Questions tagged [stress-strain]

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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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46 views

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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18 views

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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39 views

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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1answer
187 views

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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23 views

Plastic section modulus and yield strength relationship

Wikipedia and many material science books claim that: The plastic section modulus is used to calculate the plastic moment, $M_p$, or full capacity of a cross-section. The two terms are related by ...
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1answer
43 views

Why does elongation occur

Consider a rod having some mass. This rod is subjected to 2 equal and opposite forces ($F$) on both ends. Since these forces are equal and opposite the center of mass does not move. The rod, however, ...
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1answer
59 views

Why are eggshells so strong?

The usual explanation that someone can find on internet is that it is shaped like an arch, but it is not exactly an arch. Does anybody knows something more on this?
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I want to know why engineering strain is not a tensor

One of the most classical examples in the mechanics of materials is that engineering strain is not tensor. I want to know why the engineering strain doesn't meet the tensor definitation. ...
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2answers
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Why are shoes curved upwards? [closed]

Why are shoes curved upwards? I guess that the toes of the feet are stressed in tension but for what that upward curvature?
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42 views

Effect on Impurities on Young's Modulus

What effect does addition of Impurities have on Young's Modulus of a material? Does the Youn's Modulus Always increase or Always decrease or depends on the Additive? What is the intuitive explanation ...
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113 views

Direction of shear stress on the top plate

This is taken from Munson et al. Introduction o Fluid Mechanics The figure below is example 1.5 in the 8th edition. Then we have this figure: And the solution: I do get the solution; however, I am ...
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1answer
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Physical meaning of internal bending moment

Here's the setup: The textbook, where this is from, first walks through how to find the strain and stress as a function of z, which is fairly straightforward. Then, it calculates the "total internal ...
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1answer
63 views

About Springs Nature [duplicate]

Why when we coil some straight wires (may be metallic or nonmetallic) then it gives a restoring force (some what like spring)?Why when the wire was straight it doesn't give that appreciable amount of ...
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3answers
70 views

Finding a single component of a strain tensor ($E_{yy}$) knowing $E_{xx}$ and $E_{yx}$

I know $E_{xx}$, $E_{yx}$, and $E_{xy}$ but I can't figure out how to find the value for $E_{yy}$. I think it has something to do with the phrase 'homogenous $2D$ strain' as a big hint since there's ...
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1answer
64 views

Stress-Strain Relation in thin layer : Why should divide Force by Thickness?

I have question about equation (2) which is the stress-strain relation. The left side means strain so the right side should be (Stress/Young's modulus). And Stress can be calculated by dividing the ...
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1answer
45 views

Do you know the stress-strain-temperature equations?

The case is that there are 3 layers which are bonded to adhesive joint. And there are the stress-strain-temperature equations. However I cannot understand what do these 3 equations mean. The left side ...
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1answer
71 views
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Finding distance of forces for maximum bending moment

I'm having a hard time looking for the distance ($x$) on which the forces must be located for a maximum bending moment. The reaction forces in $A$ and $B$ are dependant of the value of $x$, and so ...
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1answer
99 views

What are the partial differential equations for Solid Stress Analysis?

When using Finite Element Analysis for Fluids we solve the Navier Stokes Equation and continuity equation, when solving for temperature we solve the heat equation and fouriers law, when dealing with ...
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Demonstration of Cauchy stress - strain energy relation

I'm looking for a demonstration of the formula : $$\mathbf{T}=\frac{\mathbf{A}}{\operatorname{det}(\mathbf{A})}\frac{\partial W}{\partial\mathbf{A}} -p\mathbf{I}$$ where $\mathbf{T}$ is the Cauchy ...
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1answer
42 views

Buckling load of beam

What is Euler buckling load of a beam in axial compression when the axes of loading pins at top and bottom are skew, instead of being parallel? Should the ends be considered fixed because skewed ...
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3answers
85 views

Do Atomic Nuclei Experience an Analog of Mechanical Fatigue?

I'm wondering about the force that holds atomic nuclei together. When I bend a paperclip back and forth, eventually the paperclip weakens and breaks in half. Is it possible for the nuclear force to ...
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1answer
87 views

Can I determine a transformation matrix for a stress tensor with respect to the axes $O x_1 x_2 x_3$ to define new axes of maximum shear stresses?

Is it possible to determine a transformation matrix for a given stress tensor with respect to the axes $O x_1 x_2 x_3$ to define new axes $O x'_1 x'_2 x'_3$ of maximum shear stresses? To make my ...
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1answer
87 views

Strain in a freely falling body

I wanted to know if there would be any extension in a freely falling body due to gravity . I know that a rod tied to the ceiling at one end will show an extension $MgL/2AY$. But if the same rod is ...
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2answers
348 views

Is Young's modulus a measure of stiffness or elasticity?

Young's modulus seems like a modulus of stiffness. It tells us how difficult is it (how much stress is required) to produce longitudinal strain in a solid. It does not tell anything about how an ...
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1answer
32 views

Does stress depend on the intrinsic properties of the body?

I'm trying to understand the difference between stress and pressure. Assume a body, a box with 4 sides. We apply pressure to this body, and because the body's right side is 'weak', it deforms. Does ...
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1answer
117 views

Origin of antisymmetric $\ell=2$ irrep in direct product of two symmetric second-rank tensors

In the excerpt below from Chapter 18 Section 6 of the textbook Group Theory -- Application to the Physics of Condensed Matter by Dresselhaus, Dresselhaus, and Jorio, the irreducible representations of ...
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What is the strain energy around a stressed configuration ? Is $W_{13}=W_{12}+W_{23}$?

Strain elastic energies are generally defined around a stress-free configuration. Is it possible in some case to define it around a stressed configuration ? Meaning in general we have $W=W(\mathbf{F}...
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1answer
112 views

How to calculate the total strain-energy for a deformation from a sphere to a cube?

Is there an analytical solution to compute the elastic energy cost to deform an incompressible sphere into a cube ? Or at least a scaling law ? Let's assume we would do it with a compressive stress ...
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39 views

Why does integrability imply compatibility?

In mechanics, we have the so called compatibility conditions, which quarantee that when a body deforms, the strains are "compatible" in such a way to no discontinuities or gaps for inside the body as ...
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Can we change the volume of a wire by applying force on it in order to stretch it, if yes is there any way to calculate it?

Can we change the volume of a wire by applying force on it in order to stretch it, if yes is there any way to calculate it ??
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1answer
27 views

Why don't we consider the reduce cross-sectional area while calculating stress in a metallic wire?

Consider a wire which is being pulled by a force (within elastic limit) then the reaction force will be equal to the applied force then we say that the stress will be equal to applied force/cross-...
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2answers
101 views

Pressure needed to compress iron to double the density? [closed]

What is the pressure needed to compress iron to twice its density? (with "its density" meaning solid iron at room temperature and atmospheric pressure, reference 7.874 g/cm³ from Google. )
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1answer
89 views

Solid discs and coeff. thermal expansion mismatch

Consider a solid disc of radius $R$ and height $h$ which we glue onto an infinite plane surface. If we now change the temperatur and the assume that the (linear) thermal expansion coefficient of the ...
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38 views

What does elasticity with torque and twist depending on normal strain and normal stress look like?

A twisted rope has a relation between normal stress, along the rope, and twist of the rope. If a rope is twisted more it becomes shorter. If it is untwisted it becomes longer. Likewise for coils and ...
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2answers
135 views

Why can we assume long structural members to be in plane strain?

In plane strain, the strain in one direction is assumed to be zero. It is taught that if we have a structural member that is very long in one direction compared to the others, the strain in the long ...
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1answer
77 views

Hydrostatic stress and principal stress relation and Eigenvalue calculation

Why does the Eigenvalue in a Stress matrix calculate out to be $$\sigma = \dfrac{1}{3}\text{tr}(\hat{\sigma}).$$ I pretty much understand why Eigenvalues of a Stress matrix equals principal stress, ...
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155 views

Why should the bulk modulus of a perfectly rigid body be infinite?

Also, what can we say about the Young's modulus and Shear Modulus of a perfectly rigid body and why?
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2answers
232 views

How does stretching of a coil involves shearing stress?

My book has this true/false question $$\pmb {Question}$$ The stretching of a coil is determined by its sheer modulus. $$\pmb {Answer}$$ True But I am not able to comprehend as how does ...
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1answer
76 views

Calculate tire stress [closed]

I'm trying to figure out how much stress is experienced by a tire while driving. Each tire can carry a maximum amount of weight, for a tire of 98kg this is 750kg per tire. A Tesla Model 3 weighs in at ...
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21 views

Decomposition of Stress Components

When we are separating the stress matrix into two,mainly into hydrostatic and deviatoric the diagonal elements are the one which are only supposed to be affected then why are we writing a prime symbol ...
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103 views

Stress tensor and second invariant

While calculating yield stress in case of Von Mises and Tresca and proving that Von Mises in 15% above Tresca they assumed uniaixial loading while applying distortion energy theorem and pure shear in ...
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Is there a pictorial geometric interpretation of the Saint-Venant compatibility equations?

Is there a pictorial geometric interpretation of the Saint-Venant compatibility equations? Other than being a pretty system of equations possessing many symmetries, they don't mean much to me. The ...
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41 views

Deformation and strain tensor

While reading books of continuum mechanics I noticed that authors call some tensors deformation tensors and other strain tensors. My doubt is: why is right and left Cauchy-Green tensors commonly ...
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3answers
204 views

Is stress dependent on strain?

Stress-strain curves are drawn with strain on X-axis and stress on Y-axis. Usually the quantities placed on X-axis are independent quantities whereas the one placed on Y-axis are dependent. So which ...
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33 views

Total stress and total strain in thermoelasticity

For a solid undergoing thermoelastic deformation, we can write the total stress as $$ \sigma_{total} = \sigma_{mechanical} - \sigma_{thermal} $$ Where $$ \sigma_{mechanical} = C:\epsilon_{mechanical} ...
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A problem on thermal stress [closed]

Here's the question: There are 2 rods placed between rigid supports. Where $Y_{i}, \alpha_{i}$ and $A_{i}$ are the Young's Modulus, Coefficient of linear expansion and Cross sectional area of the ...

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