Questions tagged [stress-strain]

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7
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2answers
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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 ...
0
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0answers
25 views

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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0answers
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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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0answers
14 views

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 ...
0
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1answer
28 views

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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0answers
32 views

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 ...
1
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1answer
85 views

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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2answers
21 views

Stress v/s Strain in a heated frustum between 2 rigid walls

So consider a situation where we have a frustum b/w 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 Say we ...
2
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0answers
11 views

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 ...
0
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1answer
34 views

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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0answers
39 views

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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1answer
89 views

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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1answer
26 views

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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2answers
39 views

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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0answers
12 views

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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3answers
85 views

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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2answers
68 views

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 ...
176
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8answers
13k views

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 ...
2
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0answers
71 views

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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0answers
10 views

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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0answers
42 views

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 ...
0
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1answer
32 views

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 ...
0
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1answer
61 views

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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1answer
115 views

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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0answers
24 views

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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0answers
16 views

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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0answers
14 views

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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1answer
36 views

FEM: Distributed loads over adjacent quadratic bar elements

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 ...
0
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2answers
85 views

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 ...
2
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0answers
74 views

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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0answers
38 views

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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0answers
32 views

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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0answers
25 views

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 = \...
0
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1answer
47 views

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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2answers
61 views

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 ...
0
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1answer
120 views

Why is the partial derivative of strain energy function with respect to strain equal to stress

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}} \...
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3answers
55 views

Confusion Regarding Hookes law

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 $\...
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4answers
134 views

Stress in a rod clamped between two rigid walls when the temperature is increased

The usual approach to calculate stress is to equate thermal expansion in the unclamped condition to the magnitude of contraction caused by strain produced due to the walls. I have some questions about ...
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0answers
186 views

Elongation of rod in two cases

Case 1: Suppose there is a rod hung vertically from the ceiling. It experiences gravitational force W (its weight).It's Young's Modulus is $Y$. Now I know that the end connected to the ceiling ...
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0answers
33 views

Deformation of a circle ring under tensile force

How will it deform when I apply a tensile force to a circle ring? Can I estimate the force applied on the ring by knowing the major and minor axis of the deformation elliptic ring? For simplicity we ...
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0answers
34 views

2D Linear Elastostatics with Displacement Boundary Conditions

I am new to this type of problem and feel as if I am going in circle with regards to boundary conditions. I am interested in finding an analytic solution for: $\mu\nabla^{2}\underline{u}+(\lambda+\mu)...
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0answers
16 views

Derive Porosity from Stiffness Value

I have the Young's modulus (stiffness) values of a hydro-gel scaffolds, and I need to know the porosity of those scaffolds. I read about Nielsen Equation, which is this: $$ E = \frac{E_0 (1 - P) ^ 2}...
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0answers
40 views

Momentum in capacitor field; How can an EM field have zero momentum density but non-zero momentum flux?

Consider the case of a simple, stationary parallel plate capacitor oriented with its plates lying in the x-y plane. The E-field is simply given by: $$\vec{E} = \frac{Q}{\epsilon_0A}\hat{z} $$ with ...
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0answers
18 views

What component of the strain tensor is a strain gauge measuring in a bend test?

I am studying a bend test of a beam. The beam is set up like a 4 point bend. The force is applied at 2 locations on the top surface, and 2 locations on the bottom surface are fixed in place. It is ...
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1answer
27 views

What type of stresses occur during bending of steel rod? [closed]

When an external weight (and/or sometime by weight of its own) is tied to a horizontal metal rod, whose ends are supported by two opposite walls, the rod sags, bends due to the weight. My question is ...
0
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1answer
24 views

Determine whether a body breaks due to mechanical stress

How to determine if a body breaks if I know ultimate tensile stress of that body, other mechanical properties of the material and Cauchy stress tensor applied to the body? It is simple if only one ...
0
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1answer
35 views

Does increasing the stroke of a pneumatic cylinder create a need for a thicker wall?

So say you have a pneumatic cylinder (ram) with a certain length and wall thickness. The ram is pressurized to the same pressure each time (1000psi) Force is equal to pressure x area. So as the ...
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2answers
86 views

How to calculate materials ability to resist penetration

I would like to ask you this question which I struggle to answer. If I have a plate of some material X to which I am shooting at with a tank main gun with ammunition parameters: weight $= 10\text{kg}...
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0answers
41 views

Stress Tensor decomposition into Compression & Tensile forces

this might be a little more of an engineering question that physics but physics is my background so asking here... I'm working on a project that does a finite element simulation of a mesh. I can ...
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2answers
46 views

Question on the invariance of Hooke's law for isotropic materials

Hooke's law for an elastic isotropic 2-d material is a rank 4 tensor with 16 elements $$ \begin{pmatrix} a_{11} & a_{12} & 0 & 0 \\ a_{12} & a_{11} & 0 & 0 \\ 0 & ...