# 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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### Pressure Applied by Sphere Embedded in Elastic Medium

Consider a sphere embedded inside of an infinite elastic and isotropic medium. If a force $F$ is applied to the ball from a distance (e.g. via a magnetic field), then the ball will in turn apply a ...
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### Proof that $det \, {\bf F} = 1 + tr \bf \, H$ in a linearized setting, where $\bf F$ and $\bf H$ are deformation and displacement gradients

I am looking for a proof of that the determinant of deformation gradient $\bf F$ in a linearized setting is $det \, {\bf F} = 1 + tr \bf \, H$ Where $\bf H$ is the displacement gradient.
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### How to derive the equation of a spline inside a pipe

Let's suppose a pipe with some curves. We put an elastic bar inside. The diameter of the elastic bar is much smaller than the diameter of the pipe. We know that the elastic bar bends to minimize the ...
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### Elastic moduli interrelations for homogeneous isotropic materials

The classical equation for the Young modulus in elasticity theory for a homogeneous isotropic material in one-dimension is commonly given in the formulation $$E = \frac{\sigma}{\epsilon} \quad,$$ ...
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### Young Modulus in Finn's Thermal Physics

In Finn's Thermal Physics (equation 2.4), the Young modulus $Y$ of a stretched wire with tension $F$ is given to be $$Y = \frac{L}{A} \left( \frac{\partial F}{\partial L}\right)_T$$ However, usually ...
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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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### Elongation of a rod hinged at the end

Suppose a rod is rotating in a horizontal frictionless plane, hinged at one of its ends. If the body is non rigid, it would change its length, but I am not sure whether it would elongate or get ...
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### When compressing liquid, how much energy is converted to increased temperature vs increased pressure?

If you compress liquid in an infinitely stiff and infinity insulated cylinder such that the cylinder does not expand and no heat can transpire, how much of the energy will converted to increase in ...
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### Design an Experiment based on Castigliano’s Theorem to Determine Young’s modulus of the Unknown Member

The question states: "You need to design an experiment based on Castigliano’s theorem to determine Young’s modulus of the vertical member (unknown material) without destroying the structure." Is ...
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### Hyperelasticity: relating two PK2 stress tensors in terms of two nonlinear displacements

I am working on numerical analysis for a nonlinear hyperelasticity problem. Given that the second Piola Kirchhoff stress tensor $S$ depends on the Green strain tensor $E$, which in turn depends on the ...
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### How are body deformations modeled in Lagrangian mechanics?

With rigid-body systems, we choose a finite number of generalized coordinates to model a system, i.e. a pendulum. However, I've read that deformable bodies like elastomers have "infinite" degrees of ...
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### Why does a ball bounce bounce higher when the pressure is higher? Why does it fly faster when kicked?

A student of mine is doing a project on this topic, and I have realized that I cannot answer the question. If we are talking about dropping the ball, and assuming a completely elastic ball, it ...
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### What causes increment in volume when compressive forces are applied on an object

Doubt When compressive forces are applied on a body, what causes increment in volume. According to me the volume should remain constant since the mass and density of body are constant.
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### Work done by elastic force

I have a doubt about the work done by elastic force. The general formula of the work is: $W_{Fe} = \frac{1}{2}k(x_0^2-x^2)$; if we take that the state in which the spring is at rest, we have: \$W_{Fe} ...
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### How to measure the displacement of a force over a sphere [closed]

I know it seems like a broad answer but since it is really straight forward to measure the displacement of a beam, how do you measure the displacement of a "steel" sphere when a force is placed over ...
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### Independent Elements of Elastic Stiffness and Compliance Tensor for ALL Space Groups

In short: Does anybody know if there exists a compendium, a document, a book or a stone tablet listing the independent elements of the elastic stiffness and compliance tensors ( that is, naming the ...
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### Why do towels go crispy when air-dried but not in the tumble-dryer; when other materials don't have this effect so noticeably?

Our tumble dryer recently broke, so we've resorted to hanging our clothes on banisters etc. I've noticed that, when air-dried, towels (as well as cotton "muslin" cloths) go crispy, kind of hard, ...