New answers tagged continuum-mechanics
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Continuity equation derivation from trajectories of point particles
In such context, it may be suitable to define a function $w$ that to any point of space $\mathbf{x}$ is capable of associating a fictional mass value which takes into consideration the mass $m_i$ of ...
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At what speed does information move through the atoms of a rigid object?
A mechanical impulse will travel along an iron bar at the speed of sound (which will depend on the material and also possibly on the frequency and amplitude of the impulse). But in the video the ...
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At what speed does information move through the atoms of a rigid object?
The question in the title is formally contradictory. A model is always a simplification of the real world for the sake of understanding and making predicions (usually mathematically) A "rigid ...
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Wavelength of a mechanical wave in different media
The velocity v in wavelength equation can be calculated as a square root of elastic modulus devided by material density. Velocity obtained from this equation is called transversal speed of sound and ...
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What is the gradient of deformation gradient $F$?
Answer
The deformation is the application
$$
\begin{array}{rl}
\boldsymbol y:\Omega_0 &\longmapsto\Omega\\
\boldsymbol X &\longmapsto \boldsymbol y(\boldsymbol X)
\end{...
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How is the work done by rotational dry friction distributed over the surface?
@mmesser314 made a useful simplification, that the pressure is uniform over the surface. Than I specified that I want the work of friction after one rotation, and to do that I need to find the average ...
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Accepted
If the curl of the gradient is always zero why isn't it in vorticity definition? Kosterlitz - Thouless - Berezinsky topological transition
The statement that $\nabla\times\nabla f = 0$, makes a tacit assumption about $f$. It is an "ordinary" function $f: R^2\rightarrow R$.
In contrast, one can have $\nabla\times\nabla\theta = T ...
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If the curl of the gradient is always zero why isn't it in vorticity definition? Kosterlitz - Thouless - Berezinsky topological transition
As you mentioned, taking $\vec{u}=\vec{\nabla}\theta$ is equivalent to placing a line vortex at $r=0$ along $z$ . In Cartesian coordinates
$$\vec{u}=\left(-\frac{y}{x^2+y^2},\frac{x}{x^2+y^2},0\right)$...
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What's the difference between constitutive laws and equation of state?
I will answer this question the context of relativistic hydrodynamics (RH).
While in the non-relativistic case, we use the "Navier-Stokes + continuity" equations to describe the dynamics of $...
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How is the work done by rotational dry friction distributed over the surface?
The force of friction is proportional to the pressure squeezing the surfaces together. For a simple example, you might assume uniform pressure over the surface.
$W = Fd$, so you are interested in how ...
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Why is the number of independent elements of a stiffness tensor 21?
This will depend upon your constitutive equation. Under generalized hooks law you begin with a total of 81 constants. If the strain energy function has the commutative property this reduces to 45 ...
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