Questions tagged [stress-strain]

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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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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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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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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
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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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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
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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
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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
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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
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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
28 views

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
48 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
53 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
62 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
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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
93 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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1answer
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Shear stress for mountain rocks

Why is the stress on the rocks at the bottom of a mountain due to the weight of the mountain shear stress and not compressional or longitudinal stress? If we try to understand why a mountain cannot ...
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2answers
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What is a coordinate-free formulation of deformation theory?

For example how are stress, strain and shear tensors described invariantly, without any coordinates, purely in a geometric manner? A formulation that avoids indices coordinates and matrices, even in ...
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If one material has “half the strength” of another, do its elastic and shear moduli both get halved?

In a textbook problem, we are asked to calculate the compression and shear displacement of a object that has "half the strength of hardwood." The Young's and shear moduli for hardwood are given, ...
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2answers
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Do mechanical stresses propagate in time as EM waves do?

If someone may, I expect a mathematical comparison of the governing equations "Maxwell Equations" for wave propagation and "Conservation of momenta & equilibrium equations" for stress and ...
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1answer
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Strain energy of plate bending

I am currently doing some research for my university thesis and I am dealing with plates. Right now I am trying to figure out the potential (strain) energy of a plate under bending. So basically I ...
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1answer
123 views

Is Young's modulus of elasticity a measure of ductility?

I've learnt that the Young's modulus of elasticity is defined as the ratio of stress and strain when the material obeys Hooke's law. So it has no significance beyond the proportional limit in the ...
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Force due to pressure at a corner

Say we have a closed box with a uniform internal pressure $P$. Consider a point on the intersection of the two faces. I know that the net force on each face is given by $F = PA \hat{n}$. Is there a ...
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Normal Stress in Fluid

When will the normal stress be the same in all directions at a point in a fluid? Is it when the fluid has zero viscosity and is at rest or one fluid layer has no motion relative to an adjacent layer? ...
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1answer
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Why do we get a different result when we calculate it by parts?

Assume a wire is 5 m long and we want to find how much force is required for increasing the length of it 5 m and make it 10 m long. $$F = \frac{YAl}{L}\, .$$ If Y=5 and A=1 we will find the answer 5....
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When tyres skid on a dry road, is it because friction is too low or because the rubber is not strong enough?

All other things being equal, a car with wider tyres is less likely to skid on a dry road than one with narrower tyres. As answers on related topics have made clear, the simple formula $F=\mu N$ does ...
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Design an Experiment based on Castigliano’s Theorem to Determine Young’s modulus of the Unknown Member

The question states: "You need to design an experiment based on Castigliano’s theorem to determine Young’s modulus of the vertical member (unknown material) without destroying the structure." Is ...
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1answer
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What happens between the point corresponding to ultimate tensile strength and fracture point?

A rod is subjected to tensile stress and it is plotted against the strain developed. This graphs can be found in any standard material science and mechanical engineering text books. If the load is ...
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Hyperelasticity: relating two PK2 stress tensors in terms of two nonlinear displacements

I am working on numerical analysis for a nonlinear hyperelasticity problem. Given that the second Piola Kirchhoff stress tensor $S$ depends on the Green strain tensor $E$, which in turn depends on the ...
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1answer
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How are body deformations modeled in Lagrangian mechanics?

With rigid-body systems, we choose a finite number of generalized coordinates to model a system, i.e. a pendulum. However, I've read that deformable bodies like elastomers have "infinite" degrees of ...
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1answer
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What causes increment in volume when compressive forces are applied on an object

Doubt When compressive forces are applied on a body, what causes increment in volume. According to me the volume should remain constant since the mass and density of body are constant.
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Independent Elements of Elastic Stiffness and Compliance Tensor for ALL Space Groups

In short: Does anybody know if there exists a compendium, a document, a book or a stone tablet listing the independent elements of the elastic stiffness and compliance tensors ( that is, naming the ...
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1answer
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Difference between Viscous stress tensor and Shear stress tensor?

I am trying to learn about fluid dynamics in the context of incompressible, Newtonian fluids, Laminar flows. Unfortunately, different authors use different notations and every time I found my self ...
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1answer
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Can stress matrix be complex?

Stress matrix gives the values of physical deformation due to stress. So, it is usually real. But in complex spaces are physically realizable spaces. Then, is it possible to have complex strain matrix?...
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Force acting on a cube on all sides [closed]

A metallic cube of length L is stretched out uniformly by force F normal to each of its faces. Given Young's modulus and Poisson ratio, what is the deformation in the cube?
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Riemann curvature tensor in infinitesimal strain

Continuous deformation from 3-dim Euclidean space $y^\mu=x^\mu-u^\mu(\boldsymbol{x})$ implys trivial Riemann curvature tensor. It is clear to see that a single-valued continuous displacement field $u^\...
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What Changes a Stress-Strain Curve?

If stress is applied to a material but does not exceed the yield point, when the stress is relieved, the material such as steel returns to its original size and does not experience any permanent ...
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How to calculate impact of falling weights with zero distance and time at impact

The motivation for this question is building a power rack for my basement due to corona Virus and not being able to visit the gym, and want to make sure it can hold the weight I desire including the ...
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Problems regarding Searle's Experiment

Recently I came across a problem on Searle's Experiment where we had to find the maximum possible error in Young's modulus calculation due to an error in the calculation of extension of string. ...
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Euler beam equation sign confusion

Euler beam equation is defined as follows: $$M=-EI{\frac {d^{2}w}{dx^{2}}}$$ There is a negative sign, so if the second derivative of the deflection is negative, the moment is positive. When the ...
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Second-order tensors as linear operators

A tensor is formally defined as an object whose components obey some transformation rules. I, however, find it more intuitive to look at (second-order) tensors as a linear operator/function between ...

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