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. P

    I Can Propeller Speeds and Wave Breaks Challenge the Speed of Light?

    Hi, I have two topics: 1) Suppose a propeller is spinning very fast (say it's in a vacuum, no drag) and we arbitrarily lengthen its blades. Eventually the velocity of the tips of the propeller will approach the speed of light. That should be a speed limit, but that implies that the blades of...
  2. P

    So what is the precise role that thickness plays in the resistance of a specimen to deformation or fracture during a collision?

    From Stress-Strain curves in static loading conditions, we know the stress in force/cross-sectional area that's needed to deform a material. So with a bigger specimen, there's also a bigger cross-sectional area so you need a bigger force to generate the necessary stress. This same concept should...
  3. P

    Tension in a deformed cylindrical bag on a surface

    A cylindrical bag is made from a freely deformable fabric, impermeable for air, which has surface mass density σ; its perimeter L is much less than its length ##l##. If this bag is filled with air, it resembles a sausage. The bag is laid on a horizontal smooth floor (coefficient of friction µ =...
  4. P

    Contact Mechanics: Deformation of a ball on a surface

    A solid ball of radius R, density ρ, and Young’s modulus Y rests on a hard table. Because of its weight, it deforms slightly, so that the area in contact with the table is a circle of radius r. Estimate r, assuming that it is much smaller than R. I have no issues understanding the...
  5. J

    Pull-off force: hose, pipe, clamp

    Was surprised by a study recently where we tested 6 samples for pull-off force at a 10% reduction in clamp Torque and noticed negligible shift in results. Is it possible that at higher torque the clamp is deforming the pipe, reducing the surface contact (friction) between the hose and pipe? The...
  6. Yossi33

    Engineering Mechanics of materials -- deformation problem

    Hi, i'm struggling with that problem , i need to find the distance that point N went down.My way of thinking is that the structure is twice not statically determined because of the beam MN and beacuse of the left support which is also unnecessary in order for equilibrium. My 2 equations of...
  7. Krismein

    Calculate deflection of rod/axlepipe due to distributed load

    Summary:: Calculate the deformation on a rod/axle/pipe due to a distributed load. I’m manually trying to calculate the deformation on a rod/axle/pipe due to a distributed load. The rod has an outer diameter of 62mm and an inner diameter of 50, is 170mm long, made from a material with an...
  8. patric44

    Exploring Nuclear Quadrupole Moment and Deformation

    hi guys I have read the other day about how the nuclear quadruple moment descries the deformation of the nucleus, however i can't get my head around how is that!, I am familiar with the multiple expansion in which we can describe the potential of an arbitrary charge distribution by the following...
  9. U

    Engineering Elastic Deformation of an Axially Loaded Member

    Sum of forces in the y-direction = 0 and downwards is +ve P + Fab,y = 0 P + Fab (4/5) = 0 Fab = -1.25P ẟ = FL/AE -> ẟab = FabLab/AabE ẟab = (-1.25P*.75)/(pi*(.01)^2*(200*10^3)) = -0.0149P After this step, I am uncertain of how I can relate the vertical elongation with AB's elongation to find...
  10. M

    Engineering Spring Deformation: Potential Energy Balance Incorrect?

    In the initial position the spring is previously compressed, then the block adds a force, and the spring is again deformed. I think the energy balance is incorrect; the potential energy of the spring is repeated.
  11. F

    Derivative of the deformation gradient w.r.t Cauchy green tensor

    What's the derivative of deformation gradient F w.r.t cauchy green tensor C, where C=F'F and ' denotes the transpose?
  12. A2148

    Automotive Need assistance in Abaqus simulation

    I'm doing static analysis. I have already set up all the prerequisites, preprocessors such as material addition, sectioning, defining boundary conditions, and displacement. However, I'm not getting the results. Please suggest anything. Kindly find the attachment. regards
  13. B

    Formula for the energy of elastic deformation

    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. ##...
  14. shk

    Material properties -- Elastic and Plastic deformation in automobile crashes

    a)plastic deformation because of permanent deformation b) the other parts that have been destroyed have stored the energy and this saved the passenger compartment. C) the alloy crash barrier is stronger than the car body and and saves more of the energy by deforming shape. I'm not sure about my...
  15. baldbrain

    A basic doubt about stress and strain

    While introducing tensile stress, we're shown a bar fixed at a support being subjected to a force in the axial direction at the opposite end. Then, since the bar is in translational equilibrium, we say that internal forces must balance it out, and this internal resistance per unit area is known...
  16. person123

    I Maximum Strain For Samples of Different Cross-Sectional Areas

    I would assume that because the samples are made of the same material they would fail at the same stress and so the same strain. However, the data shows that the sample with a greater cross-sectional area fails at a greater strain, and the two are roughly proportional. Does anyone know what...
  17. person123

    Does Sample Strain Decrease At Failure?

    My guess is that the deformation immediately before would be the sum of elastic and plastic deformation, and the deformation after would be just the plastic deformation, and it therefore would decrease. Is this correct?
  18. person123

    I Stresses Caused By Deformation For Bending

    Hi. Say you apply a moment on a beam and bend it into an arch. If you take a free body diagram of a section of the beam you would need normal stresses in the radial direction to balance the forces: I have never seen this brought up before though -- is it correct logic? Also, is this sort of...
  19. loophole

    Water deformation subjected to ultrasound waves

    Hello everyone, in one of my projects I am dealing with the following problem: We have a tank filled of water. If we assumed that a focused ultrasond beam hit the water perpendicularly to the surface. How can I calculate the displacement of the water surface? In particular, I am interested in...
  20. O

    I Coordinate Systems After Deformation of Axes

    Disclaimer: I am a physics student and I have very little knowledge of topology or differential geometry. I don't necessarily expect a complete answer to this question, but I haven't really found any reference that approaches what I'm trying to ask, so I'd be quite happy to simply be pointed in...
  21. K

    I Quadrupole deformation in nuclei

    Hello! I am confused about the definition of the quadrupole moment in nuclei. One definition I found, in Wong, says that the quadrupole moment of a nucleus is given (ignoring some numerical constant) by: $$<J,M=J|r^2Y_{20}|J,M=J>$$ so the expectation value of a second order spherical harmonic...
  22. J

    Kinematics of deformation (Continuum mechanics)

    Question is extracted from "Ellad B Tadmor, Ronald E Miller, Ryan S Elliott - Continuum mechanics and thermodynamics From fundamental concepts to governing equations". I just got stuck at part (a). I think if part(a) is solved, I may be able to do the other parts.
  23. J

    Collapse and deformation of a circle (tube)

    Hello: I am looking for a formula that can help me determine the collapse and deformation strengths of plastic tubing. I have been scouring the internet for this information and i have yet to find a satsifactory formula. I have found a formula that seems pretty wide spread ~ however it gives me...
  24. Like Tony Stark

    Deformation of a spring being accelerated

    I wrote Newton's equations for the block seen from the non inertial frame. The axis are inclined. ##x) Fe+W_x-f*cos(\alpha)=0## ##y) N-f*sin(\alpha)-W_y=0## Where ##f*## is the pseudo-force and ##Fe## is the elastic force. I set the acceleration as 0 because they are in equilibrium. The thing...
  25. G

    I Quantifying deformation of a shape

    Hello all, I hope this post is in the appropriate thread. Would anyone have any insight on a method to quantify deformation of a shape? For example, I attached two images of a white shape of interest at the center (one deformed and one undeformed). I'm trying to develop a metric/parameter...
  26. E

    What are interesting/cool topics about material deformation?

    Hey guys, so I have to give a 10 minute presentation for my class. I am absolutely terrible at memorizing stuff. Its pretty bad. If I can find an interesting or cool topic I would be able to remember material better. It needs to be about deformation or fracture of a material in terms of micro...
  27. R

    Time-dependent axial deformation

    This is highly speculative, and I very much doubt that it is actually correct. If anybody knows of a correct equation for time-dependent axial deformation, or at least how to go about deriving a more correct equation, I would greatly appreciate any feedback.
  28. S

    How to decide which component is best in terms of stress and deformation?

    Summary: In terms of stress, strain & deformation, what is better for a given component. 1) low stress or high stress 2) less strain or large strain 3) less deformation or large deformation? Some dimensional changes were made in an existing component to study how these changes effect the...
  29. A

    I Variation of geometrical quantities under infinitesimal deformation

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  30. C

    Rate of change of area with deformation

    Could I please get a hint on how I should start this question/how I should parameterize these variables? I'm going to head to sleep as I am from the eastern time zone. I apologize ahead of time for my delayed reply.
  31. W

    Deformation under eccentric shear stress

    Hi, Starting with an example to clarify what I am looking for. Assume an extension force applied on a distance from the centroid/neutral axis of a body: see attached, please. As result, bending force besides the tensile force will be generated in that body as presented in section A-A in the...
  32. M

    Nature of displacement and the deformation tensor

    If we have two points P and Q in undeformed material and after deformation they become P' and Q'. The deformation tensor is the derivative of the displacement. What is the displacement? vector PP'? or the change from PQ to P'Q'? is the second question is the strain "change in length". Why the...
  33. Nayef

    Effect of the load sequence on the deformation of a spring

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  34. S

    Eigenvalue problem -- Elastic deformation of a membrane

    Homework Statement An elastic membrane in the x1x2-plane with boundary circle x1^2 + x2^2 = 1 is stretched so that point P(x1,x2) goes over into point Q(y1,y2) such that y = Ax with A = 3/2* [2 1 ; 1 2] find the principal directions and the corresponding factors of extension or contraction of...
  35. J

    Deformation of a metal sheet with a tip force applied

    Homework Statement Stretch forming[/B] A 38.1 cm-long sheet with a cross sectional area of 3.2258 cm2 is stretched with a force, F, until alpha = 0.35 rad. The tip of the force is fixed to the strip by some means, thus maintaining the lateral position of the force. (The left portion of the...
  36. V

    ANSYS Workbench -- What does "extra deformation shapes" mean?

    Hello! I read from ansys element reference that for solid 65 the key option (1) is used to include or suppress extra deformation shapes. I would like to ask what extra deformation shape mean.
  37. T

    I Origin of Deformation Energy in Curved Spacetime?

    If a gravitational wave passes an elastic body it will be deformed. The source of the work done on it comes from the energy of the gravitational wave. In curved spacetime e.g. an accelerated expanding FRW- or static Schwarzschild-spacetime an elastic body will be deformed too. What is the...
  38. D

    A How to Calculate Young's Modulus for Deformation of a Sphere into an Ellipsoid?

    I need to calculate Young's modulus based on deformation of sphere into ellipsoid. I assume the deforming force acting along one axes. Initial dimensions of the object before (sphere) and after (ellipsoid) deformation are known.Does anyone know or familiar with good reference?
  39. B

    Extension of a rod segment dx due to a passing longitudinal wave

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  40. M

    Solving Statics Deformation Problems: Rod Equations & Attempt at Solution

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  41. J

    What causes the bending of this rod?

    In this video, a man applies an angular acceleration to the base of a rod. While the rod rotates, it bends. Why? What force is there that causes the bending, aside from rod's own weight? It seems to me to be the work of a fictitious inertial force. I was always taught that those forces don't...
  42. mertcan

    Large deformation in solid mechanics

    Hi initially I am aware that large deformation in solid mechanics requires non linear strain theory in the lieu of infinitesmall strain theory. But I wonder that if we can approximate large deformation of material using infinitesmall strain of small elements employing and summing linear strains...
  43. S

    How does adding material affect stress in FEA results?

    Hello, I have a fairly simple question but I guess I am having a hard time trying to understand it. I have a plastic connection of two different geometries (see attachment). When I hold end of the front portion (of the uniform diameter) and apply torque at the bigger cylinder geometry, there...
  44. H

    Plastic Deformation: Power Law & Strain Hardening Exponents

    Is there any relation between power law exponent of of P-h curve and strain hardening exponent of stress-strain curve?
  45. pHartless

    How Much Weight Can a 45-Degree Square Steel Tube Structure Support?

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  46. G

    Thermal Expansion of A-36 Steel Rails: -20F to 90F

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  47. Mike J

    Internal stresses of an accelerating body

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  48. Stef

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  49. 1

    A Deformation in static and transient case

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  50. F

    I Deformation of contour of integration or shifting poles

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