Questions tagged [stress-strain]
The stress-strain tag has no usage guidance.
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Are you more likely to break a string when bending behind the nut of a guitar vs. when bending on the fretboard?
When I refer to 'bending behind the nut', I am referring to the action of fretting a note and then applying a downward force to one of the strings in the section labelled 'L1' in the image below to ...
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Creep mechanism (thermal and irradiation induced/enhanced) and embrittlement in fcc and bcc
When comparing FCC (Face-Centered Cubic) and BCC (Body-Centered Cubic) metals, I typically consider their packing efficiency and the number of active slip planes. FCC structures exhibit higher packing ...
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Stress in elastic material for spherical symmetric solution [duplicate]
Let $A$ be a ball of radius $R_0$ made of an elastic material. We compress the ball by applying an uniform force on the external surface till the radius of the ball is reduced to a radius $R_1<R_0$....
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Equation for the deflection of a flexible wing due to bending moments with a non-negligible rate of deflection when a point load is applied to its end
Suppose I have a model wing made of some flexible (easily bendable) plastic, I want to find a function which can describe the amount of deflection as a function of the distance from the support of the ...
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Calculation of displacement field from a strain field
I am trying to calculate the displacement field from a given strain field in 3D. It is quite a cumbersome calculation, as presented in Applied mechanics of solids by Bower;
\begin{equation}
u_i(x) ...
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Does a cube under high pressure transform into a ball?
Will a material in the shape of a cube, under high pressure, crumble into the shape of a ball?
One would expect that there will develop strains and stresses, after which the corners crumble and ...
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Stress/forces on elements in continuum mechanics
When looking at small elements in continuum mechanics, why do we draw that the stress/force the way shown in diagrams? How do we know the "pairs" of forces on opposite faces always opposite, ...
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Confused about stresses in a small element in solid mechanics
So in the diagram of a stress tensor, the normal and shear stresses on opposite faces of the small cube are equal and opposite. This is justified by equilibrium.
On the other hand, in the differential ...
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Are bodies in fluids stressed?
If air applies pressure isotropically in all directions normal and into the object, then does it mean that anything in air is stressed by the air pressure? I know that the pressure is all the same in ...
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How to conceptually explain diagonal elements of viscous stress tensor in a fluid?
How can the diagonal components of viscosity tensor be explained conceptually? In other words, how can viscosity affect the normal stress (pressure) on the cube element of the fluid?
$$\sigma_{ii} = 2\...
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Force-free condition from Cauchy stress
I have an outer Stokes problem, i.e. I want to solve (outisde of the ball $\{ r \leq l\}$):
$$ \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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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Generalizing the von Mises Criterion to Complex Stress Tensors
I was deriving the von Mises maximum distortion energy criterion:
$${\displaystyle \sigma _{\text{v}}={\sqrt {{\frac {1}{2}}\left[(\sigma _{1}-\sigma _{2})^{2}+(\sigma _{2}-\sigma _{3})^{2}+(\sigma _{...
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Is there a way to theoretically estimate the restitution coefficient of a rubber ball?
Let's consider a rubber ball like the ones shown in the picture:
When dropped onto the floor, the ball will rebound, but it won't regain its initial height.
The restitution coefficient is defined as ...
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Why lateral strain occurs when volume is not conserved on applying longitudinal stress?
I first thought that lateral strain occurs to conserve volume on applying longitudinal stress but later I realised that I was wrong. But now I have a confusion that why lateral strain occurs if volume ...
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How is the coupling between order parameter and strain determined from symmetry?
In the article
Ehrenfest Relations for Ultrasound Absorption in Sr2RuO4, Sigrist M., Progress of Theoretical Physics, Vol. 107, No. 5, May 2002
A superconductor with proposed p-wave pairing and ...
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What is a general definition of bulk modulus?
For a perfectly elastic body, Bulk modulus always remains constant and is defined as,
$$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)$$
But, ...
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Calculate bending moment for cantilever with uniformly distributed load
I am trying to understand how to calculate the bending moment for a cantilever with a uniformly distributed load so that I can build an equation of moments, as shown in this example:
I tried ...
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How to add a transverse force to a point on a simple wave equation?
Background
Imagine simple wave equation, say of a string fixed at both ends, in this form:
$$ρ y_{tt} = \frac{T}{A}y_{xx}$$
Or with an added velocity damping term like:
$$ρ y_{tt} = \frac{T}{A}y_{xx} -...
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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 ...
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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&...
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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 ...
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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 ...
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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 ...
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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 $...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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)...
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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 ...
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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 ...
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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 (...
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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 ...
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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 ...
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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 ...
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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:
$$
- \...
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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 ...
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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
$$\sigma_{xx} = 2*\mu\frac{\partial u}{...
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Question about the general Schmid’s law expression to calculate the critically resolved shear stress
I have a question about Schmid’s law for an arbitrary stress state. I found conflicting expressions and I would like to know which one is correct.
$\boldsymbol{s}$: slip direction
$\boldsymbol{n}$: ...
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Normal Stress Components of Viscous Stress Tensor for Incompressible Fluid
I am trying to get an intuitive understanding of the normal components of the stress tensor for a Newtonian Fluid.
The stress on the x face in the x direction is
$$\sigma_{xx} = 2*\mu\frac{\partial u}{...
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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}{...
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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 ...
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