Chapter 3 Week 3 notes: Progressive deformation 3.1 Reading assignment Progressive strain histories are covered in section 15.5 (pages 308ff.) of Twiss and Moores. Also read pages 352 to 357 ("Strain in shear zones"). Nice treatment of this sort of thing is also found in the introductory chapters of Passchier et. al. (2005) Microtectonics. 3.2 Progressive strain in pure shear In lecture, we discuss possible strain histories for lines of various orientations that undergo progressive strain. (In lab, we deal with the case of pure shear). By progressive strain, we simply indicate that in our analysis we will break down the deformation history into many small steps. At each step we will consider both the inﬁnitesimal strain that accrues at that step, and the ﬁnite strain that has ac crued up to that point. Even in very simple cases, some rather complex behavior can result. The analysis considers one of the "simplest" kinds of strain: pure shear in two dimensions, i.e.:plane strain, �2 = 0 and λ2 = 1. The following four ﬁgures accompany the inclass discussion. These ﬁgures are meant to be incomplete. Use these to help you follow the class discussion; you should annotate and complete these. Figure 3.1: Mohr circle for Inﬁnitesimal strain Figure 3.2: Mohr circle for ﬁnite strain, unstrained state reference frame Figure 3.3: Mohr circle for ﬁnite strain, strained state reference frame 4 Shortening only L . eg d 5 in of ite n tio a ng elo n of e in Lengthening only Figure 3.4: "Real world" reference frame. Shaded area shows region where material lines have suffered shortening followed by lengthening. Line of no ﬁnite elongation separates subregions deﬁned by whether extension exceeds shortening.