Questions tagged [stress-strain]

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132 views

Compute stress tensor in finite element simulation

I have implemented a finite element simulation using a tetrahedral mesh that minimizes a linear elasticity potential energy. Among the main quantities I compute for the simulation is the deformation ...
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137 views

Making sense of the stress tensor for elastic deformations

I've seen this kind of formula a number of times, in the context of elastic deformations. $$ -\nabla \sigma = f $$ whete $\sigma$ is "the stress tensor" and $f$ is force. I never understood it even ...
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Why does an axially loaded column break along a 45 degrees plane?

In this video, at 7:57, the speaker mentions that columns under compression roughly break along a plane that is at 45 degrees to the axis of loading. If this is true, can someone explain why this ...
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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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A Good Book for Solid Material properties

I want to know a book which provides all solid material properties: Linear/Non-Linear Stress-Strain Data, Thermo-Elastic data (with specific heat function of temperature)... I will need them for ...
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316 views

Calculate the stress tensor on the surface of a tube

I am studying engineering and I was doing some preparation for the exam but stumbled accross the following problem: I would know how to solve task 2-4 but I am stuck at task 1. I do have multiple ...
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1answer
41 views

Pressure in a drop at equilibrium diverges at $r=0$

Assume a spherical drop. The force equilibrium writes, since the divergence of the stress tensor is null and the stress is isotropic: $$ \nabla \cdot (\underline{\underline{\sigma}})=\underline{0}\...
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1answer
284 views

Stress tensor and traction vector

Hey all. I have this problem with the above figure. The lengths of the three sides are $AB=a, AG=b, GB=c$. Also, P,Q,R are forces perpendicular to each side as you can see and P,Q,R are their ...
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1answer
116 views

Trouble connecting stress and force in continuum mechanics with my concept of force from point mechanics

I'm not very familiar with continuum mechanics and have a hard time combining my knowledge of forces from simple mechanics with what I read about continuum mechanics. Let's suppose we have a metal ...
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1answer
91 views

Why shear stress is developed only in the two set of planes for a rotating pressurized solid cylinder? Why not in the third set of plane?

In case of a rotating pressurized solid cylinder,why shear stress is not developed in the $ABCD\ \& \ EFGH$ planes while the other two set of planes are having shear stress component?
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455 views

Horizontal Beam Bending Due to Gravity

I just thought about this problem recently but am not sure where to find a solution. I am not certain which parameters are important in this problem, so please bear with me. Assume that a beam of ...
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172 views

Stress tensor decomposition and names for different components

The stress tensor can be decomposed into a spherical component (which is a scalar multiple of the identity tensor) and a deviatoric component which is the original tensor with the spherical component ...
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851 views

Where does the use of tensors to describe orientation dependence of physical phenomena arise from?

In the context of anisotropy, I have often read that the use of a rank 2 tensor is "a model". But what is the idea behind this choice? Can anyone describe in what sense the use of tensor in this ...
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1answer
273 views

Is the coefficient of thermal expansion a symmetric tensor?

Is the coefficient of thermal expansion (CTE) a symmetric tensor? For thermal stresses, CTE has to be symmetric otherwise the stress tensor would not be symmetric. So does this mean that CTE tensor is ...
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78 views

Stress tensor associated with centrifugal/centripetal load

I have some trouble to understand the relationship between internal stress tensor and the external traction force (in this example, the traction force is a volumic centripetal force). Consider a cube ...
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1answer
517 views

What is the physical meaning of the third invariant of the strain deviatoric?

In continuum mechanics of materials with zero volumetric change, the material condition can be expressed by the strain deviatoric tensor instead of the strain tensor itself. To express the plasticity ...
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2answers
259 views

Dynamic boundary condition

I need to compute the dynamic boundary condition for a small drop slowly spreading on a completely wetting, solid substrate . We are using cylindrical coordinates (s,z), and there is no flow in the $\...
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3answers
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Clarifying the actual definition of elasticity. Is steel really more elastic than rubber?

Yes, I know it's steel. It's everywhere on the web and I did google. But I seek enlightenment. My physics textbook defines elasticity as: Property by virtue of which a material regains its shape. ...
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What are the diagonal and off-diagonal elements of the stress tensor?

what does a typical diagonal element $\sigma_{xx}$ and off-diagonal element $\sigma_{xy}$ of the second rank stress tensor $\sigma_{ij}$ physically signify?
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What is the maximum tensile stress of Atomic Layer Deposition (ALD) $Al_2O_3$?

I am looking for the maximum tensile stress of ALD (Atomic Layer Deposition) Al2o3, but I have only found this paper, where they found the maximum tensile strain: https://doi.org/10.1063/1.3567912 ...
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1answer
111 views

Why is the force on a cross section of a rigid body equal to the force over the entire body?

If we have a block of mass $m$ (distributed uniformly) and a force $F$ acting on it, the block would begin to accelerate with an acceleration $a$. Obviously, the mass of half of the block is $\frac{m}{...
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16 views

What stresses should be considered to determine the effective stress and FOS?

This question I tried to solve by considering the torsional shear and transverse shear and axial loading. But the answer is not clear. But the answers that I got by different trial and error method ...
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1answer
39 views

Debris ring formed from breakup of extreme-high rotation rate of rigid ring

In Larry Niven's Ringworld, where there is a rigid rotating ring with a radius of 1AU with the Sun at the centre, he introduces a fictional material "scrith", which apparently is strong enough to ...
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1answer
58 views

Wave equation on Air- Solid interaction

Suppose that there is, due to an explosion $h$ meters above the ground, a wave in the air with high density, velocity and pressure, capable of inducing an elastic wave on the earth's surface. How does ...
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1answer
413 views

Calculating the pressure between a housing and a shaft in an interference fit

I'm trying to calculate the pressure between a journal/shaft and a housing bore in a case of interference fit. Considere a 2D axisymmetric (effectively 1D) journal bearing with interference fit: ...
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1answer
813 views

If fluids have zero shear modulus, how do I make sense of graphs like strain rate vs shear stress (to classify fluids as Newtonian or non-Newtonian)?

Following the definition on the wiki: Fluids are substances that have zero shear modulus, or, in simpler terms, a fluid is a substance which cannot resist any shear force applied to it. If fluids ...
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172 views

Strain/displacement field dynamics

I am trying to model a viscoelastic fluid and I am having a difficulty understanding the equations. Basically what I want to model is the dynamics of the system, which is confined between two ...
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3answers
5k views

Why is stress a scalar quantity, even though mathematically, it is (Internal restoring force/Area)?

Basically, what I need to know guys is that when we divide a vector by a scalar, we get a vector. Then what is different in the case of stress?? I mean, WHY IS IT STILL A SCALAR?
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Intuition behind non-local stress tensor

Starting from the following Reisz Fractional Integro-differential formula (see for example https://www.amazon.com/Fractional-Integrals-Derivatives-Theory-Applications/dp/2881248640, chapter 25) $$ I^{...
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1answer
125 views

Curvature of a beam when subjected to an axial force

How do you calculate the curvature of a beam due to any forces acting parallel to the beam? Intuitively, a beam in real life would bend perpendicular to the force to form an arc. How is this ...
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2answers
814 views

Strain on a steel wire explanation

I want to ask a question about strain in a steel wire that I read in a book titled Advanced Physics by John Miller. A passage of the book on Materials reads: Consider 2 steel wires being stretched by ...
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1answer
378 views

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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1answer
58 views

Why does a rotating flexible disk have wave shape?

I found a video on which they shatter CD with a high RPM tool. Before the CD shatters it has a wavy shape, so I guess an axial force shatters the CD instead of a radial force, probably some kind of ...
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1answer
140 views

Thermal expansion stress and strain [closed]

I'm having trouble with this question: https://i.imgur.com/rWK0RNI.png and this is the work i've done so far: https://i.imgur.com/wy0IeTQ.jpg Am I going along the right lines? It seems its a 3 ...
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1answer
3k views

Solid Mechanics — how to find pure shear stress state?

I have a question regarding Solid Mechanics and Mohr's circle. In my test today, we had a plane stress state represented in a Mohr circle which was not centered at the origin. The question asked to ...
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2answers
2k views

How to find increment in length of rope due to its own weight?

I used stress/strain = Young modulus and am getting mgl/AY. . where m=mass l=length A=cross-sectional area and Y= young modulus.The correct answer is mgl/2AY. Where is my mistake?
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49 views

Why moving plunger in cylindrical tube can be considered as plain stress condition?

The plunger moves in the tube as you can see in the picture. This situation is plane strain, but i don't see it, i mean there are stresses in all directions so how is it possible to view this as plane ...
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1answer
133 views

Pressure of electrons in a metal

Suppose we apply a tensile/compressive stress of, say, 2 atm on a metal rod. If we consider a metal as consisting of electronic and lattice subsystems, could we say the the pressure of the conduction ...
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1answer
171 views

How to determine the increment term of normal and shear stress in infinitesimal cube ?

Consider a solid body, if it is in equilibrium then every infinitesimal part of the body is in equilibrium so i take an infinitesimal cube with side lengths, $dx$, $dy$ and $dz$ and try to write the ...
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1answer
573 views

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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1answer
48 views

Total Differentials Fluid Mechanics

I'm having trouble with total differentials in relation to the attached picture (fluid deformation). I don't understand how the expressions for ${\rm d}u$ and ${\rm d}v$ come about. It looks like $u =...
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2answers
332 views

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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1answer
81 views

concept of pressure

i am at a stage where i really need to have an in depth intuition about properties governing nature; and when i look at force, i can picture its effects it in my mind(change in movement,deformation) ...
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159 views

Forces on arbitrary surface from the shear tensor

I'm doing CFD calculations using an Open source code. The code solves Navier-Stokes equations and I can get the velocity and pressure fields. From the velocity field I managed to reconstruct the shear ...
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54 views

Vector Interpretation Equivalent of Tensor Interpretation

Take the stress tensor as an example. Given a coordinate system, the state of stress is uniquely determined by the 9 components of the stress tensor. I interpret this statement as (please correct me ...
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2answers
8k views

When a rubber band is stretched, it returns slightly larger. What is this effect called? Is there a material/property that doesn't exhibit this?

A rubber band that has a 5 cm diameter (Assume a perfect circle). The rubber band is then stretched. The rubber band returns to it's original shape. The rubber band now has a 6 cm diameter. What is ...
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189 views

Plastic deformation in steel cable [closed]

Assume we have a steel cable with length 1m and it's diameter is 15mm. The cable has a youngs modulus = 200GPa, yield strength = 500MPa and tensile strength = 580 MPa. We attach a brick that weighs 10 ...
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2answers
159 views

Continuum mechanical analogous of Maxwell stress tensor

Maxwell stress tensor $\bar{\bar{\mathbf{T}}}$ in the static case can be used to determine the total force $\mathbf{f}$ acting on a system of charges contanined in the volume bounded by $S$ $$ \int_{...
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1answer
157 views

How to deduce the following equilibrium equation?

I have seen the following free-body diagram in an engineering paper, J. Compos. Constr. 9, 388 (2005) (e-print): As it is mentioned in the paper $f_j$ is the stress in the FRP layer (which acts ...
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1answer
337 views

Principle of superposition in uniform compression of bar

With the following quantities defined as follows: Normal stress along x, $\sigma_x = \frac{F_{nx}}{S}$ Strain along x, $\epsilon_x= \frac{\Delta L_x}{L_x}$ and Poisson's Law: $\epsilon_y=\epsilon_z=...

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