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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1answer
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Cauchy tensor tensor components from Energy function

I hope someone could help me. Let $W\left( \lambda_1,\lambda_2,\lambda_3 \right) = \sum_{p=1}^N \frac{\mu_p}{\alpha_p}\left( \lambda_1^{\alpha_p} + \lambda_2^{\alpha_p} + \lambda_3^{\alpha_p} -3 \...
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Lack of plasticity of Moly wire

during re-coiling of tungsten coil wound with moly mandrel ,the mandrel is breaking in between(the mandrel is annealed before) : we don't know what exactly is causing as some length works fine and in ...
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1answer
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1. Poliamid (Nylon) Tensile Strength vs Yield Strength 2.Tensile Stress vs Tensile Strength

I am looking for mechanical properties of Poliamid PA66 and PA6. Which characteristics should be used to calculate poliamid bolts endurance? On some websites (of poliamid products), only Tensile ...
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Hooke’s Law and Energy

I have a quite a simple question that is escaping me right now. The work done on any body is just the net force multiplied by the distance the force acts on it for. For example: the work being done on ...
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2answers
424 views

What is the shear stress on a cube for a force acting tangent to one of its faces?

For a force F acting tangent to a cube's face of side length $L$, I expected the shear stress to be $F/L^2$ but my text book says it's $2F/L^2$. Also it says that this shear stress is equivalent to ...
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Tensile strain produced on two thin rods of different lengths

Suppose there are two thin rods $Y$ and $Z$ with length $L_1$ and $L_2$ respectively. $L_2$ has larger magnitude than $L_1$. Both rods have same density $p$, cross sectional area $A$, Young's Modulus $...
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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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1answer
539 views

Eccentrically loaded bolts in which the plane of loading is parallel to the bolt plane

This are eccentrically loaded bolts in which the plane of loading is parallel to the bolt plane.When deriving an equation to this particular problem almost all books start by assuming that $$\frac{F_{...
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Tensile force on a metal cable

Suppose you have a steel cable that has a certain elastic limit. Then I decide to use this cable to support an elevator of a certain mass $m$. Certainly the cable goes under some stress due to the ...
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1answer
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Area under stress–strain graph

What quantity does the area under the stress–strain graph (under the elastic limit) represent? As far as I know, the potential energy density due to strain is 1/2×(stress)×(strain). So does the area ...
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Are Rippled or Wavy Potato Chips Stronger?

I am buying some potato chips. I want to use dip. But half the time I do my chips in the dip, they break apart. Do wavy chips, with the wider bends have a greater strength? Or do the rippled chips, ...
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1answer
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Relation between decomposed stress measures

In continuum mechanics a wide range of stress measures are used. The two which I am interested in are the Cauchy stress tensor and the second Piola-Kirchhoff stress tensor. These two stress measures ...
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Cycles to failure

$$ \text{Ramberg-Osgood equation:} \hspace{41mm} \varepsilon_{tot} = \underbrace{\frac{\sigma}{E}}_{\text{elastic}} + \underbrace{\left(\frac{\sigma}{K}\right)^{\frac{1}{n}}}_{\text{plastic}}$$ $$ \...
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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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Cause of shear stress while axial loading

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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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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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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121 views

Solution of Euler-Bernolli differential equation for a simple beam

I'm trying to solve the Euler-Bernolli differential equation for an homogeneous rectangular beam without load: $$ EI{\frac {\partial ^{4}w}{\partial x^{4}}}+\mu {\frac {\partial ^{2}w}{\partial t^{...
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How much is an incandescent lamp's filament stressed by an on/off cycle?

The coiled tungsten alloy filaments of incandescent heat up greatly in use. Eventually, they fatigue and fail. Lightbulbs are rated by an number of hours of use, but along with the lit hours and any ...
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Why are the principal planes where principal stresses occur perpendicular to each other?

Equation of principal angles: $$\tan 2\theta_p=\frac{2\tau_{xy}}{\sigma_x-\sigma_y}$$ Equation of principal stresses: $$\sigma_{max}, \sigma_{min} = {\sigma_{xx} + \sigma_{yy} \over 2} \pm \sqrt{ \...
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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 ...
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How does stress change through a bar that sharply increases in diameter?

I am looking to analyse the stress through the following bar: The bar is of circular cross section, homogeneous in material, that is of a certain diameter on one half, and a large diameter on the ...
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Change of system of coordinates for the stress matrix

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 ?

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