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Force-free condition from Cauchy stress

I have an outer Stokes problem, i.e. I want to solve (outisde of the ball $\{ r \leq l\}$): $$ \begin{cases} \Delta u - \nabla p=0\\ \nabla \cdot u=0\\ B.C. \text{ on } u \text{ in } \{r=l\}\\ u(x) \...
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Why does a cantilever beam bend instead of shearing when a point load is applied?

I have just learnt about cantilever beams and that they are free on one end and supported on the other. In my class, my teacher showed an example of when we apply a point load at the end of a ...
Amrit Sanjeev's user avatar
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2 answers
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Reason for stress and strain

Do you think that the stress is due to strain or vice versa? I have this doubt because of two of the following scenarios: Consider the case of the rigidly fixed bar. It is now heated (say be some ...
Ankush's user avatar
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Elasticity theory: homogeneous deformations of a perfect lattice

I want to understand how the macroscopic (linear) elasticity theory emerges from the microscopic properties of matter. My question is about the model of the "perfect lattice", which is used ...
Plemath's user avatar
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2 answers
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Stress tensor from forces

Consider a body that is acted on by a variable external force density $\vec{f}(\vec{r})$. I want to know what the pressure and shear stress would be within the body as a result of these external ...
Connor Dolan's user avatar
2 votes
2 answers
158 views

Direction of shear-stress on fluid element

This image is regarding flow of viscous fluid between two parallel plates. I don't understand how they determine direction of shear stress above and below the element. As the flow is towards right ...
Qwerty's user avatar
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How can I identify a quarter or half wave plate from a used/modified Strainoptics polarimeter?

I'm a glassblower and I need to test glass formulas for compatibility. I'd like to use a polarimeter as it allows not only the detection of strain, but also informs if a glass needs to be softer or ...
Daniel Van Antwerp's user avatar
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Generalizing the von Mises Criterion to Complex Stress Tensors

I was deriving the von Mises maximum distortion energy criterion: $${\displaystyle \sigma _{\text{v}}={\sqrt {{\frac {1}{2}}\left[(\sigma _{1}-\sigma _{2})^{2}+(\sigma _{2}-\sigma _{3})^{2}+(\sigma _{...
User198's user avatar
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1 answer
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Is there a way to theoretically estimate the restitution coefficient of a rubber ball?

Let's consider a rubber ball like the ones shown in the picture: When dropped onto the floor, the ball will rebound, but it won't regain its initial height. The restitution coefficient is defined as ...
Mitsuko's user avatar
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2 answers
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Why lateral strain occurs when volume is not conserved on applying longitudinal stress?

I first thought that lateral strain occurs to conserve volume on applying longitudinal stress but later I realised that I was wrong. But now I have a confusion that why lateral strain occurs if volume ...
S K's user avatar
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How is the coupling between order parameter and strain determined from symmetry?

In the article Ehrenfest Relations for Ultrasound Absorption in Sr2RuO4, Sigrist M., Progress of Theoretical Physics, Vol. 107, No. 5, May 2002 A superconductor with proposed p-wave pairing and ...
Nitzan R's user avatar
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What is a general definition of bulk modulus?

For a perfectly elastic body, Bulk modulus always remains constant and is defined as, $$B=-V_i \frac{\Delta P}{\Delta V} \tag{1}$$ Which means, $$B \left(\frac{V_f -V_i}{V_i}\right)= -(P_f-P_i)$$ But, ...
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Calculate bending moment for cantilever with uniformly distributed load

I am trying to understand how to calculate the bending moment for a cantilever with a uniformly distributed load so that I can build an equation of moments, as shown in this example: I tried ...
eheshing's user avatar
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How to add a transverse force to a point on a simple wave equation?

Background Imagine simple wave equation, say of a string fixed at both ends, in this form: $$ρ y_{tt} = \frac{T}{A}y_{xx}$$ Or with an added velocity damping term like: $$ρ y_{tt} = \frac{T}{A}y_{xx} -...
mike's user avatar
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Surface tension versus stress in a balloon's membrane

I am conducting an experiment in which I am measuring how the internal pressure in a balloon varies with its circumference. To explain the relationship (shown in the graph below) I decided to ...
Patil's user avatar
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Given a stress tensor, how can you find the strain rate tensor?

What is the relation between stress and strain rate? If I had this as a stress rate: $$\mathbf \epsilon= \left[ \begin {array}{ccc} 0& \tau_{{xy}}\ &0\\ \tau_{{yx}} & gh &0\\ 0&...
meow im a weasel's user avatar
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How is it that on loading a spring, shearing stress is produced?

As far as I know, shearing stress is produced when layers shift parallel to each other, which means there is change in shape, and the layers are displaced in the direction of force applied. I imagine ...
Dumb person 's user avatar
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Why is Volumetric stress change in pressure not final pressure?

While reading about volumetric stress, I found that volumetric stress on a body is equal to restoring force per unit area if force is normal to the surface and is proportional to the area. At ...
S K's user avatar
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Shear stress for non-linear vs linear velocity profiles

In this question, I would like to consider 3 scenarios: 1) Fluid of uniform viscosity between 2 parallel flat plates with linear velocity profile, 2) 2 different fluids with different viscosities ...
Tan Yong Boon's user avatar
1 vote
3 answers
81 views

Thermal Expansion in a rigidly fixed rod

I was reading this topic, and this is what I Found: Consider a rod of length $L$ which is fixed between to rigid end separated at a distance $L$. Now, if the temperature of the rod is increased by $...
Adhway's user avatar
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1 answer
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Computing the strain in a cantilever beam under a known deflection

I intend to use a cantilever beam to calibrate a strain gauge, in a setup similar to the picture. My idea is to introduce a small known vertical displacement $\delta$ on one side of the cantilever ...
user386164's user avatar
3 votes
1 answer
106 views

Hysteresis loop of a balloon

According to this website explaining the science behind balloons made of latex rubber, If we repeatedly load and unload (stretch and release) a viscoelastic material the amount of energy lost in the ...
Patil's user avatar
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2 answers
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How is shear stress exerted onto a fluid?

I am currently studying fluid mechanics and one of the most important concepts we come across is that of shear stress. I understand that it is a force that is acting on the fluid in a direction that ...
Tan Yong Boon's user avatar
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4 answers
154 views

Proportionality: $I ∝ V$ or $V ∝ I $, are both of them correct?

I have a simple question that's been on my mind for a while. If both current is proportional to voltage ($I \propto V$) and voltage is proportional to current ($V \propto I$), are they actually saying ...
Peter swift's user avatar
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Buckling Question from Hibbler Textbook

Hello! I have a question from the Hibbler Textbook on Mechanics of Materials! The exact statement of the problem reads: "A W150 * 24 steel column is 8 m long and is fixed at its ends as shown in ...
jk gan's user avatar
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0 answers
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Sphere submerged in a thin layer of gel (fluid with yield stress) that is spread on a vertical wall

Imagine a uniform thin layer of a viscous gel sticking on a vertical wall. A small sphere is submerged in this gel. The gel has a yield stress (Bingham model). How can I calculate the yield stress ...
Movey Sasar's user avatar
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3 answers
175 views

Computing Cauchy stress tensor in a static cube of uniform isotropic material

As the title says, I'm interested in explicitly calculating the value of the Cauchy stress tensor in a static (non-moving) cube of some material that has uniform density an is isotropic (e.g. concrete)...
lisyarus's user avatar
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0 answers
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Uniquness of stress tensor

I am struggling to understand how to derive a stress tensor. In the picture above, I was asked to compute the stress tensor and the stress acting on the plane $\Sigma$. The x-axis and y-axis are in ...
T. B.'s user avatar
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0 answers
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Strain between two rotated lattices

I want to calculate what I believe is called the "Deformation gradient tensor" $\mathbf{F}$ between two crystal lattices. The matrix representation of the first 'perfect' i.e., not deformed ...
Okano's user avatar
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1 vote
0 answers
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Physical Meaning behind Diagonalizing the Stress Tensor

In classical mechanics we have the inertia tensor I, when we diagonalize it we get this very nice physical meaning to our eigenvalues and eigenvectors in terms of the principle axes of rotation (...
Physics_Boss_India's user avatar
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1 answer
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Why are the axial and circumferential normal stresses in an axially loaded fluid cylinder equal?

Some background: I posted this question on the shear rigidity of a fluid cylinder in a sloppier form earlier. Thanks to some helpful feedback from Chet Miller I went back and reviewed tensors before ...
Nf23kdr's user avatar
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0 answers
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Calculating stress tensor from the principle stresses

In the research paper "I. Krakovský et al., A few remarks on the electrostriction of elastomers, 1999" the authors stated the equations of the principle stresses that are produced in an ...
user134613's user avatar
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2 answers
200 views

Why Is True Strain More Accurate?

I saw that true strain is a sum of strains over many increments. Why would this be more accurate than using engineering strain? Engineering Strain assumes the initial length to be constant which makes ...
jk gan's user avatar
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0 answers
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Physical intuition for the Poisson Equation with Neumann boundary conditions

I am looking at a tutorial using Fenics for solving PDEs using finite element methods. One example that they use is the Poisson equation with Neumann boundary conditions. The equation itself is: $$ - \...
krishnab's user avatar
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2 answers
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Identifying the elastic limit? [closed]

Consider this problem I understand that the elastic limit is the point at which the material no longer elastically deforms, that is it doesn't return to its original shape. However, I am struggling ...
Quin Gardiner Bax's user avatar
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0 answers
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Stress Tensor Normal Component (Newtonian Fluid) [duplicate]

I am trying to get an intuitive understanding of the normal components of the stress tensor for a Newtonian Fluid. The stress on the x face in the x direction is $$\sigma_{xx} = 2*\mu\frac{\partial u}{...
remusconnor's user avatar
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1 answer
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Question about the general Schmid’s law expression to calculate the critically resolved shear stress

I have a question about Schmid’s law for an arbitrary stress state. I found conflicting expressions and I would like to know which one is correct. $\boldsymbol{s}$: slip direction $\boldsymbol{n}$: ...
Mauro Arcidiacono's user avatar
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0 answers
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Surface Isotropic and Shear Stress [duplicate]

I am going over a 1987 biomechanics paper looking at surface shear stress in a biological membrane, which behaves analogous to a liquid in the plane of the membrane (see image/sketch below). The ...
Nf23kdr's user avatar
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-1 votes
1 answer
217 views

Normal Stress Components of Viscous Stress Tensor for Incompressible Fluid

I am trying to get an intuitive understanding of the normal components of the stress tensor for a Newtonian Fluid. The stress on the x face in the x direction is $$\sigma_{xx} = 2*\mu\frac{\partial u}{...
remusconnor's user avatar
1 vote
1 answer
104 views

Navier-Stokes Equation confusion

I am trying to get an intuitive understanding of the normal components of the stress tensor for a Newtonian Fluid. The stress on the x face in the x direction is $$\sigma_{xx} = 2*\mu\frac{\partial u}{...
remusconnor's user avatar
2 votes
2 answers
94 views

How does restoring shear forces arise (in elastic conditions)? Do they arise from central forces or not?

When you apply a shear force onto a solid piece of material (say a block on a surface or a cantilever beam with a load) that creates shear stress in the elastic regime, there is a restoring force that ...
Maximal Ideal's user avatar
1 vote
1 answer
47 views

Are the physical properties of Tin-coated metals the same as of the substrate?

I am trying to perform a finite element analysis to plot static structural loading on a bare copper and compare the results with the tin plated copper. I do have the information about the electrical ...
DaSnipeKid's user avatar
1 vote
1 answer
44 views

Would anyone be able to provide a reference for the equations concerning plane strain and incompressibility?

I've been trying really hard to find a textbook or research paper that mentions the equations I mentioned in my question. Sadly, I haven't had any luck so far. Would it be possible for someone to ...
2 votes
2 answers
66 views

Why are pressure hulls machined to be nearly spherical?

Why are pressure hulls machined to be nearly spherical? According to Wikipedia, https://en.wikipedia.org/wiki/DSV_Limiting_Factor has a hull that is machined to be nearly spherical "for enhanced ...
bhuff36's user avatar
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1 answer
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Contradiction of Bulk's Modulus and Pressure exerted by a static liquid

My question is about a scenario where a certain amount of air is passed through water. Now, this air will form a bubble and due to the buoyant force acting on it, it will rise. We know that the ...
RON's user avatar
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-2 votes
2 answers
182 views

Why is pressure not a vector quantity? [duplicate]

A vector quantity has magnitude and direction. Pressure is force applied per area. Wouldn't that be the force having a direction towards the area? And 'as Newton came to realize, within the body of a ...
Sturburn's user avatar
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1 answer
62 views

Contracting a stress tensor

I'm reading this article, and they go from equation (3): $$ \left(s+\frac{\mu}{\nu}\right) \bar{\tau}_{k l}-\frac{1}{3} \frac{\mu}{\nu} \bar{\tau}_{k k} \delta_{k l}=2 \mu s \bar{e}_{k l}+\lambda s e_{...
ValientProcess's user avatar
4 votes
2 answers
442 views

Prove that an isotropic substance has only two elastic constants

I've been following the derivation from Ch. II-31 of Feynman's Lectures, and there is a bit that I don't understand. We start from the relation between the strain $T_{ij}$ and the stress $S_{ij}$, $$...
GingerBadger's user avatar
2 votes
1 answer
65 views

Definition of stress (Mechanical Properties of Solids)

See, it's a simple question.What exactly is stress? Is it the restoring force applied by the body in reaction to deformation force or is it the deformation force itself? I had this doubt because in ...
Asmita Kumari's user avatar
1 vote
1 answer
88 views

What does it mean for a material's elasticity to be non-linear?

Hooke's law only applies to materials with linear elasticity, usually for small displacements. Now, if you imagine having a material that does not deform permanently when crossing a specific limit, ...
Antoniou's user avatar
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