Questions tagged [stress-strain]

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1answer
44 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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18 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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30 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
33 views

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
60 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
59 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
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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
44 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
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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
45 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
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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
82 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
57 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
61 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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1answer
31 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
86 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
64 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
24 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
98 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
65 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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0answers
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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
57 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
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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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1answer
102 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
117 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
68 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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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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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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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
109 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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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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3answers
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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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1answer
39 views

For stress-strain curves, how can we differentiate if it is a composite or a metal?

For the following stress-strain curves we have to choose which one corresponds to aluminium and which one to carbon fiber, a composite: We think the carbon fiber should be the one with the higher ...
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1answer
23 views

Why is taper given to the top of the steel vessels?

In many form of liquid storage vessels, a taper or something similar to it is always provided. The head of a pressure vessel is connected to the main body mostly using hemispherical or tapered portion....
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0answers
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Why does brass fracture at a 45° angle?

These images were from a demonstration of a brass sample exposed to intense longitudinal (axial) pressure. Initially it was squashed resulting in some bulging outwards and sideways distortion, but ...
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3answers
52 views

Bending of a metal plate

If I have a stiff metal plate, and several forces acting on it at specific points, how would I calculate the resulting shape? What information, besides the forces acting on it, would I need?
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3answers
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Why can a rigid beam stay straight when load is applied to it when a rope can't?

I know why the rope sags but I don't understand why the same argument can't be made for the beam. What is it that allows the beam to stay straight when a mass is placed on it?
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1answer
39 views

Compute the stress curves for the half-circular arch beam

I'm very new to static mechanics and need some help to check my solution. We have that, $$R_A+R_B=0,$$ so given the equilibrium $$P r/2 + R_B 2r=0,$$ we find that $R_B=-p/4$ and $R_A=p/4$. Now, for ...
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1answer
257 views

Permanent set point vs Elastic limit

The following is what I read: If, however, the elastic limit is exceeded, only the elastic strain will be recovered, and the plastic strain will remain as permanent set. The stress in the ...
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1answer
42 views

Why are parts of a cylinder closer to centre elongated less during torsion?

Say we have a fixed cylinder with a radius of R. Looking at any cross section, the shear stress at a radius (r) is given by τ = G γ . I understand that the particles at the outer radius (R) twist (or ...
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Deriving the dynamic friction of an oversize shaft in a hole

I want to derive the force of dynamic friction of an oversized shaft in a hole. Suppose the dynamic coefficient of friction is $\mu$. Here is my attempt. Suppose the hole has diameter $d$ and the ...
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0answers
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Can we construct a (specially designed) truss that is horizontal when supported from one end?

It is not possible to support a horizontal beam from one end, and the same is true for an I-Beam. I believe this can also be proven for a pipe, but that proof is just outside of my reach. But all of ...

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