Strain Displacement Strain Strain field Strain determination in rocks
Strain • Displacement • Strain • Strain field • Strain determination in rocks
Displacement vector and displacement components
Displacement vector and displacement components x y x z y z 0 v w u
DEFORMATION 1) Translation- Change in position by lateral motion 2) Rotation- Rigid body spin about I or more axes 3)Strain-Change in shape or distortion 3
DEFORMATION 1) Translation – Change in position by lateral motion 2) Rotation – Rigid body spin about 1 or more axes 3) Strain - Change in shape or distortion 1 2 3
dilation (volume change) distortion (shape change) rotation total strain Nature of strain
Nature of strain
A homogeneous strain B inhomogeneous strain
homogeneous and Inhomogeneous deformation Rubber experiment (a) initial state(b) homogeneous deformation (c) inhomogeneous deformation after Pan Lizhou, 1976)
Rubber experiment (a) initial state (b) homogeneous deformation (c) inhomogeneous deformation （after Pan Lizhou，1976） homogeneous and inhomogeneous deformation
Domain of Homogeneous(H)and Inhomogeneous D) Strain
Domain of Homogeneous (H) and Inhomogeneous (I) Strain
… ……∵:灬"∴ ∴∵∵ ,∴ ∴…∴∵∵ ∵" ……… ∴:氵 Bending deformation inhomogeneous deformation on the whole, homogeneous deformation in small local areas
Bending deformation inhomogeneous deformation on the whole， homogeneous deformation in small local areas
extension e=(-b) B shear strain ,= tan y P(x, y) P(X,y, C the strain ellipse Extension, shear strain and the strain ellipse Stretch s=llo=(I+e
Extension, shear strain and the strain ellipse l0 l Stretch s = l/l0 = (1+e)
Two definitions of shear strain for large deformation r= tan y r=sIn y Definition of shear strain for small deformation y=tanv≈snv≈y
= sin = tan = tan sin Two definitions of shear strain for large deformation Definition of shear strain for small deformation