Deformation Definition and 207 Threads

In engineering, deformation refers to the change in size or shape of an object. Displacements are the absolute change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain is the relative internal change in shape of an infinitesimally small cube of material and can be expressed as a non-dimensional change in length or angle of distortion of the cube. Strains are related to the forces acting on the cube, which are known as stress, by a stress-strain curve. The relationship between stress and strain is generally linear and reversible up until the yield point and the deformation is elastic. The linear relationship for a material is known as Young's modulus. Above the yield point, some degree of permanent distortion remains after unloading and is termed plastic deformation. The determination of the stress and strain throughout a solid object is given by the field of strength of materials and for a structure by structural analysis.
Engineering stress and engineering strain are approximations to the internal state that may be determined from the external forces and deformations of an object, provided that there is no significant change in size. When there is a significant change in size, the true stress and true strain can be derived from the instantaneous size of the object.
In the figure it can be seen that the compressive loading (indicated by the arrow) has caused deformation in the cylinder so that the original shape (dashed lines) has changed (deformed) into one with bulging sides. The sides bulge because the material, although strong enough to not crack or otherwise fail, is not strong enough to support the load without change. As a result, the material is forced out laterally. Internal forces (in this case at right angles to the deformation) resist the applied load.
The concept of a rigid body can be applied if the deformation is negligible.

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  1. H

    Deformation due to thermal expansion/contraction

    Dear all, I have a 3D cube with a nonuniform distribution of temperature. In order to calculate the deformation of the cube using the finite element method, we need nodal forces. How we calculate the nodal force from the temperature distribution? I am aware of a the method based on the...
  2. facenian

    Is the Linear Eulerian Deformation Tensor an Exact Measure of Deformation?

    Hello, I have difficulty interpreting the following fact (I'm reading Cotinuum Mechanics by Spencer). The relative velocity between two nearby points P and Q in the current configuarion is given by: dv_i=D_{ik}dx_k + W_{ik}dx_k where D_{ik}=\frac{d}{dt}e_{ik} is the rate of deformation tensor...
  3. P

    How do I calculate the axial deformation of a member given force and dimensions?

    ---Quote--- *1. Homework Statement * http://postimg.org/image/yrbu7a0vb/ *2. Homework Equations * e(elongation of a member) = (Force * Length)/(Area * Young's Modulus) *3. The Attempt at a Solution * Is the force P distributed so that the force on each bar is P/3 so that F2...
  4. A

    Deformation gradient f(3,3) vs Coordinates

    Dear, I have a task to model the behaviour of certain interphase material. Let's say that functions which describe the change of material parameters are known. i.g. change of the Young's modulus as function of distance from neighbouring material (or (0,0) origin) - PAR=PAR(x)...
  5. E

    Contour integration (related to deformation of path)

    Homework Statement Use the principle of deformation of path to deduce \int_0^\infty t^n \textbf{cos}(bt) e^{-at}dt=\frac{n!}{e^{n+1}}\textbf{cos}((n+1)\phi) and \int_0^\infty t^n \textbf{sin}(bt) e^{-at}dt=\frac{n!}{e^{n+1}}\textbf{sin}((n+1)\phi) where a>0, b>0, c=\sqrt{a^2+b^2}, and...
  6. M

    Deformation of a dicomponent rod under tension

    For this problem, my thinking was that since the top of the rod is fixed, then the only part that is elongating is the bottom, so I found the part elongating at AB and said that was the total elongation. I am not sure if this reasoning is sound. I suppose the other possibility would be to add up...
  7. P

    Reduction of area with the elastic deformation?

    In the tensile test practical for ductile materials, up to the elastic limit, the deformation is recoverable (no line defects). My question is can there be a reduction of area with the elastic deformation? If yes, how it happens? I'm a beginner. Thank you!
  8. O

    Contact Pressure Vs Traction Vs Deformation in a wire

    Homework Statement A .1in aluminum wire is being pulled from a coil between 2 1in steel rollers. One roller is fixed to the driving motor while the other roller is loaded with a force to provide traction. What is the maximum force that can be applied before the wire is plastically deformed by...
  9. K

    Simulating deformation from impact with static load possible?

    Hi everyone, For current project at work I am looking into possibility of simulating deformation from impact with static force. Here is the input data: A ball of 0.5 kg at speed of 25 km/h crashes into a damping foam which is placed on a rigid wall. Stopping (deformation) distance in the foam...
  10. A

    Deformation of string from impact of an object with constant velocity

    If a car with no acceleration, only velocity, hits my spring with a spring constant K What will be the deformation in string? How do I calculate the force from impact while acceleration is equal to 0?
  11. D

    Finding $\mathbf{E}$ and $\mathbf{e}$ for a Deformation Field

    For the deformation field given by $$ x_1 = X_1 + \alpha X_2,\quad x_2 = X_2 - \alpha X_1,\quad x_3 = X_3 $$ where ##\alpha## is a constant, determine the matrix form of the tensors ##\mathbf{E}## and ##\mathbf{e}##, and show that the circle of particles ##X_1^2+ X_2^2 = 1## deforms...
  12. E

    Change in potential energy of elastic strip under deformation

    A linear elastic strip of natural length a and stiffness k lies between x = 0 and x = a. Each point on the strip is transformed by a differentiable, monotone increasing function f. a) Characterise the change in potential energy. b) Given the boundary conditions f(0) = 0 and f(a) = b, choose f...
  13. P

    Beam deformation. FEM (solidmechanics)

    Homework Statement I have this question. I need to know the diformation in P direction. Here is the question I use the symmetry and finally with a 1/4 modell I get the following: which is correct according to the instruction. K is the stiffness of the spring. which with symmetry becomes...
  14. E

    Continuum Mechanics deformation definitions

    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...
  15. L

    How to calculate pad deformation

    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.
  16. K

    Fluid mechanics: defition of shear flow [rate of deformation tensor]

    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...
  17. T

    Continuum Mechanics - Deformation gradient

    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...
  18. R

    Model Steel for Large Deformation: Multilinear Isotropic Hardening

    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...
  19. Q

    Do Centripetal and Centrifugal Forces Stretch a Spinning Sphere in Space?

    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...
  20. Q

    Source of deformation on Spinning oblect

    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...
  21. W

    Interpretation of deformation electron density maps (for Al alloys)

    I am posting this from a friend's account since I've been unable to register for a while. Brace yourselves for this is going to be a long post. ----------------------- TLDR: I am trying to figure out the reason for AlSi's lower than expected from atomic misfit solid solution hardening...
  22. H

    Deformation Analysis: When to Use Plane Strain vs 3D?

    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
  23. S

    Neglecting axial deformation is slope deflection method

    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...
  24. F

    Composition of infinite deformation retracts

    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)...
  25. F

    Coefficient of restitution, Karate and deformation energy

    Hello Forum, I was reading a book about the physics of sports. It talks about karate and deformation energy that gets transferred to a target when a punch hits it... The formula for the deformation energy contains the coefficient of restitution and say that a small coefficient belongs to...
  26. S

    Deformation retraction of plane RP2

    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...
  27. H

    Structural Analysis- small deformation

    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...
  28. H

    Elastic deformation of a jar lid (continuüm mechanics)

    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...
  29. ShayanJ

    Why does the circle appear as an ellipse when moving at different velocities?

    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...
  30. R

    FEA Boundary conditions for basic helical spring deformation

    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...
  31. H

    Can You Deform a Material with a Wave?

    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...
  32. L

    How to test the creep deformation of polymer

    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
  33. O

    Difference between Linear and Cubic Deformation in Bending?

    I do not really understand this as you can probably tell, but What is the difference bewteen Linear and Cubic displacement deformation functions in beam bending? For example why would one be used over another to model or calculate beam bending? or how does either type effect what bending...
  34. T

    One shaft two diameters angle of deformation

    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 =...
  35. S

    Car crumple zone deformation physics

    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...
  36. S

    How to Calculate Minimum Cross-Section for Elastic Deformation in Copper Bars?

    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...
  37. F

    Continuous deformation? Family of curves? So confused

    I understand the concept behind continuous deformations. Say we have two curves ζ1 and ζ2 from A to B on some domain D and say that Pdx + Qdy is closed. Say we can show n points A=c1,c2,...,cn=B and A=d1,d2,d3,...,dn=B, so that we can first say follow the curve ζ1 from A to c1 then over to...
  38. B

    Colision and deformation between 2 objects

    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...
  39. D

    Barrier Deformation and Impact of Car

    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...
  40. N

    Deformation Caused By Tightening A Nut

    Homework Statement Homework Equations \delta = PL/AE The Attempt at a Solution As you can see I know that F_{cd} is related to F_{be} and a second relationship can be found by the geometry of the deformations. I end up with F_{cd} = 11.9^{kN} but the answer is supposed to be...
  41. A

    Constructing Explicit Deformation Retractions

    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) =...
  42. D

    Stages in the deformation process

    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...
  43. B

    Deformation of ball in elastic collision

    Homework Statement A soccer ball with radius R = 11 cm is inflated to a gauge pressure of 9×104 Pa. The ball is dropped onto and bounces elastically off of a hard smooth floor. Find approximate expressions for the surface area of the ball in contact with the floor, the amount of time the ball...
  44. Z

    Calculating Deformation Energy for Brass Form Tests

    Hi! I'm working in a laboratory and been assigned to the task of verifying on of our machines calculations. The machine calculates the deformationenergy needed to test a sample that's been moulded in a brass form. Its this value I need to validate. The information I have at this point...
  45. S

    Where can I find Creep Deformation data?

    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...
  46. A

    How Does Mesh Refinement Affect Shell Deformation in ANSYS?

    Homework Statement A square plate of edge length L = 1 m, thickness t = 5 cm, is fixed on two edges. The other two edges are free. A load of F = 10 kN is applied at the corner opposite that where the fixed edges intersect. Use shell elements to compute the deflection at the loaded corner...
  47. G

    Axial deformation in composite beam

    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?
  48. A

    Axisymmetric deformation in ANSYS

    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 =...
  49. M

    Exploring Fuzzy Manifolds and Deformation

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

    What is the Maximum Contact Force and Forging Height of a Mechanical Press?

    deformation and forging! (URGENT!) A mechanical press is powered by a 22.4 kW motor and operates at 40 strokes per minute. It uses a flywheel, so that the rotational speed of the crankshaft does not vary appreciably during the stroke. (a) If the stroke length is 15.24 cm, what is the maximum...
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