the modulus of elasticity, some of which give answers ...
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25 views

Real and imaginary parts of derivative of complex velocity in fluids

Just by chance, I noticed that for an ideal fluid which has a complex velocity say $w=u-iv$, that its derivative with respect to $z=x+iy,$ when written out in real and imaginary parts, looks like $$\...
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Sidebands in spin-oscillator coupled devices

I am researching spin-oscillator hybrid devices (particularly those coupled to NV centers), and I have come across this paper investigating the strain field of a cantilever and its effect on the NV ...
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2answers
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Is strain during free thermal expansion zero?

If a steel rod of length 1 m rests on a smooth horizontal base is heated from $T_1$ to $T_2$, what is the longitudinal strain developed? I think that due to thermal expansion/contraction, the length ...
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26 views

Rotational invariance of the the elastic deformation in spherical symmetry

I write the elastic deformation $E$ for an incompressible material in spherical symmetry (Have a look at here Eq.(5.32) ). Since we are incompressible, $\mathbf{det} \,E=1$, so in spherical ...
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Sand cone in the attic [closed]

My question is based on Halliday books Tom 2, chapter 13 (exercise 42). There is a cone of sand laying in the attic. Consider stress of the floor under the sand cone. Why the biggest stress is in ...
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56 views

Determining local area change from surface displacement field

In continuum mechanics, deformed area elements are related to initial area elements by Nanson's formula: $$\vec{n}\ da = (\det{\pmb{F}})(\pmb{F}^{-T}\cdot \vec{N})dA$$ Assuming one can experimentally ...
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Balloon in a container inside a vacuum chamber

The question I'm trying to understand is and getting a bit stuck with: Let's say we have a put a small balloon filled with air of volume, e.g. 1cm^3 inside a container. This container is not sealed i....
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49 views

Why does burning polythene bags cause shrinkage while cutting them makes no change?

I don't know why polythen bags shrink on burning. But one of my friend informed me that it shrinks because at the time of its processing, the polymer is stretched and when burnt the internal stress ...
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44 views

Torque experienced by a body under shearing stress

Given below is a piece of information from table 9.4 on page 243 from my standard NCERT class 11th textbook: Two equal and opposite forces parallel to opposite surfaces forces in each case such that ...
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1answer
26 views

Interpretation of Goodman Diagram in Machine design [closed]

In the Goodman diagram, the max and min stresses are plotted as a function of midrange stress. If I understand correctly, these are the upper and lower stress limits that can be applied in a repeated ...
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Slip-Condition for Fluid between Parallel Plates [closed]

When we have two parallel plates separated by distance $h$, the plate at the top moves with velocity $V$, while the one at the bottom remains stationary, and we consider that the fluid flow between ...
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1answer
32 views

Sum of Stresses in a Control Volume along $x$-axis

We were looking in class at the sum of forces, acting on surface $x$, of a control volume $dV$. I see from the equation, the first term is the normal force, and then the rate of change of the force ...
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1answer
92 views

Calculating time derivatives of stress ($σ$) in the constitutive equation of a viscoelastic model without explicitly remembering the prior stress?

I am trying to understand how to work with viscoelastic models. There are numerous simple viscoelastic models (described at that link). In each, there is a "constitutive relationship" ...
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3answers
102 views

What exactly is Hooke's law defined for?

I used to think that Hooke's law was a relationship between how much a bar under uniaxial loading deformed and the internal force (per unit area) that developed within that bar. But this clearly isn't ...
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1answer
127 views

Shear Stress at Boundaries of two Infinite Parallel Plates

This is a worked example on a book I am reading (Fundamentals of fluid Mechanics). They calculate the shearing stress in the top layer, bottom layer and middle layer. The calculate 𝜏 > 0 (in the ...
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1answer
31 views

Ambiguity in taking the cross sectional area in Young's modulus

Let's say we stretch a wire and it's cross-sectional area decreased. When using the Young's modulus formula$$\frac{FL}{A\Delta L}$$ Where F is the force subjected on the body. Should we take the cross ...
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Continuity of Cauchy stresses

The question about the reason of the Cauchy stress tensor has been brought up a couple of times here. I've read through the explanations, and they all seem to rely on the fact that the six independent ...
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2answers
187 views

Interpretation of Hooke's Law

I often see people interpreting Hooke's Law $σ=Eε$ as, "The deformation $ε$ that occurs when you subject a material to a stress $σ$." This makes it sound like stress is an external ...
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Does stress and strain change density?

It seems that if poissions ratio is true then volume changes with stress and strain mass remaining same does that did mean density changes?
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1answer
36 views

Calculating poissons ratio proof?

I am new to this. $$\sigma = d(d)/d/(dl/L) f$$ $$\sigma= \frac{d(diameterf)/diameter}{d(length)/length}$$ Now volume being = V $$V= constant$$ for a rod $$(\pi d^2/4)*(l)=V$$ $$=> d^2 \ l = ...
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How could one achieve evenly distributed downward force on a silicone rubber box using rubber bands? [closed]

This is a problem I've been turning over in my head for a few days and can't seem to find much information on from various public websites or research papers. I'm learning Electrical and Computer ...
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Why is stress defined in the way as it is?

Stress is like pressure and it doesn't matter in which direction the force acts (given it is perpendicular to the surface). I read in my book that if we have a rope which is being pulled on both ...
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Principal Stresses in large deformation

Do you know if the principal stresses are invariant to the true (Cauchy) stress and undeformed (2nd Piola-Kirchoff) stress? I mean should i use always cauchy even the body deformations are significant?...
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2answers
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What is the maximum height from which an object can be dropped without breaking it?

Suppose we drop from rest, a body of mass $m$ and breaking stress $\sigma$ on the ground from height $h$ and it collides with the perfectly rigid ground and comes to rest within a short time $t$. The ...
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1answer
26 views

Why stress is differentiated while balancing torque of a body in equilibrium?

What I do not understand is while balancing the torque, why the $\sigma_{11}$ is added to the product of $dx_{1}$ and the derivative of $\sigma_{11}$?
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101 views

Why are shear-stress and momentum-flux the same in the GR?

I am investigeting the meaning of the components of the Stress-Energy tensor: My source also states, that this matrix is always symmetric in the General Relativity. That looks obvious on the image - ...
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115 views

How thick would a steel container have to be to withstand a thermonuclear detonation?

We have a completely uniform, hollow sphere made of high-strength steel. Inside this sphere a Tsar Bomba (RDS-220) is detonated. How thick (ballpark figure) would the sphere need to be to withstand ...
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34 views

Relation between stress and resonance

I am working on a project to measure the stress in metals so I am looking for a variable that changes directly with stress. I noticed that when hitting a metal (unstressed) (say iron) by another metal ...
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Can anyone explain how this rod (experiencing shear stress and deflection) mysteriously resists the downward force from the weight of the mass?

This fascinating and, in my opinion, very unique question came out of a competition lab I did in a general engineering course. I will leave out or change info about the lab to make this question more ...
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1answer
35 views

Moments by normal stress

I am a bit confused with the following formula why is that the normal stress ($z$), not the normal stress ($x$), is involved in the formula for the moment around $x$, $Mx$? Likewise, My also equals ...
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4answers
55 views

Mathematical definition of elastic materials

Physically, elastic materials are materials which return to their original state upon complete removal of applied mechanical loads under isothermal conditions. In the book "Mechanics of ...
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4answers
143 views

Why direction of stress is not pointing in opposite to that of external applied force?

Stress describes how a body responds to an external force. Or, i.e., stress quantifies the internal force that resists the applied force to maintain a state of equilibrium. So stress, as a vector ...
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19 views

Shape change of buckled sheet under change of load

I need to solve the following problem: a sheet of flexible but inextensible material (can be modelled as cable or chain in 2D) is fixed in endpoints and buckles up. Then a variable force is applied in ...
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Lack of plasticity of Moly wire

during re-coiling of tungsten coil wound with moly mandrel ,the mandrel is breaking in between(the mandrel is annealed before) : we don't know what exactly is causing as some length works fine and in ...
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Stress tensor force equilibrium in Feynman lecture book

I was reading about tensors and especially stress tensors in Feynman lectures on physics Which is on the webvsite enter link description here While reading the “31-6. The tensor of stress”, I was a ...

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