# Questions tagged [elasticity]

Questions related to the Continuum Mechanics Division of Elasticity. The bending of beams, deflection of rods, or in general, applications of Hooke's Law generalized to three dimensions.

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I was trying to understand problem regarding finding the adiabatic modulus given the isothermal young's modulus. I'm still an amateur in thermodynamics. I just didn't understand the final step where ...
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### Are the stress and strain tensor covariant or contravariant?

My question is related to this question but I don't find the answer there to be completely satisfactory. The displacement of an elastic medium is a contravariant quantity, which I think is pretty ...
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### What is the result of this Newton's cradle experiment where the initial ball doesn't bounce (exactly as in the regular case) but it has glue on it?

I have a question about a Newton's cradle type collision, but it has a twist to it. First, I will describe two well-known results, and then I'll add my twist. First, consider a cradle with five balls (...
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### Question about the elasticity matrix in metals

The most general anisotropic linear elastic material has 21 elastic constants. I am working with an HCP material and I found that it has 5 independent elastic constants. I am programming a subroutine ...
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### Longitudinal wave in a falling elastic body

Consider an elastic rod hung from a high point with density $\rho$ and Young's modulus $Y$, subject to gravitational acceleration $g$. The coordinate from the hanging point is $x$, while the ...
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### Why the total work to move a spring from point A to B equals the integral of all forces needed to hold it balance at every point between A and B?

I'm reading a Calculus book that mentions the Hooke’s Law for Springs that says the force needed to hold a spring at $x$ cm from it normal position is: $F = kx$, where $k$ is a constant. I can ...
1 vote
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### In-plane stresses on the surface of a cylinder

The three principal stresses on the surface of a cylinder are the hoop, $\sigma_\theta=\frac{pR}{d}$, longitudinal, $\sigma_z=\frac{pR}{2d}$, and radial, $\sigma_r=-p$, stresses. However, what are the ...
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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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### Spring constant of typical flute style champagne glass?

I am a high school student doing a lab report on the relationship between height and resonance frequency of champagne glasses, using the "singing glasses" method where you rub your finger ...
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### Equations of motion for two masses connected by the Kelvin-Voigt Model

I have a system where two particles $x_1$ and $x_2$ in one dimension are connected by a spring and a dash in parallel. This is analogous to the Kelvin-Voigt model for viscoelastic materials. The two ...
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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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### How do I define the initial jerk and yank of a cylinder subjected to impact of a rigid body at it's base?

I am trying to solve an axisymmetric longitudinal wave propagation problem during the impact (collision) of a rigid body and the base of a cylinder. On one end the cylinder is rigidly bound to the ...
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### Would anyone be able to provide a reference for the equations concerning plane strain and incompressibility?

I've been trying really hard to find a textbook or research paper that mentions the equations I mentioned in my question. Sadly, I haven't had any luck so far. Would it be possible for someone to ...
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### How to derive properly the stress-strain relation of an hyperelastic material?

I'm trying to implement a Yeoh hyperelastic model for a FEM simulation. The program requires a function that returns the second Piola-Kirchhoff stress tensor $\mathbf{S}$, with the Green-Lagrange ...
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### Contradiction of Bulk's Modulus and Pressure exerted by a static liquid

My question is about a scenario where a certain amount of air is passed through water. Now, this air will form a bubble and due to the buoyant force acting on it, it will rise. We know that the ...
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### Since when has the formula $I = \frac{b h^3}{12}$ (second moment of area) has been discovered and applied in building construction?

A question about history of physics: since when and by who has the formula for the second moment of area $$I = \frac{b h^3}{12}$$ been discovered? When has it started being applied in building ...
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### Is the restoring force equal to the deforming force in the case of plastic deformation?

I've been told by my professor that the restoring force (a reaction force) is always equal to the deforming force due to Newton's third law, and this is why stress is calculated using deforming force. ...
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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 ... 