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4
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2answers
46 views

First-principles derivation of cutting force

I know that the amount of force required to separate a material from itself is linked to the surface energy of that material. However, looking at just the surface energy laughably underestimates the ...
1
vote
1answer
53 views

Why is elastic modulus greater than shear modulus?

I was looking at data for elastic modulus $E$ and shear modulus $G$, and found that $G$ is always lower than $E$. So I'm wondering what are the underlying principles that may be the cause of this. ...
3
votes
1answer
56 views

In continuum mechanics, why is the stress vector $T=\sigma\cdot n$ not a covector?

In continuum mechanics, the stress vector (see Cauchy stress tensor) $T=\sigma\cdot n$ is the surface density of a force. Forces are covectors, since they map a displacement vector to a scalar energy. ...
0
votes
1answer
68 views

How to derive this equation? [closed]

How to derive this equation? It comes from a book named Seismic Wave Propagation in Stratified Media.
0
votes
1answer
16 views

Why are stress forces considered as acting on a cross-sectional area through a solid?

I'm trying to understand the Cauchy-Stress tensor, in which the stress acting on a body at a point is analyzed by considering the cross-sectional area through which a force passes. And my question is ...
2
votes
2answers
33 views

Bending along an axis for strength?

I read about this law / property a couple of months back, but I've forgotten what it's name was and I can't seem to find it by Googling. I was hoping someone could give me the name for this property. ...
2
votes
0answers
31 views

How to calculate the strength of a silicon joint in an aquarium?

I'm building an aquarium, and i'm trying to answer the question "Will it catastrophically fail?" by reading the datasheet of the Silicon glue and doing a bit of calculation for worst-case scenario. ...
3
votes
3answers
76 views

origin of the major symmetry property of the elasticity tensor

In linear elasticity theory the stress tensor $\sigma$ is related to the strain tensor $\epsilon$ via the elastic tensor $C$. Specifically $$ \sigma_{ij} = C_{ijkl} \epsilon_{kl} $$ Because $\sigma$ ...
0
votes
1answer
43 views

How to derive time derivate of strain?

Data Time(s) Strain ----------------- 100 0.31 200 0.52 300 0.74 400 0.92 500 1.10 600 1.28 700 1.46 800 1.64 900 1.82 1000 2.00 I want to deduce ...
0
votes
0answers
53 views

Second moment of area of a rod (not circular cross section)

I'm trying to calculate the stress induced in a rod by an end mass with an initial rate of rotation. My current idea to calculate this is: 1) Calculate the rotational stiffness of the rod 2) ...
0
votes
1answer
45 views

how to increase the moment of inertia of a hollow aluminium pipe without changing the outer diameter [closed]

how to increase the moment of inertia of a hollow aluminium pipe with external diameter fixed and only allowed to change the shape of internal section for example rectangular hole or extruded section ...
0
votes
3answers
77 views

Ideal, isotropic fluid and stress tensor

An ideal fluid is the one which cannot support any shearing stress. It also doesn't have viscosity. My question is what does it mean by a fluid to be isotropic? Is an ideal fluid necessarily isotropic ...
1
vote
1answer
26 views

Problem on bending plates in Newtonian Mechanics?

I am reading a book on interesting physics problems and demonstrations. One of the problems in the section on buildings, structures and equilibrium talks about a plate with one side attached to the ...
2
votes
1answer
76 views

How much weight would I need to put on the end of a tube to break it?

Say I have a tube with a circular cross-section made from some material (for an example, I'd like to use acrylic). I support it horizontally from one end and hang a weight from the other end. How ...
0
votes
0answers
37 views

Tricky question (physics) [duplicate]

I know this may not be the place for this question, by stackexchange physics has banned homework questions :( A piece of hair taken from a goat has a radius of $3.1\times 10^{-5}\text{ m}$. What ...
4
votes
2answers
500 views

Will a diamond break if I hit it with a hammer [closed]

I was having this discussion with my friend about the hardness of diamonds. I would like to know if a diamond will break or not if hit with a hammer. Different sources across the internet mention ...
2
votes
2answers
74 views

Efficiency of Bicycle Pedalling

Consider a bicycle with multiple gears. Suppose that you are in a starting position with someone holding your bike upright (so when you start there's no issue with clipping in etc). It's well-known ...
0
votes
0answers
29 views

Impact strength test of a container filled with liquid

as a university project I have to project(choose material and dimensioning) a liquid container (NaClO, density 1100 g/L), we ...
1
vote
0answers
42 views

unknown stresses in double-layer glass window

I live in cold place where outside temperature drops to -20. Currently, we have -20 and on my window, which is doubled layer glass with trapped air in between, I found a "polarized stress spectrum" ...
1
vote
1answer
59 views

Question concerning the diagram for stress tensor

I have a couple of questions related to the diagram in the answer by Kyle Kanos to this question, Why is stress a tensor quantity?. Q1. If the box shown is of finite size why are there not three ...
1
vote
0answers
25 views

LOCAL Temperature Gradient and Stress

I'm investigating the thermo-migration failure mechanism in nanoscale ICs interconnects. Typically, a nano wire under thermal stress suffers from material/mass migration or void nucleation if it ...
1
vote
0answers
30 views

How much will a round tube deflect under load? [closed]

I'm trying to determine the materials I need to complete a hobby project, and I'm having trouble estimating how much flex a given steel tube would have under different configurations/loads. My setup ...
15
votes
2answers
1k views

Why is stress a tensor quantity?

Why is stress a tensor quantity? Why is pressure not a tensor? According to what I know pressure is an internal force whereas stress is external so how are both quantities not tensors? I am ...
1
vote
2answers
84 views

Is there a way to calculate strain energy based on stress and deformation gradient?

We know that we can obtain stress from strain energy density and deformation gradient, for example: $$\mathbf P=\frac{\partial W}{\partial \mathbf F}$$ However, is there a way to calculate $W$ from ...
17
votes
5answers
1k views

How is potential energy actually stored in a steel spring at the atomic level?

Elasticity is one the most intriguing phenomena, wiki gives a summary explanation of what happens in a steel spring: the atomic lattice changes size and shape when forces are applied (energy is ...
-1
votes
1answer
649 views

Prove Poisson's Ratio is 0.5 [closed]

Poisson's ratio is the negative ratio of the transverse strain (_T) to the axial strain (_A). For an incompressible (density doesn't change), homogeneous (everything is the same molecule), ...
1
vote
1answer
135 views

Degree of anisotropy of crystal tensors

Does there exist a scalar that can describe how anisotropic the elasticity of a crystal is? What about other tensors such as the permittivity or susceptibility? I found a Wikipedia article that was ...
1
vote
1answer
222 views

Divergence of Cauchy Stress Tensor

On the wikipedia page for the Cauchy Momementum Equation, it's stated that the equation can be written as $$\rho \frac{D\,\textbf{v}}{D\,t} = \nabla \cdot \sigma + \textbf{f}$$ Where $\sigma$ is ...
0
votes
1answer
85 views

Is there a difference between spring fatigue and plastic deformation in springs?

Is there a difference between spring fatigue and plastic deformation in springs? Plastic deformation means permanent deformation in springs caused due to stretching in springs.
0
votes
0answers
30 views

Strain-Displacement relationship symmetrization

In the context of infinitesimal elastic strain theory, one writes the relationship between displacement and strain as $$ \epsilon_{ij} = \frac{1}{2}( \frac{\partial u_i}{\partial x_j} + ...
1
vote
1answer
74 views

Is shear modulus only applicable to cubical solids?

Do we have any real life/theoretical examples where shear modulus is applicable to non-cubical shapes?
0
votes
2answers
59 views

Why don't we consider both the forces while calculating the magnitude of stress in an elastic body?

Consider a wire being stretched from two ends with equal forces. We know that both of these forces collectively participate in elongating the wire; had there been one force the wire would have ...
0
votes
0answers
24 views

allowable compressive stress in discretely laterally supported lateral buckling

The maximum allowable compressive stress corresponding to lateral buckling in a discretely laterally supported symmetrical I beam does not depend upon : the modulus of elasticity can anyone please ...
0
votes
3answers
78 views

What is the net force experienced (at the lowest point) by a wire being rotated in a vertical circle with a mass 'm' at its free end?

A metallic wire is being rotated in a vertical circle with a mass $m$ fastened to its end. My understanding says that the net force experienced by this mass should be the centripetal force: $T - mg ...
0
votes
1answer
145 views

Modulus of rigidity inside the water

Transverse wave can't travel inside the water. It travels in solid and on the surface of water because they have modulus of rigidity. What is modulus of rigidity? and why there is no modulus of ...
2
votes
2answers
269 views

Why is steel-reinforced concrete stronger than ordinary concrete?

Is it only because steel has higher elasticity? What other factors are involved?
2
votes
1answer
81 views

Why eigenvector points to principal stress plane?

I can represent a tensor by a matrix. Suppose we are talking about a 2nd order tensor, and the matrix is therefore 3x3. If I find one eigenvector of that matrix; that vector represents normal vector ...
1
vote
0answers
47 views

What is the yield strength of a bar of different cross sections?

Will the yield strength of the combination will be same as that of the rod of uniform cross section?
0
votes
1answer
34 views

Difference between various shear forces

What is the difference between $\tau_{xy}$ and $\tau_{zy}$; because as far as i know the first character of subscript represents the direction to which the stress is perpendicular and other the actual ...
0
votes
6answers
329 views

Does large acceleration have to cause damage to the human body?

My whole life, I've heard that large accelerations cause damage to humans (e.g. g-forces in space movies). However, after reading about general relativity, it seems to me that a strong force which ...
0
votes
1answer
85 views

Why don't we take into account the width contraction of the wire in calculating the stress strain relationship for a stretched wire?

In the stress-strain relationship for a stretched wire, we say that $\frac{F}{A}=Y\frac{β}{l}$; where β is the change in length and the rest have their usual meaning. We also say that there is a ...
0
votes
0answers
51 views

Young elasticity modulus anisotropic media

Im studying anisotropic system composed by a elastic matrix (Young modulus $E_m$) filled with oriented rods. Given this filler orientation, the material is elastic-anisotropic, with Young elastic ...
1
vote
0answers
107 views

Double dot product in Cylindrical polar coordinates - Strain Energy

I'm working with a problem in linear elasticity, and I have to calculate the strain energy function as follows: $$2W=σ_{ij}ε_{ij}$$ Where σ and ε are symmetric rank 2 tensors. For cartesian ...
2
votes
2answers
160 views

what is the static pressure in a yield stress fluid?

Suppose I have a tank filled and there is no slip at the walls. If the tank is filled with a Newtonian fluid and is in static equilibrium, we know that the pressure is defined as $p = \rho g z$. But ...
2
votes
1answer
180 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 ...
0
votes
1answer
238 views

wall thickness for a very large, low-pressure vessel?

I'm working on a space colony simulation, and I'm at the point where I need to calculate the thickness of the habitat walls, as a function of air pressure and geometry (and assuming some common ...
2
votes
0answers
68 views

buckling of tube - shell thickness vs. momentum of inertia optimum

is there any simple formula (perhabs semi emperical, or aproximatively derived model) for buckling of tube under axial compression load given its crossection and wall thickness? ( and naturraly ...
5
votes
4answers
431 views

Why are stresses of continuum systems described via a tensor?

The tittle pretty much says enough. I have always been told so but no one really motivated it. So, I would like to know why do we use a tensor to describe the stresses in continuum mechanics.
8
votes
2answers
634 views

Tearing a piece paper along a crease

Why is it easier to tear paper along a crease? To word it differently: why does a "tear" progress along a crease, if one is present?
0
votes
0answers
185 views

Volumetric and Deviatoric Strain Equation in 2D

Strain is defined as $$\epsilon=\frac{1}{2}\left( \nabla u + \nabla u^T\right).$$ I found a formula for the strain tensor in 3D decomposed into volumetric and deviatoric components: $$\epsilon= v + ...