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

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  7. P

    Reduction of area with the elastic deformation?

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  8. O

    Contact Pressure Vs Traction Vs Deformation in a wire

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  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

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  11. D

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

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  12. E

    Change in potential energy of elastic strip under deformation

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  13. P

    Beam deformation. FEM (solidmechanics)

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  14. E

    Continuum Mechanics deformation definitions

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  15. L

    How to calculate pad deformation

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  16. K

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

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  17. T

    Continuum Mechanics - Deformation gradient

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  18. R

    Model Steel for Large Deformation: Multilinear Isotropic Hardening

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  19. Q

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

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  20. Q

    Source of deformation on Spinning oblect

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  21. W

    Interpretation of deformation electron density maps (for Al alloys)

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  22. H

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

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  23. S

    Neglecting axial deformation is slope deflection method

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  24. F

    Composition of infinite deformation retracts

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  25. F

    Coefficient of restitution, Karate and deformation energy

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  26. S

    Deformation retraction of plane RP2

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  27. H

    Structural Analysis- small deformation

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  28. H

    Elastic deformation of a jar lid (continuüm mechanics)

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  29. ShayanJ

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

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  30. R

    FEA Boundary conditions for basic helical spring deformation

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  31. H

    Can You Deform a Material with a Wave?

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  32. L

    How to test the creep deformation of polymer

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  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

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  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

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  39. D

    Barrier Deformation and Impact of Car

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  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

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  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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