Elasticity Definition and 203 Threads

[I do not know if this is the right subforum] The answer to the question to the title is: for very long time. However the tuning fork clearly has to stop at some point because some of the energy will turn into heat. However I want to quantify for how long. More specifically I am interested on...

TL;DR Summary: Pretty much confused about an advanced elasticity book.Resource recommendation is asked. My last semester in freshman year of bs physics included a chapter on elasticity,it was not at the advanced level and by advanced level i mean atleast the tensor stuff.Well,I want to read...

First, my ignorance... I know there are classes of equations: Laplace, Poisson, Wave, Diffusion, etc. (I suppose Laplace is a subset of Poisson, but that is not the issue). Into what category of mathematical equations would you place the field equations of elasticity (stress/strain/displacement)?

I'm trying to make a DIY 'ECG' machine, except that it'll only record heartbeats on a piece of paper. Basically the piece of paper will be wound round a cylinder like object, which will be being spun slowly by a motor. A pencil at the end of a stick or something will be writing to this piece of...

Hello, today we learned about elasticity, whose formula was the change of pressure over the volume change (∆p/∆v), which seemed very weird compared to the use of the adjective elastic daily, my question is can we say that a piece of wood is very elastic? because even applying a large pressure...

Hi, Looking for the Elastic Constants for any rubber-like material such as Natural Rubber. It can be inorganic or organic. The constants I am looking for take the form of a fourth-rank tensor. I only need the first order elasticities, not the zeroth or higher (not Cij or Cijklmn.. just Cijkl)...

I have a problem where I have a metal tube that I am modeling as a cantilever beam which is fixed at one end and has a point load at the other end. The material of this beam is 304 stainless steel, the inner diameter is 0.5mm, the outer diameter is 2mm, and the length of the beam is 4.15mm. With...

What I do not get is why should a stress much lower than yield point cause deformation in a material? If temperature is high intermolecular attraction is reduced and thus even low stress can deform things. But if it is low Then a force lower than yield point should be less than intermolecular...

Could I please ask for help with the following question? Four uniform rods of equal length l and weight w are freely jointed to form a framework ABCD. The joints A and C are connected by a light elastic string of natural length a. The framework is freely suspended from A and takes up the shape...

[Mentor Note -- Thread moved to the ME forum to get better views] Let's consider an incompressible block of Neo-Hookean material. Let the initial reference geometry be described by ##B=[0,b] \times [0,b] \times [0,h]##. The professor gave me the following task: Of course there can be many...

Hi everyone, studying the bending of an incompressible elastic block of Neo-Hookean material, one finds out the first Piola-Kirchoff stress tensor as at page 182 (equation 5.93) where $e_r = cos(\theta)e_1 + \sin(\theta)e_2$ and $e_{\theta} = -sin(\theta)e_1 + \cos(\theta)e_2$ How is the...

I am studying the finite bending of a rubber-like block, assuming Neo-Hookean response. In the following, ##l_0##,##h##, ##\bar{\theta}## are parameters, while the variables are ##r## and ##\theta##. The Cauchy stress tensor is ##T= - \pi I + \mu(\frac{l_0^2}{4 \bar{\theta}^2 r^2} e_r \otimes...

I'm studying elasticity from classical Gurtin's book, and my professor gave us the following example, during lecture. Unfortunately, this is not present in our references, so I'm posting it here the beginning of the solution, and I will highlight at the end my questions. First I need to state...

Hi all! :) I'm a physician who regularly punctures blood vessels with needles. This is successful when the needle punctures the superficial surface to enter the lumen, but does not puncture the deep surface. If this happens, nearby structures (lung, nerves, heart) are damaged. Increasing force...

In every book I checked, the energy (per unit mass) of elastic deformation is derived as follows: ## \int \sigma_1 d \epsilon_1 = \frac{\sigma_1 \epsilon_1}{2} ## and then, authors (e.g. Timoshenko & Goodier) sum up such terms and substitute ##\epsilon ## from generalised Hooke's law i.e. ##...

If you take a rubber band and fix it in a stretched position for an extended period of time, would it eventually lose its elasticity? If yes, then how can you calculate how long it would take until its elasticity decreases by a certain amount, say, fifty percent? If no, why not? How does the...

θ = 4 μs = 1 Fnet = Wpararell + fs m.a = 1/2.m.g.sinθ + μs.1/2.m.g.cosθ (divide by m) a = (g.sinθ+μs.g.cosθ)/2 a = ((9.8)sin4 + (1)(9.8)cos4)/2 a = 5.23 m/s^2 hello guys, I'm having trouble with this problem. Can anybody help me correct my attempt and explain it to me?? thanks

Does spacetime have elasticity ? I was reading this and they are talking about the stiffness of spacetime.

When my professor solved it, he wrote ##k## in the equations. But there are four springs, so why didn't he write ##4k##?

1. Drawing Free Body Diagrams for all components we get : 2. Following this we can find total elongation using ##\Delta L = \frac {1}{AY}(F_1*L_1 + F_2 *L_2+ F_3 *L_3) ## My questions : a) I am assuming that the internal forces (3t) are neglected in the FBD because of Newton's third law whereby...

Given, ##2A_P = A_Q## (cross-sections) ... (1) and, ##Y_P = 2Y_Q## ... (2) We have ##\frac {Y_P * x}{\Delta L} = \frac{Y_Q (L-x)}{\Delta L}## Using (2) in the above expression we get ##x = L/3## whereas the correct answer is ##x = 2L/3## I feel my initial idea is flawed, and that I am...

I'm trying to find the Yield strength, that is how much force can be applied to carbon nanotubes so that they stretch to the limit before plastic deformation. And also how much they stretch at this limit. Do they stretch at all? Or are they always the same length until the Ultimate Tensile...

Homework Statement The torsion balance shown in the figure consists of a 40 cm long bar with lead balls with a diameter of 2 cm on each end. The rod is hanging by a 100 cm long silver thread with a diameter of 0.5 mm. When two bigger lead balls (density = 11.4 g/cm3) with a diameter of 30 cm...

Consider a spring balance with no initial deflection. Let an object of mass 'm' be attached to it. We allow the spring to come into equlibrium, and 'd' is the deflection at this eqb position. We add another object of mass 'M', while m is also present, so that the final position is x, and hence...

I am 2nd year physics undergrad. Just want to study a bit about materials in my free time. I have no idea about engineering books. Please suggest some good books. Thanks.

Homework Statement Hello, I'm studying anisotropic elasticity. One of the books I'm using is Lekhnitskii's. The book presents the general equations of the theory of elasticity for an orthotropic body as follows: Homework Equations The Attempt at a Solution However, when I combine the...

Special relativity requires any substance to be compressible. Indeed, if an item were made of a perfectly rigid substance, then move one end of it, and the other end must move at the same moment - the movement must be transmitted instantly, faster than light. Thus, the special relativity sets...

Elasticity The Demand function for a product is modeled by P=20-0.02x, less than or equal to x less than or equal to 1000 Where p is the price per unit in dollars and x is the number of units. A. Determine when the demand is elastic, inelastic, and of unit elasticity. B. Use the result of...

Homework Statement The experiment : How the elasticity of material might change under heat treatment? The experiments conducted in two different way, first one the hot bobby pin set to cool down slowly after heated (the professor called annealing treatment), and the second one the pin set to...

Which modulus define a property of fluids?? The above mentioned question was asked in my college internals. The answer they suggested was sheer modulus. Any explanations??

Let's say I have a metallic beam that is held so that it is parallel to the ground (0 degrees). What are the factors that affect the oscillating period of this metallic beam? I release it from a specific height so that isn't a factor. Elasticity - won't a highly elastic metallic beam have a...

I would like to know if it has any sense to talk about the concept of elasticity of spacetime. So, if spacetime is like a clothing that can be deformed by a big mass or a big energy, does this “clothing” has some elasticity considering for example the deformation that makes a big star in the empty?

In mechanical engineering we have various courses in strenght of materials, and I've noticed that graduate students learn the Theory of Elasticity. I've researched a little bit about it, and I know that the Theory of Elasticity is more general than strenght of materials. But I have some doubts...

I have been studying structural physics lately, in particular the linear elastic eqns, governed by the equation of motion. https://en.wikipedia.org/wiki/Linear_elasticity I am trying to solve these equations numerically. I was thinking of a scenario of a rod being compressed on one end by some...

Homework Statement What is it: Practice Paper 1 b question for SL Economics IB Question: Discuss why it may be important for a firm to have a knowledge of price elasticity of demand. PS: It isn't stated explicitly to use a diagram, but my understanding is all Paper 1 questions need to be...

Homework Statement So, my professor gave a test this weekend. I missed a problem concerning price elasticity of demand, but that's only because I assumed the opposite direction. Now, I'm considering challenging this question, because the price elasticity was listed as a positive number...

Hi everyone, I'm having some difficulty comprehending "normal" transmission of stress/strain through a solid body and "shock" transmission of stress/strain. Imagine I have two bodies, one rigid - the other elastic. If the rigid body is fixed in space, and the elastic body is flying at the...

NOTE: I seem to have a dental implant in which there has been a mechanical failure of the abutment, which has piqued my interest in this. The paper is here: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4668729/ About 40% down, there is: *** The most commonly used retaining screws are either...

Homework Statement A 12.0-kg mass, fastened to the end of an aluminum wire with an unstretched length of 0.70 m, is whirled in a vertical circle with a constant angular speed of 120 rev>min. The cross-sectional area of the wire is 0.014 cm2. Calculate the elongation of the wire when the mass is...

Hello, I am currently looking at a way to calculate brine density using temperature, pressure and salinity. I found the following page which describes the change in fluid density with pressure and temperature : http://www.engineeringtoolbox.com/fluid-density-temperature-pressure-d_309.html...

Hi, I know this may seem like a dumb question, but I just can't seem to get by one part of each elasticity of demand problem I come across. For example: Use the​ price-demand equation below to find​ E(p), the elasticity of demand. x=f(p)=20,000-550p I know that E(p)=pf'(p)/f(p), so in this...

I am new to elastic theory. I have a question about elasticity. We assume we have a body with no internal forces. Surface forces are applied on the border. Can we leave the elastic domain (reach the yield surface) in an interior point without leaving the elastic domain on the boundary? If no...

Hi, I would like to do an experiment for my physics class about which balloon has the highest stretch ratio and found the following page on this forum: https://www.physicsforums.com/threads/hookes-law-for-a-balloon.670566/ First of all, can you please explain this function? σ=σ(λ). I'm...

Hi I've been trying to get a simple solution to the 2D Navier-Lame equations using finite difference on a rectangular grid. I want to see the displacements, u and v, when a simple deformation is imposed - e.g. top boundary is displaced by 10%. The equations are as follows: \begin{eqnarray*}...

Hi PF, As you may know, is the the elasticity/stiffness tensor for isotropic and homogeneous materials characterized by two independant material parameters (λ and μ) and is given by the bellow representation. C_{ijkl} = \lambda\delta_{ij}\delta_{kl} + \mu(\delta_{ik}\delta_{jl} +...

Supose we have a ¨U-shaped" metal bar, stuck in the ground, and I aply a force on the top of the part on the right, trying to make it wider. If I were to avaliate the forces acting on a specific part of the bar that includes the point that I´m applying the force, let`s say the portion from that...

Homework Statement Consider a spring of natural length L_0 with constant k which rests on a horizontal frictionless surface. The spring is attached at one end to a fixed post and at the other end to a mass m. Suppose the spring is rotating around the post in a circle with angular velocity w...

Hello, I`m studying amyloid fibres, which are filamentous proteins that intertwine between them (from 2 to 4 and more) and form fibres (2-20nm thick). I see that when that below a threshold length, the fibre is linear, beyond the threshold length, the fibre bend always with the same, constant...

I am studying the following phenomenon for my project: Thin horizontal elastic rod is fixed at both ends and small perpendicular force is applied at middle of the rod perpendicular to its length. I want to study this dynamics and extend it to cylindrical shell. Please suggest books/papers or...

I am trying to find a formula to show the modulus of elasticity (MOE) of a panel of three layers of different materials when I know the MOE value of the three individual materials. This is for a Plastic Laminated Panel where, the top and bottom layers are plastic laminate (i.e. Formica) .028"...