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2
votes
1answer
42 views

Out-of-Plane Phonons

I am trying to derive the out-of-plane phonon dispersion relation for a membrane. As far as I can tell, one of the simplest ways to do so is with a Lagrangian of the form: ...
0
votes
2answers
69 views

Potential energy of an infinitesimal length of elastic rod

I am having an embarrassingly hard time with the derivation for the potential energy of an infinitesimal element of an elastic rod of area A. The picture shown below is an element of the rod that has ...
8
votes
3answers
175 views

Continuum limit for solid mechanics

Is there a rigorous derivation of the limits for continuum properties in solid mechanics? For instance, the stress-strain relationship may be linear for large samples (the slope being the Young's ...
0
votes
1answer
82 views

Limits of Poisson's ratio in isotropic solid

For an isotropic solid, Poisson's ratio can be expressed in terms of stiffness constants as: $$\sigma = \frac{c_{11} - 2c_{44}}{2c_{11} - 2c_{44}}$$ Alternatively we may express Poisson's ratio in ...
2
votes
0answers
26 views

Simple model of fiber interaction for pressurized braided tubes

I am trying the understand the failure modes of braided tubes containing high pressure gas. Here is an example of such a braid with a variable radius: The tubes have an internal liner for sealing ...
0
votes
2answers
105 views

Compression and expansion

Why is it that solids on compression [As in striking a hammer etc.] heat up, but liquids and gases on compression [Pressurizing liquids causes them to freeze or gases to liquify] cool down? Can ...
0
votes
1answer
129 views

Area moment of inertia of regular $n$-gons over polygon center $O$

Is it possible to consider the regular polygons ($n$-gons) as deformed circles and use a pseudo-polar coordinate system to calculate their moment of inertia over its center $O$. Inasmuch as I know (I ...
1
vote
0answers
37 views

Movement of a gyroscope with non-fixed axis

Assume one has a gyroscope rotating around an axis with both ends leaning on a dedicated semiplane as shown on the picture below. There is no friction either between the rotor and the axis or between ...
-1
votes
1answer
92 views

What is the $n$ in the formula in Solid Mechanics? [closed]

The formula is about the critical force for the elastic beam that is supported by its joints: $$ P_{cr} ~=~ n^2 \pi^2 \frac{EI}{ L^2} $$ It should be based on the book Parnes - Solid ...
0
votes
1answer
191 views

What is physics of Collision between solid and liquid (or gas)? [closed]

My mind has been busy recently by this question: What is physics of Collision between solid and liquid (or gas)? What is Conservation law's of such Collision? Why, when we drop a solid object in ...
2
votes
0answers
158 views

Mechanics of Materials (pressure and temperature)

A solid right cylinder of rock core is surrounded by four rods made of mild steel (all-thread rods). The rods are placed equidistantly around the core in a square formation. The tops and bottoms of ...
0
votes
1answer
46 views

Does 'maximum principal stress fracture criteria' only apply in tensile loading?

I'm working on 3d simulation of solid fracture, primarily for graphics applications. I have one question about the Rankine fracture criteria, which is widely used in the computer graphics community. ...
2
votes
2answers
284 views

Determination of mass density distribution of an object

This is a follow-up to a previous question How can you weigh your own head in an accurate way?. My purpose is not to restart the flurry of more or less humorous jokes (which are not such a bad thing ...
0
votes
1answer
116 views

Deformation due to isostatic compression

When loading a solid material in the shape of a cylinder in isostatic compression, what is the relationship for the change in length versus change in diameter? For example. If I know that when I ...
2
votes
1answer
39 views

Organs & Oscillations: An Analysis on the Temperature Dynamics of Solids

Does temperature have an influence on the frequency of an oscillating organ pipe?
1
vote
0answers
448 views

Materials with Zero Poisson Ratio

Poisson's ratio is defined as negative ratio between transverse and axial strain. So, a material with zero poisson ratio must necessarily exhibit no transverse strain. After checking the wikipedia, ...
1
vote
1answer
79 views

Modeling elastic moduli as a continuous function in space for a single solid material

I've read a number of solid mechanics papers where a single material is modeled with constant elastic moduli (lame parameters $\lambda$, $\mu$). I've also seen composite materials modeled with ...
1
vote
1answer
229 views

Interpretation of lame parameters in solid mechanics

I think I have a pretty good understanding of the physical interpretation of young's modulus $E$ and poisson ratio $\nu$ in solid mechanics. However, I often find in mathematical papers that the ...
9
votes
1answer
734 views

Why doesn't a bus blow due to internal pressure?

When one travels in a bus, if he's sitting at any window, he will feel that the air is coming inside. If someone is standing at the open door of the bus, he'll also feel that the air is coming ...
2
votes
1answer
445 views

How to interpret the constraints on Poisson's ratio values, physically?

If I'm not mistaken, a Young's modulus $E$ can theoretically take on any positive value without bound. Physically, I interpret this as though a solid can have any arbitrary "stiffness" (within the ...
2
votes
1answer
119 views

Equivalence of turbulence in solid materials

The governing equations for a fluid and a solid are effectively the same and many times analysis can be done for a solid using the Navier-Stokes equations with the equation of state and/or the stress ...
4
votes
3answers
317 views

Does zero strain always imply zero stress?

In solid mechanics, can I always assume that if an object undergoes no strain, then no stress is applied to it? I think it's true only because I can't seem to find a counter-example.
0
votes
1answer
135 views

Why are momentum balance equations formulated in terms of net stress rather than net force?

In engineering, a steady state equilibrium force balance is typically expressed as $$\nabla\cdot \sigma=0$$ where $\sigma$ is the stress (force per unit area) applied at a point. It seems more ...
0
votes
1answer
328 views

Definition of quasi-static assumption

I'm reading this paper, where atop pg 3, the author mentions the "quasi-static" assumption for earth displacements which leads to the mechanical deformation of a fluid-solid system to be governed by: ...
2
votes
1answer
262 views

What is the spatial derivative of strain tensor?

I'm looking for a metric that contains enough information of a 3D solid's deformation: stretch, bend and twist, etc. Stretch, bend and twist may be ambiguous for a 3D solid, since unlike a rod, it ...
0
votes
1answer
144 views

what to use for mass in a 2D FEM simulation

I am trying to find the energy of a wave travelling through a solid material in a 2D Finite Element Method (FEM) - Simulation. As a general approach I would try to use $E_{kin}=\frac{1}{2}mv^2$ at ...
3
votes
1answer
859 views

Formulas for compressibility of solids

I am taking a course in mechanics this semester, as well as a course in reservoir physics. Both courses have sections devoted to pressure/compressibility of solids, but the formulas look slightly ...
1
vote
1answer
1k views

How thick does steel have to be to be able to withstand 300 bar (sphere)

How thick does the material in a sphere have to be to withstand the (inner)pressure of 300 bar if the material is steel? (With an inner-radius of 2cm) Atmosphere pressure = same as 0 meter above sea ...
8
votes
2answers
1k views

Why and how is sound produced when two objects hit each other?

When two objects collide and undergo a partially inelastic collision (so every one we experience in every-day life), they rebound to a certain degree, but kinetic energy is not conserved. Thus, the ...
2
votes
1answer
95 views

Why are rebar grooved?

Just what the title states, please. Iron reinforcement bars used to provide the framework over which concrete solidifies always appear to bear grooves. Do the grooves behave as the thread of a screw ...
4
votes
1answer
207 views

How to write classical dynamics of solids in tensor form (relation of stiffness and viscosity tensor)?

This is a question about dynamics. If I have understood correctly there should be a tensor that describes the dynamics of a (solid?) body (= viscosity ?). I mean, tensor that includes the time ...