Questions tagged [continuum-mechanics]
Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles.
887 questions
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Will a frictionless rope in space retain its shape if all segments move tangentially with equal velocity?
Suppose we have a uniform, massive, flexible, frictionless and non-stretchable rope in space, initially shaped arbitrarily. Each infinitesimal segment of the rope is given the same velocity in the ...
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2 answers
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Stress tensor transformation in fixed coordinate systems
I have two fixed coordinate systems with different oriented inclined planes and I know components of stress tensor $\sigma_1$ for the first coordinate system. How to find components of stress tensor $\...
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3 answers
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Does the maximum amount of energy a spring can store depend on spring geometry?
I have two springs made from the same metal, one is a helical torsion spring, and one is a spiral watch spring. Both springs contain the same volume of metal in their active region. I wind up both ...
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1 answer
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How can the EverTune electric guitar bridge possibly maintain intonation?
There is a (relatively) recent invention in the guitar world known as the EvertTune bridge. This system has many aficionados: people have it in their instruments and swear by it. This mechanical ...
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Reynold's transport theorem in the context of compressible fluids
Reynold's transport theorem states : $$\frac{d}{dt}\int_{\Omega (t)}q\rho dV=\int_{\Omega (t)}\frac{\partial}{\partial t}(q\rho)dV+\int_{\partial\Omega (t)}q\rho \vec{v_{b}}\cdot d\vec{S}$$ where $q$ ...
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1 vote
2 answers
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Derivation of wave equation in a string without circular reasoning
The derivation for the wave equation that i found in my textbooks is using Newton's second law. However they use the formula $v=\sqrt{T/\mu}$ in the derivation. In the same textbook it is written ...
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2 answers
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In what situations may we use the center of mass for calculations?
On the Wikipedia chapter on the center of gravity, there is a calculation that shows that the center of mass is a point about which a uniform, unidirectional gravitational force does not cause torque. ...
3 votes
1 answer
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Finite Speed of Propagation for 2D Elastic Green's Function
$\newcommand{\RR}{\mathbb{R}}\DeclareMathOperator{\diag}{diag}$I'm working on deriving the analytic solution for wave propagation in an infinite homogeneous 2D linear elastic material, as a warmup for ...
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1 answer
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For the stress-energy tensor, is there an analogue to Hooke's law for $\sigma_{ij}$?
Hooke's law for the Cauchy stress-tensor is: $$ \sigma_{ij} = \lambda u_{kk} \delta_{ij} + 2 \mu u_{ij} $$ with the deformation tensor $u_{ij}$ which is calculated by $u_{ij}=1/2(\partial_iu_j + \...
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Some questions about the Reynolds' transport theorem (RTT) and continuity equations [closed]
I have been (self)studying this topic for a while now, and several questions have formed in my head by now, so this post may be a bit lengthy. Apologies for that... My first question is about the ...
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How do I calculate the time required for a super-cooled water droplet undergoing heterogeneous nucleation to complete its phase change?
Consider a super-cooled water droplet impacting a solid substrate. Upon contact, the droplet begins to undergo heterogeneous nucleation. How can one calculate the time required for the droplet to ...
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Understanding the mathematical definition of stress [duplicate]
I don't properly understand how this equation defines stress- $$\sigma=\lim_{\Delta A \to 0} \frac{\Delta F_{\rm internal}}{\Delta A}$$ How does it relate to the intutive defination of stress-"...
5 votes
2 answers
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Does glass shatter when hit by projectiles with a threshold momentum or a threshold kinetic energy?
Consider a sheet of glass (or any other breakable solid). Suppose you have many identically prepared copies of the same sheet, and you launch a bunch of fast-moving projectiles at the sheet from a ...
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Shear strain (upright cylinder) when the displacement of a layer, $x$ increases non-linearly with $y$, the layer's distance from the fixed base
We define shear strain using a simple model: an upright cylinder fixed at its base, subjected to a tangential force so that each of its cross-sectional plane (layer) slides away relative to the one ...
-1 votes
2 answers
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Normal stress of a wire (vertically hung, supporting a weight), when its cross-sectional area isn't constant throughout the length
It's easy to calculate the normal stress of a wire—whether it’s pulled along its length or supporting a mass when hung vertically—by using the formula $\frac FA$, but only if its cross-sectional area ...