Questions tagged [solid-mechanics]

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18
votes
3answers
10k 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 ...
15
votes
4answers
17k views

Hollow shaft vs. Solid shaft: Which one's more resistant to torsion?

I recall being told once that hollow rods/shafts tend to resist torsion more than solid rods/shafts...but I wasn't told why this is the case. Now that I'm a little older, running this "fact" through ...
12
votes
2answers
1k views

Is Young's Modulus a Lorentz Scalar?

If a spring is at rest and lies along $X$ axis in a frame $O$ with a spring constant $k_{0}$ then its spring constant in a frame $O'$ which is moving with a speed $v$ at an angle $\theta$ with the $X$ ...
11
votes
1answer
960 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 inside....
11
votes
3answers
1k 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 ...
9
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3answers
366 views

Is there any dynamical reason for the winter solstice to happen close to the perihelion?

When the winter solstice arrives, the angular momentum of the Earth, its orbital angular momentum and its radius vector with the orbital focus in the Sun are in the same plane. This happens quite ...
8
votes
3answers
263 views

Is it possible to reassemble a perfectly cleaved crystalline solid?

This is a purely theoretical question about "perfect" solids under "perfect" conditions. Assume you have a crystalline solid with a perfect crystal lattice (i.e. no defects). Let's imagine a cube of ...
8
votes
6answers
20k views

Why rubber is incompressible material?

Why rubber is incompressible material? I know its Poisson's ratio is nearing to 0.5. So I don't understand physically, what it means by 0.5 Poisson's ratio and incompressibility. When I tried ...
7
votes
2answers
504 views

Why are springs spiral-shaped? [duplicate]

I've had this question on my mind for quite a while and looking at the web, I couldn't find an answer to this question. I've had a lot of physics experiments involving springs, unintentionally ...
7
votes
1answer
1k views

Is there a solid material with low acoustic impedance and low attenuation coefficient?

Is there a solid material with both a low acoustic impedance (specifically, an acoustic impedance as close as possible to that of the air) as well as low attenuation? In other words, is there a ...
6
votes
4answers
7k 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.
6
votes
5answers
247 views

General plane motion and freely floating rigid body

Consider a rigid rectangular plate of length $l$, width $w$ and thickness $t$ which is at rest and is floating freely in space (no gravity). The center of the plate is at $O_L$ with respect to global ...
6
votes
1answer
121 views

Why do ribbons curl when we stroke them with scissors?

I have recently learnt how to make quilling swirls [also called paper filigree] ,one of the methods to curl the paper strips is to quickly run your fingernail on the underside of the strip you want to ...
6
votes
0answers
87 views

Is there a scale at which all solids can be treated as fluids?

I was answering an Earth Science SE question that involved the reasons why Earth has an equatorial bulge, and wanted to make an offhand comment such as "Real planetary constituents aren't this strong; ...
5
votes
2answers
6k views

Question regarding thermal expansion of a bi-metallic strip

I was reading about bi-metallic strips and came to know that on heating it forms an arc like shape. I also read a sentence that said the radius of such an arc can also be calculated which will be ...
5
votes
2answers
2k views

Why plane stress condition is taken for thin plates

Why plane stress is taken for thin plates? It says in the books that the stress variation is small for thin components and is close to zero. Why is that so? Also why stress at free surface is zero? (...
4
votes
1answer
155 views

Why isn't there a “parallel” Pressure as there is a parallel or shear Stress?

I had this question while I was reading the differences between pressure and stress. As I have read: Pressure is the intensity of external forces acting on a point, and it always act normal to the ...
4
votes
2answers
187 views

Interpretation of Hooke's Law

I often see people interpreting Hooke's Law $σ=Eε$ as, "The deformation $ε$ that occurs when you subject a material to a stress $σ$." This makes it sound like stress is an external ...
4
votes
2answers
168 views

Why is it harder to situp on solid floor?

When I situp on solid floor it is harder for me to lift my body upwards versus on a soft/foamy floor which I can do a lot.
4
votes
1answer
1k views

Hookes law and objective stress rates

Often, in papers presenting updated Lagrangian simulation methods for solid dynamics, the following procedure for updating the (Cauchy) stress tensor is presented: First, the Cauchy stress tensor is ...
4
votes
1answer
30 views

Why does squashed clay 'hug' the press rather than spreading out?

In this demonstration a piece of clay (or clay-like material) is squashed under a press. The lump of clay initially spreads out under the ram of the press. But once it reaches the edge of the ram ...
4
votes
1answer
172 views

Is it a law of physics that all machines will break?

The question sounds kinda dumb when I say it out loud but at the same time I'm very curious. When things break, is it solely due to an intrinsic design flaw or is it due to entropy? And is the ...
4
votes
1answer
973 views

Wall stress of a hexagonal pressure vessel

Problem: I want to calculate the stress in the walls of a hexagonal pressure vessel but I can't manage to get coherent results. For long vessels, cylinders are supposed to have the lowest hoop stress ...
4
votes
3answers
98 views

Why solid objects create a sound if you tear them apart?

For example, if you are strong enough to tear apart a piece of plastic - it will make a distinctive sound. If you break it - it too makes a sound. Even if you tear apart paper - it makes sound. But ...
4
votes
1answer
360 views

Why does sawing action increase the effectiveness of cutting knives?

From practical experience, it's obvious that a sharp non-serrated knife will cut items with more ease if the user attempts a sawing motion. The intuitive reasoning for how a non-serrated knife cuts -...
4
votes
1answer
388 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 ...
4
votes
0answers
96 views

Existence of solid mechanics problems that cannot be solved through Lax-Milgram approaches

Very often, solid mechanicians employ finite-element analyses to solve problems in linear solid mechanics. This approach is guaranteed to work because the Lax-Milgram theorem, along with some ...
3
votes
4answers
452 views

Can we write “Normal force” as a function of underlying surface's intrinsic properties?

We usually tend to use Newton's second law for finding equations relating the forces being applied on the (not rotating) rigid body located at a plane surface and then calculate "Normal force" by ...
3
votes
1answer
16k 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 ...
3
votes
1answer
323 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 ...
3
votes
1answer
4k 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 ...
3
votes
2answers
422 views

Question regarding bending of beams (solid mechanics)

I'm still in High-school, and we've just finished a chapter on solid-mechanics. A scenario we were supplied with by our teacher, involves a cuboidal beam supported at two ends, like this: Now if a ...
3
votes
1answer
4k views

How to determine plastic strain rate

Equivalent plastic strain rate is defined as $$ \dot{\bar{\epsilon}}=\sqrt{\frac{2}{3}\dot{\epsilon_{ij}}^{p}\dot{\epsilon_{ij}}^{p} } $$ Where, $ \dot{\bar{\epsilon}}$ is equivalent plastic strain ...
3
votes
1answer
7k 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, ...
3
votes
2answers
4k 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 ...
3
votes
1answer
4k 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 ...
3
votes
2answers
2k views

Why is the partial derivative of strain energy function with respect to strain equal to stress

In Elasticity, we have a strain energy function , $W$, that is a function of strain tensor, $E$. Then the cauchy stress tensor, $T$ can be determined by: $$T_{ij}=\frac{\partial W}{\partial E_{ij}} \...
3
votes
2answers
873 views

How does stress change through a bar that sharply increases in diameter?

I am looking to analyse the stress through the following bar: The bar is of circular cross section, homogeneous in material, that is of a certain diameter on one half, and a large diameter on the ...
3
votes
2answers
987 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 ...
3
votes
1answer
7k views

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

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 ...
3
votes
1answer
61 views

Wave equation on Air- Solid interaction

Suppose that there is, due to an explosion $h$ meters above the ground, a wave in the air with high density, velocity and pressure, capable of inducing an elastic wave on the earth's surface. How does ...
3
votes
1answer
54 views

Qualitative understanding on why solids expand

I'm trying to understand better why solids expand, and what I've been looking at to help guide my understanding is the following graphic from my lecture notes: Now, to illustrate what I think is ...
3
votes
3answers
923 views

Why traction vector depends on surface(section) orientration?

Need help with stress tensors. Every book says that traction vector at a point P depends on orientation of surface cutting this point. But as far as I know traction is defined in this way: Traction is ...
3
votes
0answers
4k views

Most rigid materials

Ordinary web searches are not turning up lists of the most rigid materials for me. I am interesting in finding out the relative rigidity of commonly available materials and how to measure that ...
3
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0answers
641 views

Plastic deformation energy dissipation due to inelastic collision

I have been attempting to determine an analytical expression for the coefficient of restitution (or any similar collision parameter) for an inelastic collision. So far, I've looked at Hertzian contact ...
3
votes
1answer
292 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: $$L_{bending}=\frac{1}{2}\...
2
votes
3answers
2k views

Elongation of a wire of non-uniform cross-section under it's own weight (solid mechanics)

Recently finished a chapter on Solid Mechanics at school. Among the numerous scenarios/examples our teacher provided, was a case of a wire of non-uniform cross sectional area allowed to stretch under ...
2
votes
1answer
530 views

von Mises yield criterion when all 3 principal stresses are equal and in tension

Based on the von Mises yield criterion, a material begins to yield at a point when the state of stress at that point is such that the scalar known as the von Mises stress, exceeds the yield strength ...
2
votes
1answer
65 views

Solid Mechanics -$\nabla\times\nabla\times\varepsilon = 0$ - having trouble with Einstein notation

Note: this is not an assignment for a grade, just me trying to improve my solid mechanics. The task at hand is to show that the compatibility condition $$\nabla\times\nabla\times\varepsilon = 0$$ ...
2
votes
4answers
245 views

Are rocks and other solid objects just very slow moving fluids?

Will a rock or other solid object under the influence of gravity, given enough time, behave like a fluid and slowly flatten out? Or do the properties of matter that make it solid prevent it from ever ...

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