Questions tagged [stress-strain]
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What do the different elements in strain tensors tell us?
I'm working with strain tensors of all sorts at the moment, and I think I've understood how they're derived. However, I'd like to get more intuition of what they're actually telling us.
More ...
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Stress and Deflection of a curved elliptical beam with circular cross section and fixed at both ends loaded by a point load at the center [closed]
Can someone help with the max stress and deflection analysis of an elliptical curved beam with 2 fixed ends, loaded by a point load F at the center of the arc, with a and b as the large and small ...
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Why does the torsion in a circular bar result in shear stress along the axial direction?
In the case of pure torsion, how does a differential area on cross-section of the cylinder with dx length undergo a shear force that is perpendicular to the cross-section ?
I can understand that a ...
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Necking point in a Stress-Strain plot
Why doesn't the necking start after the yield point but starts from the point of maximum tensile stress in a stress strain curve? Volume being constant during elongation, the reduction in area should ...
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Why am I wrong when calculating the atomic system's stress?
Assume a static non-periodic-bounday-condition $N$-atom system in a cuboid box only have potential energy $U$, which is merely the function of all atom positions, i.e.,
$$U=U(\{{r_i}\}) \tag{1},$$
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Mass conservation in a deformed membrane in cylindrical coordinates
This is clearly an obvious question but here is my issue.
Context :
We assume an axisymmetric deformation of a membrane, and work with cylindrical coordinates $(r; \phi; y)$. At time $t = 0$ we let $r$...
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FEM: in-plane rotation of a plate
I'm writing finite element code in 3D, and I wish to connect vertical (Euler-Bernoulli) beams to a horizontal plate. The deformations of a beam are well described, but for the plate it is more ...
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About the stress generated inside an object
Case 1 is the case where the external force F acts on a point of an object passing through the center of mass, and Case 2 is the case where the external force F acts evenly on the surface.
In both ...
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Using Hertzian contact mechanics to explain fracture cones when an elastic sphere is pressed onto an elastic half space
I'm trying to understand the Hertzian cone fracture process from a continuum mechanics point of view. I'm considering a problem where an elastic sphere is pressed quasi-statically onto an elastic semi-...
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Stress strain diagram for a spiral spring
I know that the stress strain diagram for steel looks like:
If this is experimentally determined usually a cylindrical piece of steel or a straight wire is used (from beginning of the experiment).
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Is there a way to mathematically model the stress/strain graph of a material after the limit of proportionality? [closed]
I am currently working on an application that simulates physics experiements, and am struggling to find a way to model the graph after the limit of proportionality. I have constrained the simulation ...
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Why the Cauchy Stress Tensor & the Stress-Energy-Momentum Tensor have the same SI units?
Shouldn't adding time as a dimension changes the Stress-Energy-Momentum Tensor's units? What math operation(s) (if any) would transform the 3D Cauchy Tensor into the 4D Energy Momentum Tensor of GR?
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What is a Poisson Solid?
I've found on a few places on the internet references to a solid where both Lamé parameters are equal ($\mu=\lambda$), making its Poisson ratio $\nu=0.25$. It seems to be some sort of an 'perfect ...
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Why is the extension in the rod not same in both case?
I know that when you pull a rod from one end as shown in the figure
such that it is accelerating on a smooth horizontal floor with no friction, the average tension would be $F\over{2}$. And So stress ...
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Minimizing the potential energy in a hyperelasticity problem
I am currently using the FEniCS/DOLFINx package to simulate deformations on a mesh volume.
Following this tutorial, I am using the following equation to find $u$ such as $L(u)=0$:
$$L = \vec{\nabla} \...
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Maximise rigidity of tube/rod [closed]
I understand that for a given quantity of material a tube is stronger than a rod.
I have a 1.4m clear acrylic rod with 16mm diameter however it is too flexible for its intended purpose (imagine ...
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What is the difference between elasticity and stiffness? [closed]
Modulus of elasticity indicates Elasticity(E) but stiffness(specifically in case of axial deformations) is given as EA/L where A is area and L is length of body. These expressions led me to believe ...
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Why is the stress on a body not a vector?
In my textbook, Physics, Part II—Textbook for Class XI, there's a line which talks about why stress is not a vector:
Stress is not a vector quantity since, unlike a force, stress cannot be assigned a ...
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Finding strain in an aluminium plate
I am trying to find strain theoretically in a aluminium plate to compare it against strain gauge value. The aluminium plate of dimension 400x99x4 mm (lxbxh) is fixed in cantilever structure and a ...
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Relationship between the von Mises criteria and Johson-Cook & Johnson-Holmquist 2 model
I'm new to the world of material physics so please bear with me.
Von Mises Criteria
The von Mises criteria states that a material starts to yield when its equivalent von Mises stress:
$$\sigma_V = \...
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How to solve this equilibrium equation for a scarf joint? [closed]
I was reading a book on bonded joint analysis and it references Erdogan and Ratwani 1971. On page 11 of this paper they write an equilibrium equation from their freebody diagram. I don't understand ...
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Follow up question to: Continuum mechanics cauchy stress
Follow up question to: Continuum mechanics cauchy stress (Sorry for the late reply, I wrote this comment on the existing question and it was deleted be the admin)
thank you very much for the ...
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Where would a string break if an instantaneous UNEQUAL tensile force is applied on the ends?
Similar to a question asked previously except this time with unequal tensile forces at the ends: Where would a string being pulled from both sides snap and why?
Assume the string is homogenous.
Would ...
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Poissons ratio for a 1x1x1 cube made into a 2xYxZ
Consider a 1x1x1 cube. It has a volume of 1. If the material is isotropic and the poissons ratio is 0.5 the volume should be conserved.
consider then I stretch one side so it has a length of 2. The ...
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Does (supporting) rope tension at angles below 45 degrees, increase under load & how?
A (semi) cantilevered object such as a door canopy / porch bolted to the face / lintel area of a wall, often requires rod/rope support at the free end. The "lightweight" supporting rope or ...
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Vector Form of strain Compatibility
I was reading the book called energy principles and variational methods in applied mechanics-J.N Reddy. In that I came accross this ∇×(∇×ε) = 0 notation for strain compatibility equation. I understand ...
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Continuum mechanics cauchy stress
I have a question regarding the stress tensors. In a publication I found the following definition:
I havnt seen this equation before, and I am wondering how to get there. T is the Cauchy stress, Je ...
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Is there a lower limit for a force to create strain in a material? [duplicate]
According to Hooke's law, any stress, as small as it may be will result in strain. Since stress is the internal force per unit area, it arises that any force, as small as it may be, will result in ...
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How to obtain the equivalent Young Modulus in Hertzian contact?
I would like to understand why there's a $\nu²$ in the expression of the equivalent Young modulus in the Hertzian contact theory.
Here's a common expression for an elastic sphere crushed on a rigid ...
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Radial stress of a cylinder that is longitudinally excited
Consider a cylinder that is longitudinally excited on one of its ends and fixed on the other one as shown in the picture below.
In the cylindrical coordinate system, the displacement vector $\bf u$ ...
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Derivation of the Navier–Cauchy elastostatic equation in cylindrical coordinates
I found the Navier–Cauchy elastostatic equation in a lot of literature expressed in the Cartesian coordinate system. However, I didn't manage to find it anywhere in cylindrical coordinates, so I tried ...
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Can the universe break like a balloon that pops?
I have been investigating inflation and the big difference in the theoretically predicted value of the cosmological constant and the actually measured value of it. There would be 120 orders of ...
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Cyclic values inside stress tensor in given configuration
i have majored in mechanical engineering and implemented a fully working FEM-Solver for structural mechanical problems for 2 and 3-dimensional problems. I have lately been working on bringing this to ...
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Error of deriving the variable cross section rod wave equation
On page $519$ of the book Engineering Vibration (which can be downloaded from here), the following wave equation of a variable cross-section rod is derived:
$${ {\partial}\over{\partial}x} \Big( EA(x){...
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Strength Calculation of a Simply Supported 3D rectangular beam Under Loading As Shown In Image Attached
For a 2D and 3D circular beam we can easily calculate the strength of beam and reactions using beam theory.
The same can be used for 2D rectangular plate.
Also for a 3D rectangular plate with uniform ...
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Symmetric stress tensor in fluid Mechanics for a cube
In textbooks and online I read that conservation of angular momentum of a cubic element of fluid guarantees the symmetry of the stress tensor. I am not sure how to make this work. See the figure below,...
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If Strain is change in dimension upon original dimension, then shouldn't shear strain be change in angle upon original angle? [closed]
Strain is defined as change in dimension upon original dimension. Shear strain expressed as Δx/l, doesn't seem to fit the earlier definition of strain.
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Torque equilibrium of a cylinder
In the process of deriving the stress tensor of a cube which is shown in the picture below, it is concluded from the torque equilibrium equation that $\sigma_{ij}$ is equal to $\sigma_{ji}$. I am ...
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How to figure out if stress is distributed uniformly?
What causes us to think that the stress is distributed uniformly over
the cross sections A and B?
Figure: Force F applied to a stationary bar
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Why would the stress-strain diagram differ for tension and compression in inelastic region?
The question came to me when I read the following statement: "The stress-strain diagrams
may differ in the inelastic region for tension and compression. But these differences may be reasonably ...
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Two Different Forearm Movements
I came up with this thought 2 3 days back that when my move my forearm in two different sense I feel different strain/pain.
First start assuming that your hand is like this.(i.e. the forearm and arm ...
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Young's modulus for a string that is being applied by two unequal forces at the both ends
In space for example if we apply two forces 10,6 respectively at the end of an elastic string (10 at the right end and 6 at the other) then obviously that body will expand and accelerate. But how ...
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Computing the maximum force a rod can bear [closed]
Suppose I had a rod of diameter $d$ composed of some material with tensile strength $T$. If I then exterted a pulling force $F$ on the ends of the bar, how do I compute the force $F$ for which the ...
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What is the divergence $S^{k}{}_{i,k}$ of a force component of a stress tensor called?
The following is from Hermann Weyl's Space-Time-Matter. Notice that
$$\mathfrak{p}=-\left\{ p_{i}=S^{k}{}_{i,k}\right\}$$
is equivalent to a volume force. But, from the infinitesimal view, it is the ...
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Electromagnetic stress-energy-momentum tensor and stress tensor
The purely spatial components of the energy-momentum-stress tensor for a perfect fluid are clearly related the components of the ordinary stress tensor inside the fluid. My question if this case is ...
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Stress and equilibrium
By newton's third law, all internal forces in a portion of volume must be zero. Thus the total force is due to other volume portions exerting force onto the surface of said portion. However, if one ...
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Continuum Mechanics: Momentum Balance Equation of infinitesimal square [duplicate]
Introduction:
According to the theory, the stress tensor should be symmetric. On This page, and on many others, the explanation is: Taking the rotational equilibrium around the center of this 2D ...
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Deriving the wave equation of a variable cross-section rod subjected to non-uniform pressure
On page $519$ of the book Engineering Vibration (which can be downloaded from here), the following wave equation of a variable cross-section rod is derived:
$${ {\partial}\over{\partial}x} \Big( EA(x){...
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What is the intuition behind the ${\nabla u^T}$ term of the stress/strain tensor for a Newtonian fluid?
$$\epsilon=\frac{\nabla u+ \nabla u^T}{2},$$
$u$ is vector displacement, and $\nabla u$ is the gradient matrix of $u$.
Now for a Newtonian, incompressible fluid, this describes the shear stress forces ...
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How to interpret XRD results?
I am given several datapoints of XRD strain information. It comes from XRD measurement of a thin layer (100 nm) of semiconductor deposited on top of another semiconductor.
The result I'm given is ...
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