Deformation and Strain

Question 1

displacement and displacement field

Answer 1

P becomes P’, the straight line from P to P’ is the displacement vector

the actual path taken may not be a straight line
-figuring out the actual path is very difficult
-cant be certain where it started from and what path was taken

for every point (particle) you have a displacement vector
-unlimited displacement vectors
-deformation is the array of displacement vectors

Question 2

homogeneous vs inhomogeneous

Answer 2

homogeneous: all points move by the same degree in all ways (orientation, distance, direction)

even if one point is different, it is not homogeneous (ie. if all lines remain parallel except for one, its not homogeneous)

Question 3

deformation and strain

Answer 3

deformation is any change in shape (strain/distortion), position (translation), and orientation (rotation) of a body under stress

individual components make up the final deformation

most times deformation refers to strain

Question 4

homogeneous strain

Answer 4

describes the final state in terms of the initial state (dont worry about what happens in between)

Question 5

measures of strain

Answer 5

to quantities to describe strain:

change in length
-elongation,e (change in length divided by initial length)
-stretch,S (new length over initial length = 1+e)

change in angle
-angular sheer (angle between initial angle and final angle)
-shear strain, gamma (tan of angular sheer)

dilation (change in volume)

Question 6

what are the values of e and S when there is a) no change in length, b) lengthening, c) shortening

Answer 6

no length change, e=0, S=1
lengthening: e= , S=
shortening: e= , S=

Question 7

strain ellipsoid and circular sections

Answer 7

no change in length between the two planes

x is always the longest, z is the shortest

Question 8

types of homogeneous strain

Answer 8

a) general strain

b) axial symmetrical extension (cigar-shaped)
S1>S2=S3
X>Y>Z

c) axial symmetrical shortening (pancake shaped)
S1=S1>S3
X>Y=Z

d) plane strain
-no length change in y direction
S2=1

e) simple shortening (volume loss)

Question 9

Flinn Diagram

Answer 9

K tells you the shape of the strain ellipsoid

K=∞, cigar-shaped
strain ellipsoid
K=1, plane strain
K=0, pancake-shaped strain ellipsoid

Question 10

Determination of strain

Answer 10

shape and orientation of strain ellipsoid

measure long axis and short axis and get ratio

elongation:
-find final and initial length to get stretch

angle:
initial angle, angle after deformation, tan of angle in the middle

Question 11

clasts in 3D

Answer 11

-long axis vertical, S2 and S3 equal
-linear features on the side, circles on top (like a bunch of pencils)
-might get the wrong impression if you only saw the top

Question 12

coaxial deformation

Answer 12

The principal axes of the incremental strain ellipsoids always have the same orientation as those of the total strain ellipsoid during deformation. Consequently, the principal directions of total and incremental strain are fixed to the same lines of material particles throughout deformation.

Question 13

pure shear

Answer 13

coaxial deformation
homogeneous deformation

Question 14

simple shear

Answer 14

simple shear is similar to non-coaxial but more complication
-not all non-coaxial is simple shear

homogeneous deformation involving plane strain
- a single family of parallel material planes remain undistorted and parallel throughout deformation
(if you bend a deck of cards, thickness of the deck remains the same and cards remain parallel)

-involves both strain and rotation