Deformation Definition and 175 Threads

Homework Statement What do you understand by the following terms; (i) principal stretch (ii) an anisotropic material (iii) a dilatant deformation, (iv) a Lagrangian description of a deformation, and (v) a pure deformation. Homework Equations Am just trying to find descriptions for...

Could someone please show me how to calculate the deformation of a pad (ideal material with the same elasticity at all directions) under a cylinder ? Thank you very much.

fluid mechanics: defition of "shear flow" [rate of deformation tensor] I'm studying old undergraduate chemical engineering notes for an exam in grad school. Can't recall what this really means, can anyone explain to me what "off-diagonal elements" means and why the trig function velocities...

Hi all, I am trying to self-learn continuum mechanics, and I have a question regarding the development of the deformation gradient (which ultimately leads to green's deformation tensor). I have attached the specifics of the question in a attached photo. Ultimately, there comes a point...

I am trying to do a problem on Material Non-linearity , to model steel for large deformation , beyond yield point , I have tensile testing data for the steel ( in form of Engineering stress vs Engineering strain). for defining the model , I chose Multilinear Isotropic hardening now there...

Homework Statement Hello guys! Now this is not a homework question, but it may sound like one. If a uniform sized and massed sphere was spinning in space away from any source of forces that could affect it, wouldn't the only forces that act on it are the centripetal and centrifugal? And if this...

Homework Statement Hello guys! Now this is not a homework question, but it may sound like one. If a uniform sized and massed sphere was spinning in space away from any source of forces that could affect it, wouldn't the only forces that act on it are the centripetal and centrifugal? And if...

Hi all, I have a question regarding deformation analysis. For materials with non-zero Poisson's ration, when is it justified to use plane strain analysis rather than three-dimensional? Perhaps one case is when we are going to analyze a thin sheet. Are there other cases too? Thanks, Hassan

Hello, When we use slope deflection method in frames we neglect axial deformation in order to get the same delta when the frame is sway,(that what i understood) So i have two questions 1. Neglecting axial deformation means ignoring axial force??Or what?? 2. How to neglect axial...

I'm trying to give an answer to the following problem, I hope someone could come in help! Consider a smooth n-dimensional manifold M with smooth (nonempty) boundary \partial M, and suppose given a function f: M\setminus \partial M \to \mathbb{R} (which one can assume to be differentiable)...

Let RP2 denote the real projective plane (it can be obtained from glueing a Mobius band and a disk whose boundary is the same as the boundary of the Mobius band). I know if one punches a hole off RP2 then the punched RP2 is homotopy equivalent to a Mobius band which is in turn deformable to a...

Structural Analysis-"small deformation" Hi all, Assume a cantilever beam fixed to a wall. We let the beam bend under its own weight. In practice the bending could be significant and as the bar bends, the distance between the tip of the bar and the wall decreases. Now my question are...

For a day and a half now we have been trying to calculate a self-assigned problem. However, this has not turned out to be easy and build-up frustration has lead us to this forum. Our challenge was to calculate what under pressure a food packing company needs in it's jars to make sure the lid...

Imagine a circle lying on xy plane and initially at rest w.r.t. frame S. Then S' comes and gets the circle and moves it with velocity v along x axis. The radius which is along x axis,should be contracted but not other radii and this means that the circle becomes an ellipse and because its sth...

Hello, I was wondering if anyone can help me with my FEA approach. I want to check that my boundary conditions for a simple quarter torus (representing a section of a helical spring) are correct. I'm neglecting the helical angle at this stage. I have fixed one end in all axes, and applied...

I have a little question about waves. Waves deform its medium elastically. For example: sound waves will propagtae through air because of local compression and decompression of the air. Is it possible for a material to get ductile deformation by means of a wave. Can I deform a material...

Dear all, I am Levy , I am glade to take part into physics Forums, I hope I can share my know with everybody and study from you, Thank You! I test the PET of creep deformation recent days, who has some reference about this aspect. Thank you

Homework Statement Compute the angle of twist of the free end relative to the fixed end of the steel bar: 200 N*m, 80 x 10^9 GPa (shear modulus of elasticity) (Length 1: 1.2 m, dia of .040 m on left, length of .4 m dia of .020 m, on right) Homework Equations angle =...

Hi, I got confused thinking about cause and effect. If force is applied to a car due to collision, it deforms car. The longer is the time of a collision, the smaller is average force applied. Longer time is achieved by crumple zone deformation, which is affected by force. I find here circular...

I am not sure which formula to apply, can anyone help me out? Homework Statement 28. A square copper bar experiences only elastic deformation if it is stressed less than 95MPa. To support a load of 1340kg without exceeding this stress, the minimum square cross-section ( i.e. width of one...

I am a forensic engineer trying to find the solution to a physics / metallurgy problem. No one in my office seems to know how to approach the problem. I was hoping I could get an answer from the folks in the forum. Please help. A 440C steel ball having a diameter of 1.0” is propelled...

Homework Statement Force exerted on a car by a crash barrier as the barrier crushes is F=-(4.5+140s) kN where s is the distance in metres from the initial contact. If a car of mass 2000 kg is traveling at 100 km/h when it hits the barrier the barrier deformation required to bring the car to...

I don't really know why, but I'm having trouble actually building deformation retractions, although I understand the concepts behind homotopies, etc.For example, when constructing a deformation retraction for \mathbb{R}^n-\{0\} to S^{n-1}, I found that you could define the mapping F(x,t) =...

The deformation process involves different stages. I was wondering how do you call the process where the materials return to their orginial state? Just as given in the bold text. And, moreover, what is the formula which calculates the time it returns back to the orginal state for a random...

Hello, I am developing an analytical approach to determine the creep constants of a constitutive model for nickel-base superalloys. I require creep strain versus time data to valid my approach. I've searched through literature and have found very little usable data. I need creep...

I have to calculate the elongation of a pencil under a load. I know I have to use deflection = PL/AE but since the pencil has 2 materials in it I have to modify that equation. I know that both materials extend by the same amount. Could anyone explain to me how to get that equation?

Homework Statement A cylindrical sample of soft tissue, with diameter = 8 mm, height = 6 mm, is firmly glued to two steel compression plates. Using axisymmetric elements, find the force needed to compress the sample by 0.5 mm. For the purpose of this problem you may assume that E = 1 kPa, ν =...

Hii all :smile: What is Fuzzy manifold ? and what is deformation ? thank u >>

Homework Statement Let a and b be two given orthonormal vectors around a fixed point O. The motion of a continuum is defined by the following velocity field: [tex] v(M) = \alpha \vec{a} (\vec{b} . \vec{OM}) \\ [\tex] where [tex] \alpha [\tex] is a known positive constant. 1...

Homework Statement 2. The attempt at a solution Ok. so I'm a little bit confused as to how to approach this problem. I would know how to do this problem if it was laying right to left, but because it's vertical, that makes it a lot more confusing for me. I know A = (1/4)(pi)(d^2) =...

Hey everyone I am wondering if someone can just double check my work and formulas to see if I did this correctly. Thanks! A 1.0-m rigid horizontal support is hung by two cables as shown. One cable is brass and the other is high density polyethylene plastic. At room temperature (21° C) the...

Homework Statement [PLAIN]http://img826.imageshack.us/img826/8600/217yf.jpg The attempt at a solution This is my work for part (a): \delta = \frac{PL}{AE} \delta = \frac{(6*10^3 N)(0.4 m)}{(70*10^9 Pa)(\frac{\pi}{4})(0.02^2 m)} \delta = 0.1091 mm However, the solution for...

I have some basic question about spring force. The anchor position for spring is its equlibrium position. As the spring is stretched, when released, it is expected that it should come back to its equilibrim position. But I found when less force is applied, the new equilibrium position is a bit...

Homework Statement A circular shaft AB has a torque T acting at the middle of the shaft, defined as plane C. Shaft end A is fixed while shaft end B is free to rotate (mounted in a thrust bearing). Finding the twist angle from A to C is not difficult, but the question requires that the twist...

I want to see what effects placing a steel cable on a reel of size of OD 3,51 m will have on the properties of the material? How will I go about doing this? A appreciate any help I can get :-)

I want to see what effects placing a steel cable on a reel of size of OD 3,51 m will have on the properties of the material? How will I go about doing this? A appreciate any help I can get :-)

Homework Statement the graph below shows the behaviour of a sample of a metal when it is stretched until it starts to undergo plastic deformation. what is the total work done in stretching the sample from zero extension to 12.0mm? simplify calculation by treating the region xy as a...

how can X be continuously deformed to Y?

Hi.. I need a good explanation for the following question. an explanation with a small mathematical calculation to prove the answer would be highly helpful. A copper rod of cross-section 10 mm  10 mm is stretched along its axis, changing length from 1.000 m to 1.001 m. The deformation is...

Y = (X ∪ I)/{x0 ~ 0} (disjoint union) xo - base point in X I am trying to show that X is a deformation retract of Y. I understand I need to maps f:X -> Y and g:Y -> X and show homotopic equivalence Where f is the inclusion map, is the identity ok for f? i.e f:X->Y , x in X ->...

Let' say two steel or rubber disks hit each other moving on friction-free surface. During the interaction, both disks deform elastically. My question is, does part of deforming energy gets converted to heat ? Why not ? Why this effect is never mentioned ? Is it negligible ? I know from...

Spring Constant and Deformation! Homework Statement If a spring with a constant K were to be cut in half, what would the spring constant be for each half? Homework Equations K = F/x, where F = force applied and x = length of the spring, or deformation. The Attempt at a Solution...

I am befuddled over how to calculate the force acting on a surface point of a deformed balloon (filled with water or air). I have drawn a picture to help illustrate. I have written a small program in c++ that uses the Runge-Kutta algorithm to simulate simple physics systems, like networks of...

This is a bit technical and I'm not exactly sure how to formulate my problem, but I'll try my best. I've been reading Landau & Lifgarbagez - Theory of Elasticity, and got not further than page 10, where they derive the free energy of deformation. So, what they do is that they assume linear...

the strain, as a function of the angle is K*sin2(x) now i know that the change in length is the integral of the strain =\intK*sin2(x)dx from 0->2pi =K/2*\int1-cos(2x)dx =K/2*(2pi - 0.5*sin(4pi) ) =K*pibut the answer says K*pi*R where does the R come from? i realize that the change in...

Homework Statement Determine the deformation of a composite bar is subjected to a centric force P. This is a general question. The composite bar is made of 2 materials. The top and bottom layer is material 1, and the middle layer is material 2. I can't think of a better way to describe...

Homework Statement Prove that in the homogeneous deformation, particles which after the deformation lie on the surface of a shere of radius b originally lay on the surface of an ellipsoid. Homework Equations homogeneous deformations are motions of the form: xi=ci + AiRXR where ci...

Homework Statement A body which in the reference configuration is a unit cube with its edges parallel to the coordinate axes undergoes the following deformation: x1=a1(X1+sX2), x2=a2X2, and x3=a3X3 (where a1,a2,a3,s are constants). determine the lengths of its edges after the...

If a soft malleable metal pipe has a bend in it and is then pumped up with high internal static pressure, would this soft metal pipe seek to straighten out or would it simply remain in its bent shape due to pressure acting in many directions. I wonder if the most natural position of a pipe is...

A cylinder is aligned along zz' and both ends are closed, one with a rigid plate which has a smaller tube and valve attached. If the other end is covered with an elastic material and the edges are thin enough so that at time t, if the pressure is lowered in the cylinder by evacuating air, the...