Questions tagged [stress-strain]

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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
69 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
68 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
972 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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668 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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55 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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69 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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148 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 ...
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1answer
42 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 ...
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1answer
41 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
161 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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82 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
98 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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1answer
46 views

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
238 views

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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59 views

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
81 views

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
236 views

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
25 views

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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6answers
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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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246 views

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
592 views

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
29 views

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
1k 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
40 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
138 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
228 views

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
332 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
2k views

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
241 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. ...
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1answer
352 views

How to find ultimate stress given true stress - true strain relation?

I am given the following problem: Consider a brass whose true (plastic) stress-true (plastic) strain is given by: $$\sigma_{T,p} = 530 \ \rm{MP}\times(\epsilon_{T,p})^{0.36}$$ To simplify the ...
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3answers
511 views

Forces in a staically determinate cantilever Truss, why some experiences compression while others experience tension?

The Redundant Truss Apparatus is constructed with units of basic triangular pin-jointed. At joint 1, it is fixed firmly due to a support. At joint 2, it is fixed to a movable support. Suppose at ...
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2answers
69 views

Is $\sin\left[2\alpha\right]\cos\left[2\alpha\right]\ge0$ a valid restriction on the angles of the principal stresses in 2D elasticity?

This question pertains to Elasticity: Tensor, Dyadic, and Engineering Approaches By: Pei Chi Chou, Nicholas J. Pagano, Section 1.4. The objective under discussion is to find the directions of ...
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2answers
81 views

Why stress always flows through the shorter/stiffer path?

Why load has a preference at which way to act? What is the reason behind this preference? Any link or comment would be welcome
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143 views

Derive mechanical pressure from strain energy density

Similarly to thermodynamic pressure, when we have: $$P_{therm} = (\frac{\partial U}{\partial V})_{S}$$ Can we define the mechanical pressure for a fluid as: $$P_{mech} = \frac{\partial \psi}{\...
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2answers
169 views

Why is torsional shear for a circular cross-section maximum at the biggest radius

Equation: Tao = (T*C)/J i know the equation but it just seems counter-intuitive that the maximum shear stress is at the biggest radius for 3 reasons that I have(thought of). 1- imagine/assume that ...
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2answers
185 views

Stress/strain within an object experiencing a single applied force

If I push an object in space, will any strain/stress happen within the object, though there is only 1 force rather than a pair of opposite forces on the object? Can be any (even if trivial) stress/...
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Drag calculation from pressure + shear stress distribution

If I know the shape of a body, pressure and shear stress distribution over it, how can I calculate the total drag acting on it ? More exactly, can I calculate it this way: Drag = [Pressure difference ...
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1answer
283 views

Strain compatibility

From this link, strain compatibility for 2D problem with strains as $$ \varepsilon_{11} = \cfrac{\partial u_1}{\partial x_1} ~;~~ \varepsilon_{12} = \cfrac{1}{2}\left[\cfrac{\partial u_{1}}{\...
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1answer
48 views

young's modulus vs longitudal deformation modulus

Young's modulus is typiccaly denoted with E. I have come accross a similar quantity called longitudal deformation modulus (in Russian literature, they call it модуль продольных деформаций) and it is ...
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1answer
211 views

Landau and Lifshitz argument for symmetry of stress tensor

In Landau and Lifshitz's book on the theory of elasticity (vol 7, theoretical physics series), specifically section 2 of the first chapter, the authors present an argument for justifying the symmetry ...
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How non-tensioned wheel scales? [closed]

As I was reading "Bicycle The history" by Herlihy I noticed something confusing. Book says that typical weight of draisine was forty to fifty pounds. But typical weight of bicycle with wooden wheels ...
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1answer
42 views

How much stress do elephants feel due to weight?

While we humans weigh around 70 kg, elephants weigh around 5000 kg. My question is: While moving or standing, how many more times than humans does the elephant feel the stress due to weight? Is there ...
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1answer
951 views

Torque exerted by pressure in a fluid

If I have a solid rigid body (let us call it a duck) in a static regime submitted to the forces of pressure $P$ of a fluid (no shear forces) I can easily calculate the total force $\mathbf{F}$ exerted ...
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1answer
1k views

Definition of Shear strain

From Wikipedia article on deformation, the shear strain is defined as the angle of the deformation. I had always thought of it as the limiting ratio of the difference in perpendicular displacement of ...

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