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Questions tagged [stress-strain]

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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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1answer
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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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1answer
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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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If you chuck a rigid triangle into a curved space, what happens?

As a follow up to How exactly does a real object (e.g. a triangle) behave considering the effects of non-euclidian geometry?, let's say you take a large steel triangle (in a region of space that is ...
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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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1answer
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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 ...
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2answers
38 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 ...
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0answers
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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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1answer
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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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2answers
54 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 ...
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1answer
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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
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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
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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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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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23 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
25 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
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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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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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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
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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 ...
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1answer
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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 ...
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1answer
33 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
73 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
39 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
41 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 & ...
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0answers
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Kelvin solid and deformation in transverse direction with Poisson ratio

A Kelvin-Voigt material is a material with such a behavior : I'm wondering if there is a way to model in a similar way the deformation in the transverse directions $y$. Meaning we have for the ...
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1answer
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Statics and dynamics in elasticity : how to add time in elasticity

In elasticity, there is are static relations of the form $R(\sigma,\epsilon)=0$. In fluid dynamics, there is a dynamics relation with the conservation of momentum leading to Navier-Stokes equation. ...
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2answers
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True strain, engineering strain, strain gauges

I've been somewhat confused over the concepts of true and engineering strain, and I just want to see if I am understanding this correctly. Let us denote true and engineering strain as $\epsilon_t$ ...
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impossible Poisson's ratio of Lennard-Jones potential type solid (cubic cristal for example), or any potential depending on $r$

We know (for instance : https://en.wikipedia.org/wiki/Poisson%27s_ratio ) that the Poisson ratio is $\nu=1/2-Y/(6B)$, with $Y$ the Young modulus and $B$ the bulk modulus. Let's assume we have a ...
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1answer
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Why does the stress strain curve depend upon strain rate?

I was going through this website :https://www.tf.uni-kiel.de/matwis/amat/iss/index.html where it answered a question: Why is the maximum of the (nominal) stress-strain curve and the beginning of ...
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2answers
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Can a diamond pipe prevent water from freezing and bursting the pipe?

I know a diamond vacuum blimp is not possible because it will implode under air pressure. Is it possible for a diamond pipe to keep from bursting with frozen water? I found nothing online except ...
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1answer
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Relation between strain and velocity

The strain tensor writes $\epsilon_{ij}=\frac{1}{2}\Big(\frac{\partial u_i}{\partial x_j}+\frac{\partial u_i}{\partial x_j}\Big)$ with $u_i$ the displacement in the $i$ direction. Then $\frac{\...
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1answer
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Why is principal strain parallel to principal stress for high symmetry crystals

Let say we obtain $\epsilon_{11} = S_{1111}\sigma_{11}$, for a single stress in a 11 direction, meaning that $E=\dfrac{1}{S_{1111}}$. Due to high isotropy of material the Poisson ratio is constant. ...
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Can any body be uniform in the universe?

If I take any body in the shape of a rod and stretch that, after it reaches breaking stress it breaks at one point. Even though we apply the same the stress on each and every part of the rod it broke ...
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0answers
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How to explain a strength of the sphere in simple terms?

In our high school's physics book (in Turkish), a strength of the material is discussed in simple terms given by Galileo: The strength of the material is proportional to its cross-section area divided ...
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1answer
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Strain gauge vs linear variable displacement transducer

For measuring deformation experiments, it seems that strain gauges and linear variable displacement transducers (LVDT) are commonly used. If the material exhibits geometric linearity, then couldn't we ...
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Stress-Strain behavior of ceramics at high temperatures

Can someone explain to me why do we observe the peak in the stress strain behavior at 1400 C and then a sudden decline followed by gradual increase? What does it signify? Does it have anything to do ...
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1answer
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determine the shear stress and bending moment of the next axis

I have problems to raise the equations. They could recommend me a text to be able to solve it.
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1answer
206 views

Young's modulus and shear modulus relation - temperature effect

Young's modulus and shear modulus are related by $E=2G(1+\nu)$ (for isotropic and homogeneous materials), $E$ is Young's modulus, $G$ is shear modulus and $\nu$ is Poisson's ratio. I can do experiment ...
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1answer
34 views

Amplifying stress at near perfect vacuum?

So, I've got a vacuum chamber as part of a home freeze drying project. It is a cylindrical steel pot with a 1.5in acrylic lid. The manual is poorly translated from Chinese, so some of it is seemingly ...
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2answers
69 views

Terminology for how bendable an object is and what affects the bendable-ness of an object

I was wondering what the term is for how bendable an object is. Also, does this feature vary depending on the thickness of the object? Say, for example, I want to know how bendable a ruler is. Does ...
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1answer
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Why are there no vertical normal compressive stresses when a horizontal beam has a vertically applied load?

In a beam with a a single vertically applied load and a single vertical reaction force, as well as a reaction moment, for example, this one: We would typically consider the normal stress ($\tau_{xx}(...
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1answer
129 views

(I-beam vs rectangular beam) Which sword blade cross section is less likely to break?

Original question Assumption: i made several swords with different cross sections (lenticular, single broad fuller as in viking swords, diamond, hollow ground diamond) the blades are made using the ...
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2answers
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Is the Young's modulus the same for compressive and tensile test?

I want to know the Young's modulus for a compressive test, but I have just a tensile test. Are they of the same value?
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4answers
100 views

Uniaxial stress question

Let's have a rectangular profiled bar. Let us introduce force $\vec{F}$ which pull the bar apart. In the picture below let us make a virtual horizontal cut $A$. Well, everything is in the picture. ...