Questions related to the Continuum Mechanics Division of Elasticity. The bending of beams, deflection of rods, or in general, applications of Hooke's Law generalized to three dimensions.

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Shear flow in J section type beam

What does the distribution of shear flow look like in a J section type beam. I'm only interested in a qualitative picture of it. I'm not interested in the calculations themselves. It is the top of the ...
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1answer
25 views

Gough-Joule effect in rubber band

When a stretched rubber band is heated, surprisingly, its tension will increase. What is the physics behind this?! Another thing. The Entropic spring model says, for a good specimen, that the ...
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26 views

Specific form of Stokes's differential equation

Coming from a chemical background, I have next to no knowledge of the (as it seems to me) complex field of fluid dynamics, so bear with me here. I'm reading a paper written by seismologist Norman ...
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1answer
36 views

Is strain always relative to some initial state?

Let us say I am given a material with no knowledge about its history. Can I somehow calculate its strain ? Or a strain is always relative to some initial state (change in length/initial length) ?
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1answer
24 views

Origin of a unique stress-strain relation

In a paper by Kees Wapenaar titled, "Retrieving the Elastodynamic Green's Function of an Arbitrary Inhomogeneous Medium by Cross Correlation" (2004), the following is stated: "In the space-frequency ...
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34 views

When one blows up a latex balloon, why does it get easier to blow once it has a little air in it (after 1 or 2 breaths)? [duplicate]

When one blows up a latex balloon, why does it get easier to blow once it has a little air in it (after 1 or 2 breaths)?
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1answer
65 views

Bending moment of a cantilever beam

The following procedure is here. Consider a cantilever fixed at one end and loaded at the other one. In cartesian coordinates (if $y$ is horizontal and $x$ vertical, meaning that the load acts ...
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1answer
45 views

Coefficient of elasticity of the spring?

I know this might sound a silly question though For a spring that is compressed lets say x meters by a force F N. what is coefficient of elasticity of the spring? We are not given the equilibrium ...
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26 views

Coefficient Of Restitution of Two Balls With Different Elasticities

In a computer program, I need to simulate the collision of two balls with different elasticity values given between 0.0-1.0. I looked for a formula to derive restitution coefficient from elasticity ...
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1answer
43 views

Relationship of the volume of a plumbing system to pressure

How does the volume of water a plumbing system holds vary with water pressure? I know the ratio would include the modulus of elasticity of the plumbing material, the total surface area of the plumbing ...
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1answer
167 views

A moving brush on a vibrating surface

Hi group, I am a HS student in China preparing for a regional Young Physicist Tournament even. We are very puzzled about why would there be such movement. We would be grateful to see any inspiring ...
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2answers
60 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 ...
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1answer
82 views

Help calculating work done by stretching a wire [closed]

A wire of length 0.89 m and cross-sectional area 1.7 cm2 is stretched elastically by an amount 1.2 cm. By Hooke’s law, the restoring force is $−k\Delta L$. Calculate the work done in ...
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1answer
87 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. ...
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1answer
20 views

How can I learn about elastic bodies?

I'm writing a program that needs to be able to simulate a system of elastic bodies, that can collide with each other and with other rigid bodies, and deform accordingly. I think it would be an ...
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0answers
25 views

How to specify boundary conditions as function of curvature in dynamic elastic beam pde?

In this article (already mentioned in this question) the dynamics of a planar elastic beam with "cantilever constrains" (one clamped end and one free end) is modeled. Using the Euler-Bernoulli Beam ...
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13 views

Solution for elastic wave on plane of ideal contact between two half spaces of elastic, homogeneous, isotropic, linear solids

Please give the solution for elastic wave of arbitrary polarization incident at arbitrary angle on plane of ideal contact (meaning no slip, homothermal, nondissipative, and no transfer of material ...
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1answer
36 views

Can surface waves exist near a fixed surface

(I'll phrase this question in terms of waves in an elastic medium, but this is a more general question.) Surface waves are waves near the surface of a medium whose amplitude decreases as you go away ...
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2answers
24 views

Elastic behaviour of objects

If I strike my car with a wrench with enough force to make a dent in it, then it's obvious that I won't be able to produce any acceleration in the car. But I am applying an external deforming force. ...
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1answer
37 views

Differences between elastic moduli

Is it true that in materials like aluminum and copper, the correct order of elastic moduli, in terms of value are: Bulk < Young's < shear modulii If this is correct, why is this the case?
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2answers
95 views

Where does this formula for sagging of a beam come from?

In one of my physics textbooks there is a chapter on the elasticity of materials which contains pretty basic outline about Young's modulus, stress-strain, elastic potential energy and related stuff. ...
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1answer
72 views

Diameter of after elongation of a cylinder

This is more Material Science than Physics, but I'm doing a research project right now in computational science that involves some additional information that is outside of my background. I've done ...
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3answers
93 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 $\sigma$ ...
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1answer
44 views

Is an elastic, gravitating object stable?

As I understand, an object can contract under its own gravitantional pull. Then as it does so, different parts of the object must move with some velocity. This in turn means that their relativistic ...
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1answer
85 views

Proof that a traceless strain tensor is pure shear deformation

How can i proove that the traceless part of linear strain tensor $e$ in the Euler description: $$e_{i,j}={ 1 \over 2 } \left({ \partial u_i \over \partial x_j}+{ \partial u_j \over \partial x_i} ...
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0answers
15 views

St Venant-Kirchhoff energy from geometric principles

Is there a good reference that derives the St. Venant-Kirchhoff energy of a surface from first principles, from a geometric perspective? (Ie explaining the metric of the surface, how it can be used to ...
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32 views

Relation between area elements in finite deformation theory (continuum mechanics)

There are relations for the line and volume elements in continuum mechanics. For example: \begin{align} \ \ \ \ \ \ \ \ \ \ \ \ \frac{V}{V_0}&={\rm det}(F)\tag{1}\\ \lambda^2&=(F^TFe_1\cdot ...
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47 views

Deriving general boundary conditions from first principles for elastodynamic scattering

It seems that most of the relevant books only give the linear case and the rest say something along the lines of "here are common examples of boundary conditions." What are the most general boundary ...
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40 views

What's the relation between the type (Gender) of a balloon and its internal pressure

I'm working on a project about balloons and I need to know the relation between the gender of the balloon and its internal pressure. As far as I know, there are some parameters such as " Elasticity of ...
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2answers
43 views

On the isotropy of materials

Good morning. I am working on Honeycomb structures and first of all I would like to understand whether it is Isotropic or not, and , if the latter holds which kind of anisotropy it has. How to do it? ...
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0answers
81 views

Simple harmonic motion and elasticity

Question: One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to a massless spring of spring constant K. A mass m hangs freely from the free end of the ...
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0answers
38 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 ...
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2answers
211 views

What determines the bounce time of an elastic ball?

Consider an elastic ball is bounced off a hard flat surface. I would like to reconcile two different answers to the question "how does the contact time between the ball and surface depend on the speed ...
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34 views

How would a network of connected springs deform when connections slip

I'm working on modeling polymer networks, and I'm stuck on the following problem. If you apply a fixed force to a bunch of firmly connected springs, sort of like this... You'd expect the network ...
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0answers
76 views

Heads, Tails… Edge?

No Nobel prizes at stake, but just an idle thought and an idle question. How could one calculate the probability of a flipped coin landing stable on its edge, instead of heads or tails? I assume ...
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0answers
52 views

Positivity of Bulk modulus and shear modulus in isotropic materials

I have been searching through many resources, but could not find a proper thermodynamic reasoning for why bulk and shear moduli for isotropic materials should be positive. Some resources like eFunda ...
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0answers
41 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 ...
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1answer
73 views

On what parameters is breaking stress dependent?

I have recently studied Elasticity in materials. There was a question about breaking stress that if the area along which a linear force is applied is doubled, then what happens to the breaking stress. ...
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42 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 ...
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1answer
110 views

Elasticity of a body on which variable force is applied

Let us consider a rod of some cross sectional area $A$ and length $L$. At one end a longitudinal foce of 5x acts on the rod. At a distance of $\frac{L}{2}$ from that point longitudinal force of 5x ...
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1answer
818 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), ...
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19 views

Will a sodium bell ring clearly after being submerged in liquid nitrogen?

Lead is fairly soft at room temperature but rings clearly when cooled to liquid nitrogen temperatures. Sodium is even softer. If cooled to liquid nitrogen temperature, could it also ring?
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2answers
176 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 ...
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1answer
170 views

Confusion in Euler-Bernoulli beam theory

Euler-Bernoulli beam equation is given by $$ EI \frac{\mathrm d^2 u}{\mathrm d x^2} = M'(x) \\ EI \frac{\mathrm d u}{\mathrm d x} = xM'(x) + C_1 $$ Where, $E$ is modulus, $I$ is second moment of ...
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1answer
89 views

A question regarding collisions

Let us consider a system of 2 identical spherical bodies connected by a massless string that is taut. If one body is placed at the origin then the other is placed at some coordinate $(x,y)$. The ...
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1answer
31 views

Tensile stress, is the pressure given indicating just one side?

I'm studying elasticity right now in my chemistry class, and I'm confused as to what exactly tensile stress (and maybe compression stress too) might mean. It's given in N/m^2. And you're stretching ...
2
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0answers
17 views

Main differences between elastodynamic and light scattering when using S-matrix to find bound states

What are the main differences (top 5 if question is too broad), for using the S-matrix to find bound states, between elastodynamic and light scattering? (if it facilitates a higher quality ...
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2answers
168 views

Determining flexural modulus by performing 3 point bending test using hollow cylindrical tube

I would like to decide the flexural modulus of the material of plastic tube by performing 3 point bending test according to the ASTM D 790 procedure. In ASTM D 790, the form of the specimen is ...
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29 views

Role of the crystallographic point group on properties of tensorial elasticity

If a space point group for a crystal is known, does this automatically define the elastic tensor symmetry of the material? What further implications can be found? The crystallographic subgroups: ...
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88 views

How to calculate a Mooney-Rivlin material

Well, I'm working on a fsi (fluid-solid/structure interaction) model. I've got ready the fluid part, now I need to get ready the solid part. Since I'm working with tissues, I need to use an ...