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

2. 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.

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

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

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

6. Change in line length: Extension lili lflf Finite strain I: Measurements of strain

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

8. Change in line angle: Angular shear xx yy   Change in line angle: Shear strain Finite strain I: Measurements of strain

9. Change in volume: Dilation ViVi VfVf Finite strain I: Measurements of strain

10. 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:

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

12. 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).

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

14. 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. Finite strain I: The faith of material lines

15. Rotated boudines: Finite strain I: The faith of material lines

16. Boudinaged fold (or folded boudinage): Finite strain I: The faith of material lines

17. Pure shear: