# Questions tagged [stress-strain]

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### Mathematical definition of elastic materials

Physically, elastic materials are materials which return to their original state upon complete removal of applied mechanical loads under isothermal conditions. In the book "Mechanics of ...
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### Shear stress of a suspended sphere in a viscoelastic fluid

What I am trying to solve right now is that I have a magnetic particle (nanoparticle to be exact) floating in liquid that is viscoelastic and apply sinusoidal magnetic field. The applied magnetic ...
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### Stress-strain question [closed]

A thin uniform metallic rod of length $0.5$ m and radius $0.1$ m rotates with an angular velocity $400$ rad/s is a horizontal plane about a vertical axis passing through one of its ends. Calculate (a) ...
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### Why direction of stress is not pointing in opposite to that of external applied force?

Stress describes how a body responds to an external force. Or, i.e., stress quantifies the internal force that resists the applied force to maintain a state of equilibrium. So stress, as a vector ...
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### Origin of the major symmetry property of the elasticity tensor

In linear elasticity theory the stress tensor $\sigma$ is related to the strain tensor $\epsilon$ via the elastic tensor $C$. Specifically $$\sigma_{ij} = C_{ijkl} \epsilon_{kl}$$ Because $\sigma$ ...
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### Stress tensor force equilibrium in Feynman lecture book

I was reading about tensors and especially stress tensors in Feynman lectures on physics Which is on the webvsite enter link description here While reading the “31-6. The tensor of stress”, I was a ...
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### Shape change of buckled sheet under change of load

I need to solve the following problem: a sheet of flexible but inextensible material (can be modelled as cable or chain in 2D) is fixed in endpoints and buckles up. Then a variable force is applied in ...
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### Confused about shear elasticity and complementary shear stress

I am a self learner of continuum mechanic. I am confused about simple shear stress in situation similar to figure 1, in case $F_\textrm{ext}$ is caused by external perturbation by i.e., human, what ...
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### An intuitive explanation of the microscopic origin of the shear stress *perpendicular* to planar Couette flow of a gas?

In short: The symmetry of the stress tensor predicts that when there is shear stress parallel to planar Couette flow, there must also be shear stress perpendicular to it. Suppose the fluid is a ...
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### Does every point of a wire extend by the same amount upon tension?

Question. A wire horizontally over a bench has one end fixed and the other end holding some weight. The weight stretches the wire to produce some extension, say $\Delta x$. Someone puts a length ...
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### What's the difference between critical load and yield stress?

So far, I have learned of three quantities that are related to the failure of a beam (axial and longitudinal loads). The first illustrates the stress under which balsa wood will undergo plastic ...
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### Stress-strain relation in insane proportions

We have: $\sigma = E \epsilon$ and $\epsilon = \Delta L/L_0$. This seems to imply that for a constant strain, we will achieve a proportional change in length. However, it doesn't rest well with me ...
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### How would one derive the equation of thermal stress?

The equation of thermal stress is: Stress =$\frac{F}{A}$ = -$E$ $a$ $dT$, where $E$ is Young's Modulus, $a$ is the coefficient of linear thermal expansion, and $dT$ is the change in temperature. I ...
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### Stress and Strain lag for viscous materials

As stated here, In purely viscous materials, strain lags stress by a 90 degree phase. How can we derive this statement? Is it experimental? If not, which is its proof and what is the physical cause ...
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### Nonsensical dispersion relations for elastic wave propagation

In an earlier question about Einstein notation, a link was provided to a medical paper which used acoustic propagation to noninvasively detect the orientation of muscle fibers. In short, muscle fibers ...
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### What is an compressive stress region?

I read in some text that some areas of an object or some parts of an object are compressive. How is this defined? Is it that the maximum principal stress is compressive in these areas? But the maximum ...
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### Could somebody explain the stress versus strain curve?

I have already read: Stress- Strain curve but this does not answer my question completely. My problem is to understand the decrease of stress ($\sigma$) while the strain ($\epsilon$) is increasing, ...
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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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### Mechanism of heating during deformation [duplicate]

When a metal or rubber is bent and deformed, it heats up. What is the reason for this? I know that when deforming it, work is done on the object. If the object is perfectly elastic, all of the energy ...
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### Stress Due to Air Pressure

Consider a pipe. The pipe is not crushed by the air pressure because the same air pressure is acting from inside the pipe. But this means that the material of the pipe is being compressed on both ...
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### 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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### Constitutive relations and strain energy in finite strain viscoelastic solid mechanics

I'm an applied math graduate student, and my research is straying into hyperviscoelastic models of materials. I've had trouble finding an answer to this question I have about the mathematical theory ...
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### Why would a stationary exercise bike be subject to greater stress than a road bike?

I read this answer to another question: My indoor exercise cycle specifically cautions against using pedals which are not designated as being strong enough for indoor cycles. Supposedly, the stresses ...
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### Why does viscosity effect the normal component of stress in a Newtonian fluid?

The constitutive law for a Newtonian fluid is $$\boldsymbol{\tau} = 2\mu \mathbf{D} + \lambda\left(\nabla\cdot\mathbf{v}\right)\mathbf{I}$$ where $\mu$ is the dynamic viscosity. Assuming we have a ...
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The images below are from "Strength of materials" book by Timoshenko. As evident from the text, the author states that stress on the cross section pq can be resolved into normal stress and shear ...
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### Why does a flat sheet roll back into a cylinder when having rolled it once?

For example, if you were to roll a piece of paper into the shape of a hollow cylinder and then try to return the paper to its original, flat shape, it would naturally roll to the cylinder when you let ...
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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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### If net force is 0, why does elongation occur in a rod?

I was taught that stress is the restoring force per unit area (let us assume a rod). This stress is developed on order to resist the motion of the rod. My questions are as follows : If the rod is ...
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### How mechanical Strain developed in metal bar at molecular level?

If I have metal bar fixed to a support at one end while I apply a tensile force at the other end, the bar elongates while its cross sectional area decreases. I want to know How strain is developed at ...
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### How does stress “propagate” in beams?

I'm studying structural mechanics and I have been stuck on a thought. I drew a very simple cantilever beam situation. If I make a fictional cut like in my fig.1, I will be in the situation of the ...
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### (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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### How does stress in solids work? [closed]

How do you figure out what the stress equations are? How do you find a solution to the stress equation?
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### How does a Z-tube measure liquid tensile strength?

A z-tube measures tensile strength by placing a liquid within a z-shaped tube and rotating the tube until the water separates. Why can't you just use a normal tube? Wikipedia says the water will just ...
I have a stress matrix in cartesian coordinates : $\begin{pmatrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \end{pmatrix}$. How can I convert it to spherical coordinates ?