# Questions tagged [stress-strain]

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### Why is shear modulus also known as modulus of rigidity?

The book I am referring to states the following - The ratio of shearing stress to the corresponding shearing strain is called shear modulus of the material and is represented by G. It is also ...
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### How are transverse loading and longitudinal loading equivalent to isostrain and isostress respectively?

How is parallel and perpendicular loading equivalent to isostrain and isostress respecively?What is so same about the stress and strain conditions here?
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### Deformation without stress?

Elastic bodies are submit to stress whenever they are deformed. This eventually lead to break them. However, let's consider a rope. If i stretch it, it is submit to stress and will eventually reach ...
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### Why is the stress different when different methods are used?

A cantilever beam, and a uniform load acting on the beam (along with its intensity), is shown in the first picture. Its free body diagram and 2 diferent methods to solve for the stress at the site ...
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### Why is the direction of stress shown along the direction of deformation?

In the shown case of shear stress, which is a result of the deformation it undergoes, why is the direction of shear stress shown along the direction of deformation ? Considering that an external ...
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### What does strain actually mean?

A problem requires to find the stress in the portions AC and BC of the given figure when a given temperature change takes place. It is mentioned in the solution that total deformation of the ...
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### Clamped spherical pressure vessel

I am struggling to find the right terms to search my questions, so even just pointing me to reference material would be appreciated. 1) Suppose I have a spherical cap (thin), clamped at the edges, ...
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### Why are we even assuming $\alpha Gb^2$+$\alpha Gb^2$ on one case and again $\alpha G(2b)^2$ on the other case?

My point of interest is to know where the energy of two edge dislocation system comes from ($\alpha Gb^2$+$\alpha Gb^2$).It not really the formula that I am looking for but essentially why are we ...
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### Stress-strain relation in spherical coordinates

Hey so I have a timeless question but I didn't find a source to check it. Would you have a precise reference (or if you can write it that's also perfect for me) for the stress strain relation in ...
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### Is fractional volume compression the same as strain?

Context: Bulk modulus equals change in external pressure divided by fractional volume compression. Strain equals change in volume divided by original volume. So the two terms in question have the ...
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### Elastic energy of graphene: new idea for (non-chemical) battery

Is it possible to build a battery using the elastic property of graphene? Here is the stress-strain curve of graphene. Image source: https://www.researchgate.net/figure/Stress-strain-curves-of-...
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### Rigidity or Bodies with Triangular Shapes of Faces

Originally I read an answer on Quora wherein the author showed that by using magnets he made different shapes. Squares were easily deformed, so we're other shapes with square faces such as cubes ...
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### What are the transformation equations for deviatoric planes?

What are the transformation equations $$r=r(x,y,c),$$ $$\phi=\phi(x,y,c)$$ for a Matsuoka-Nakai deviatoric plane? Variables $x,y$ are Cartesian coordinates, $r,\phi$ are "polar" coordinates, $c$ ...
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### Why are springs spiral-shaped? [duplicate]

I've had this question on my mind for quite a while and looking at the web, I couldn't find an answer to this question. I've had a lot of physics experiments involving springs, unintentionally ...
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### Formula of Heat Generated by Continuous or Acute Force Exertion on Elastic Object

See the figure below. Ignoring friction but not elasticity, I am assuming the object will be deformed and heat up by part of the energy transferred by F. What does the general formula to demonstrate ...
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### Why is the deviatoric stress the stress that causes distortions?

I'm reading this text on stress. It is mentioned that the Cauchy stress tensor can be split into a sum of two other tensors: hydrostatic pressure $\pi$ and deviatoric stress. Hydrostatic pressure is ...
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### How to measure deformation in tissue?

I read some paper and they measured the deformation from 4D data in tissue (live imaging experiment). I was wondering is there any way to measure deformation in 3D data itself that means I have only ...
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### Tension in a string attached to a spring with deformation at a point

I am trying to calculate the tension in a string in the configuration shown in the diagram below. Here is a verbal description of the setup: The string is fixed at one end with the other end connected ...
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### Traceless stress tensor

What does it mean, when the viscous (or viscoelastic) stress tensor is traceless $\tau_{rr}+\tau_{\theta \theta}+\tau_{\phi \phi}=0$? Why if the viscoelastic model is linear it is traceless and if ...
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### Can dispersion relations be derived using Euler-Lagrange equations?

The question is long because of the demonstrations I give, but the problem is simple, so bear with me for a minute. I am trying to derive the dispersion relation of a semi-infinite system using Euler-...
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### Stress v/s Strain in a heated frustum between 2 rigid walls

Consider a situation where we have a frustum between 2 walls. We heat it , so it wants to expand but the walls prevent it from doing so. Does the stress in the frustum remain constant or not ?? ...
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### Does putting a part under stress change its natural frequency?

It is easy to imagine how tension changes the natural frequency of a wire. Intuitively it happens with a guitar string when you bend the neck. However, does putting a beam under stress (internal or ...
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### Poisson ratio and volume change

Consider a rod of 1 m diameter and 2 m length. The Poisson's ratio of the material is 0.5. Assume the rod is stretched to 2.5 m length. Now longitudinal strain is 0.5/2 = 0.25 lateral strain = ...
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### Can I combine two shear-stresses acting on one plane?

For example, I have an axial force and a torsion force applied on a rock socket installed in bedrock. So, the socket surface will have two shear stress generated, one in axial direction, and the other ...
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### Why are there lots of definitions for strain?

Why do we need Green or Almansi strains and what is True strain? I'm so confused about terminology.
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### Strains when one vertex of a 2 dimensional square element is pulled up

ABCD is a square and C is pulled up by a small amount(say x) keeping other vertices else fixed, what are the strains in the element. I assumed it would be same as pulling CD up by x/2 and then ...
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### Change in Volume of Objects on applying stress

I came across a statement that whenever any stretching or compressing is done on any object, its change in volume is always greater than $0$. This means that density always decreases (mass remaining ...
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### Finding a function that maps one surface to other. Deformation fields

I have a isotropic viscoelastic material, under a certain deformation I would like to find displacement field so I can find the strains and stresses eventually. The initial surface is a rectangle ...
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### Bending moment in a cantilever beam

If I have a cantilever beam of length L fixed at the left end to a wall and I hang a weight W from it's right free end then why should the bending moment at a point x units to right of the wall be W(L-...
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### Elasticity of an object [closed]

I was studying elasticity, and I thought of certain questions that I couldn't find an answer to. I'll will try to explain my queries If in the elastic limit, the strain on say a rectangular block of ...
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### Why do we bend a book to keep it straight?

I noticed that I have been bending my book all along, when I was reading it with one hand. This also works for plane flexible sheets of any material. Illustration using an A4 sheet Without bending ...
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### Does tilting a liquid develop shear stress on its surfaces?

Please help me these confusions I have. If I tilt a cuboidal container containing an ideal fluid (non viscous liquid), does a shear stress develop on the liquid due to some shearing force acting ...
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### Piezoelectric strain curves and magnetostrictive strain curves

I am trying to understand the differences in the strains produced in piezoelectric materials and magnetostrictive materials. Magnetostrictive materials will tend to strain the same way along the ...
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### Simple beam deflection of cantilever beam

Recently I had need to prove the beam deflection equation for a simple cantilever beam with a point load at the end. The equation would be in reference to the Euler-Bernoulli theory taught in most ...
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### Effect of Compression/Tension on the Rest Mass of an Elastic Solid

If I compress an elastic solid I will strain the material in the direction of the force and therefore do work that is stored as potential energy in the material. The resulting material will have no ...
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### Doubt in the derivation of the relation between Young's modulus and Modulus of rigidity

Please refer to the image attached. My doubt is marked in red. What i don't understand in this part of the derivation is that how and why is the extension and compression is equivalent to a shear ...
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### Stress and Strain in a standing wave

Where are stress and strain maximum in a Standing wave? what about a transverse wave? My book says "strain is maximum at the nodes in a standing wave". But since Antinodes are the position of maximum ...
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### Strain field and periodic boundary conditions

Let's say I have a lattice, and I impose periodic boundary conditions. I want to construct a tight-binding model on a strained lattice, and I can determine the change in the hopping parameter based on ...
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### Breaking the Strain Rate into normal and tangential components

I was looking through a set of notes on combustion and I found this definition of the strain rate at a point on a flame surface: $K_s = -\mathbf n \cdot \mathbf E \cdot \mathbf n$ where $\mathbf n$...
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### Is tensile breaking strength for torsional stress is significantly lower than breaking stress if force is applied along the axis or shear stress?

Today when I was screwing in a long bolt (10 cm, 6 mm in diameter) into a wall plug previously hammered into a concrete wall at home. While screwing-in the bolt when 2 cm were left (from bolt head ...
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I am an electrical engineering student trying to teach myself Finite Element Methods (FEM) through a couple of textbooks and independent study. While I believe that I understand the basic ideas ...
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### The relation between the spring constant and its radius [duplicate]

I've observed that the spring constant of a spring with a smaller radius is higher than that of a spring with a larger even though they are made of the same material , their thickness and all other ...
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### Total potential energy and equilibrium

Suppose a deformable body is under an external load. If there is no inclusion of gravity. When the body reach an equilibrium state, will the total potential energy be equal to zero? The total ...
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### calculate the shear stress from surface traction

The problem is that I am simulating a hollow cylinder under torsion and I would like to compute the shear stress for it. The output of the simulation is the shear surface tractions. See the figure ...
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### shear stress and viscocity

1)In a flowing fluid in laminar fashion we know that it flows in planes which slides over each other, Lets take a fluid element (cylindrical) in a pipe(Radius=R) the resistive force is (stress)(cross ...
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### Mechanics for non-standard shapes

The question I have arose when I was working my way through a derivation of the relationship between Young's Modulus, Poisson's ratio and the Shear Modulus (modulus of rigidity), \begin{align} G = \...
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### Stress tensor of a rope in equilibrium [closed]

First of all, let me say that I'm not a student of physics but of mathematics, so please be comprehensive. I'm currently studying continuum mechanics. As an example of applications of Cauchy stress ...
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### Stress tensor of an elastic medium

I don't understand a passage from the book I'm reading about tensor analysis. The state of stress of an elastic medium can be expressed by the stress function $\mathbf{p}(r,n)$ so that the force ...
In Elasticity, we have a strain energy function , $W$, that is a function of strain tensor, $E$. Then the cauchy stress tensor, $T$ can be determined by: T_{ij}=\frac{\partial W}{\partial E_{ij}} \...
I am used to seeing Hookes law in the form: $F = kx$ but in another one of my books it gives the equation: $\\ F = \frac{\lambda x}{l}$ where $l$ is the unstretched length, $x$ is the extension and \$\...