中国地质大学：《构造地质学》课程PPT教学课件（英文版）Lecture 22 Strain

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