Questions tagged [stress-strain]

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Calculating the bending moment ($M$) in a viscoelastic model?

Background: I am trying to understand how to work with viscoelastic models. In each model, there is a "constitutive relationship" between stress ($σ$) and strain ($Ɛ$). I am trying to work ...
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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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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
27 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
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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
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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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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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1answer
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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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2answers
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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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30 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
32 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
52 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
82 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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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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1answer
77 views

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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Hooke’s Law and Energy

I have a quite a simple question that is escaping me right now. The work done on any body is just the net force multiplied by the distance the force acts on it for. For example: the work being done on ...
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1answer
34 views

Tensile strain produced on two thin rods of different lengths

Suppose there are two thin rods $Y$ and $Z$ with length $L_1$ and $L_2$ respectively. $L_2$ has larger magnitude than $L_1$. Both rods have same density $p$, cross sectional area $A$, Young's Modulus $...
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Does every point of a wire extend by the same amount upon tension?

Question. A wire horizontally over a bench has one end fixed and the other end holding some weight. The weight stretches the wire to produce some extension, say $\Delta x$. Someone puts a length ...
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2answers
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Stress-strain relation in insane proportions

We have: $\sigma = E \epsilon$ and $\epsilon = \Delta L/L_0$. This seems to imply that for a constant strain, we will achieve a proportional change in length. However, it doesn't rest well with me ...
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59 views

Stress and Strain lag for viscous materials

As stated here, In purely viscous materials, strain lags stress by a 90 degree phase. How can we derive this statement? Is it experimental? If not, which is its proof and what is the physical cause ...
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What is an compressive stress region?

I read in some text that some areas of an object or some parts of an object are compressive. How is this defined? Is it that the maximum principal stress is compressive in these areas? But the maximum ...
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2answers
359 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, ...
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1answer
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Area under stress–strain graph

What quantity does the area under the stress–strain graph (under the elastic limit) represent? As far as I know, the potential energy density due to strain is 1/2×(stress)×(strain). So does the area ...
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Cycles to failure

$$ \text{Ramberg-Osgood equation:} \hspace{41mm} \varepsilon_{tot} = \underbrace{\frac{\sigma}{E}}_{\text{elastic}} + \underbrace{\left(\frac{\sigma}{K}\right)^{\frac{1}{n}}}_{\text{plastic}}$$ $$ \...
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Why would a stationary exercise bike be subject to greater stress than a road bike?

I read this answer to another question: My indoor exercise cycle specifically cautions against using pedals which are not designated as being strong enough for indoor cycles. Supposedly, the stresses ...
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Constitutive relations and strain energy in finite strain viscoelastic solid mechanics

I'm an applied math graduate student, and my research is straying into hyperviscoelastic models of materials. I've had trouble finding an answer to this question I have about the mathematical theory ...
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2answers
45 views

Mechanism of heating during deformation [duplicate]

When a metal or rubber is bent and deformed, it heats up. What is the reason for this? I know that when deforming it, work is done on the object. If the object is perfectly elastic, all of the energy ...
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2answers
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Stress Due to Air Pressure

Consider a pipe. The pipe is not crushed by the air pressure because the same air pressure is acting from inside the pipe. But this means that the material of the pipe is being compressed on both ...
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1answer
950 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 ...
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4answers
98 views

If net force is 0, why does elongation occur in a rod?

I was taught that stress is the restoring force per unit area (let us assume a rod). This stress is developed on order to resist the motion of the rod. My questions are as follows : If the rod is ...
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2answers
31 views

How mechanical Strain developed in metal bar at molecular level?

If I have metal bar fixed to a support at one end while I apply a tensile force at the other end, the bar elongates while its cross sectional area decreases. I want to know How strain is developed at ...
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1answer
77 views

Why are the principal planes where principal stresses occur perpendicular to each other?

Equation of principal angles: $$\tan 2\theta_p=\frac{2\tau_{xy}}{\sigma_x-\sigma_y}$$ Equation of principal stresses: $$\sigma_{max}, \sigma_{min} = {\sigma_{xx} + \sigma_{yy} \over 2} \pm \sqrt{ \...
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How does stress “propagate” in beams?

I'm studying structural mechanics and I have been stuck on a thought. I drew a very simple cantilever beam situation. If I make a fictional cut like in my fig.1, I will be in the situation of the ...
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2answers
69 views

How does stress in solids work? [closed]

How do you figure out what the stress equations are? How do you find a solution to the stress equation?
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How does a Z-tube measure liquid tensile strength?

A z-tube measures tensile strength by placing a liquid within a z-shaped tube and rotating the tube until the water separates. Why can't you just use a normal tube? Wikipedia says the water will just ...
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1answer
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How does shear-stress act on a spring hanging vertically with a mass attached to its end?

I have come to known that both longitudinal and shear strain act on a spring when it is hanging. I can understand how longitudinal strain acts but I do not understand why shear stress/strain can act ...
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1answer
49 views

Tolerability of extremely high acceleration for an extremely short period?

I've been wondering about this for a while. So let's assume a ship accelerates at 1 million G for an extremely short period of time, such that its total velocity change was (say) 1cm/s. Would the ship ...
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1answer
57 views

Self-deformation due to own weight [closed]

The goal is to calculate the total deformation due to self-weight. I understand the calculation that is shown in the picture. I forgot to include that $x$ is the length of the object's portion under ...
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3answers
67 views

Strain on heating

A steel rod of some length rests on a SMOOTH horizontal base. If it is heated for a considerable temperature difference, say $0^\circ C$ to $100^\circ C$, what is the strain produced? Strain is ...
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1answer
73 views

Is the minimum cross sectional area of the wire right? [closed]

The breaking stress of the wire is $3.5\times 10^6 \,N/m^2$. It is observed that the minimum cross-sectional area of the wire so that it does not break is $18.67 \,cm^2$. Now I need to find out if the ...
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4answers
130 views

Why is Poisson's ratio necessary, when we know that volume stays constant?

Why is the Poisson ratio necessary, when volume is conserved? I read that volume is conserved when a body is subjected to longitudinal (compressive or tensile) stress or shear stress, so given that ...

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