Finite strain I Rigid body deformations Strain measurements

Finite strain I • Rigid body deformations • Strain measurements • The strain tensor • Faith of material lines

Finite strain I: Finite versus infinitesimal strain • Infinitesimal strain is a strain that is less than 2%. • Finite strain can be thought of as a sum of many infinitesimal strains.

Finite strain I: Rigid body deformations • Translation: movement of the body without rotation or distortion. • Rigid body rotation: rotation of a body about a common axis.

Finite strain I: Strain (i. e. , non-rigid deformation) Distortion: Change in shape with no change in volume (or area in 2 D). Examples include simple shear and pure shear. • Simple shear: • Pure shear: Dilation: �Volume change

Finite strain I: Measurements of strain • Change in line length • Change in angle • Change in volume

Finite strain I: Measurements of strain Change in line length: Extension li lf

Finite strain I: Measurements of strain Change in line length: Stretch Change in line length: Quadratic elongation

Finite strain I: Measurements of strain Change in line angle: Angular shear x y Change in line angle: Shear strain

Finite strain I: Measurements of strain Change in volume: Dilation Vi Vf

Finite strain I: The strain tensor (but more precisely the deformation gradient tensor) This tensor is used to calculate the position of a material particle (or vector) in the deformed configuration for any given material particle (or vector) in the pre-deformed configuration. where:

Finite strain I: A few examples of strain tensors Rigid body rotation: Simple shear: Pure shear:

Finite strain I: The faith of material lines Material lines of geological context include: dikes, sills, layers, faults, etc. Let’s see what happens to material lines under progressive strain (show movies).

Finite strain I: The faith of material lines Simple shear:

Finite strain I: The faith of material lines Conclusions simple-shear: • Some Material Lines (ML) undergo stretching and rotation at the same time (rotated boudines). • Some ML undergo shortening followed by stretching (boudinaged fold). • Angular distance between ML changes progressively. • ML parallel to the direction of shearing neither stretch nor rotate.