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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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22 views

Calculating tension at every point on rope around pulley [on hold]

Suppose a pulley is fixed over a wall and a rope is passing over it such that both the ends of the rope are connected to boxes having masses $m$ and $M$ ( $m<M$) Assume mass per unit length of rope ...
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0answers
7 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
31 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
16 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
24 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
56 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
33 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
65 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
38 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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0answers
47 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
8 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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28 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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0answers
36 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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0answers
32 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
34 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
58 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
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 ...
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2answers
183 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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0answers
26 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 ...
2
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0answers
69 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 ...
2
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0answers
40 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
23 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
50 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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0answers
25 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 ...
2
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1answer
101 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
413 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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0answers
14 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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1answer
129 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
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1answer
128 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
84 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 ...
0
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1answer
28 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
14 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
114 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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0answers
26 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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0answers
50 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 ...
5
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0answers
104 views

Tensorial version of Hooke's law

It is well known that $${\boldsymbol F} = k {\boldsymbol x}$$ for isotropic media. Also, according to Wikipedia $$F_k = k_{jk} x_j$$ for some elastic tensor $k_{jk}$. I'm a bit confused as to how ...
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1answer
82 views

Physics of Wrinkling: Understanding inextensibility condition

I'm reading this very cool paper on the formation of wrinkles in elastic materials. The key result of the paper is a set of scaling laws for the amplitude and wavelength of wrinkles based on the ...
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1answer
59 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?
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0answers
34 views

Example of materials with 21 independant coefficients in linear elasticity?

By definition of linear elasticity, the strain et stress tensors are related: \begin{equation} \boldsymbol{\sigma}=\mathbf{C}:\boldsymbol{\varepsilon} \end{equation} and because of minor and major ...
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2answers
54 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 ...
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3answers
71 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
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1answer
106 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 ...
0
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1answer
63 views

Will a tug-of-war battle damage my climbing rope

I plan to organize a big tug-of-war with a climbing rope (70m long) with 50-60 adults. I know the climbing rope is elastic. The rope resistance is 9 kN when a chock occurs. Will the rope breaks or ...
1
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1answer
79 views

Where does elastic energy come from?

I vaguely remember reading that the elastic potential energy of a spring, $\frac{1}{2} k x^2$ comes from mass which is turned into energy according to the law $E=mc^2$. I also remember hearing that ...
0
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1answer
77 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 ...
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0answers
49 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 ...
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0answers
103 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 ...
3
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1answer
90 views

Reference Request: Fluid dynamics/Elasticity via Lagrangians

Would there be a book that does what Landau does in Fluid Mechanics and Theory of Elasticity using Lagrangian's/Action-principles, analogous to the presentation in Landau's mechanics? I have only ...
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1answer
50 views

Deformation of the cylinder

There is given a cylinder with fixed side surface. On one base is being rendered constant pressure $p$, so cylinder cambers I'm trying to calculate the form of cambering. The problem is that height ...