STRAIN I. DEFINITIONS A. Displacement - movement of material point with respect to another point in response to an applied stress 1. Rigid body -- no shape change a. Translation b. Rotation - change in orientation 2. Nonrigid body -- internal shape change a. Dilation - change in volume, line length changes, but lines do not change their orientation b. Distortion - changes in lengths and orientations, but no volume changes DV = 0 B. Line length changes: 2 types 1. Linear displacement - 2. Shear or angular displacement - Ð's change between lines II. STRAIN - RESPONSE OF MATERIAL TO STRESS A. Nonpermanent -aka- recoverable e.g., rubber band, earthquake waves B. Permanent - e.g., folds, faults, deformed grains or fossils C. Homogeneous / heterogeneous strain: 1. Homogeneous - a. Lines remain straight and parallel 2. Heterogeneous - D. Strain is scale dependent 1. Heterogeneous at (map) macro-scale - volumes of rock at different parts of the fold are in different states of strain (folding requires heterogeneous strain) 2. Homogeneous on (outcrop) mesoscopic scale - can't detect any difference in strain thin section between two different volumes 3. Heterogeneous on (thin section) microscopic scale - grain under S.E.M. 4. Homogeneous at lattice scale - atoms within the quartz lattice aren't distorted (but have been translated) E. Strain should be viewed as progressive deformation thru time F. Infinitesimal strain - at each instant of progressive deformation, material absorbs a measure of strain G. Finite strain - product of all superimposed infinitesimal strains III. MEASUREMENT OF STRAIN (FINITE) A. Length (line) changes 1. e-(extension or elongation) e = (lf - li) / li = D l / l i lf = final length li = initial length can make li = 1 unit (since hard to determine initial) e = 0.1 à line becomes 10% more elongate 2. s-(stretch) / 1+e a. Factor that we multiply initial length by to get final length lf = (s)(li) s = lf / li 3. Quadratic elongation l º(1+e)2 s2 = (lf / li)2 e, s, l = 3 parameters to study line length changes B. Orientation change -measured using unit shear 1. (unit shear) or (shear strain) = g = tan Y which is angular shear 2. If line is lengthened = + value 3. If line is shortened = - value IV. STRAIN ELLIPSE: A. e1 = x direction = max elongation (max principle e) B. e3 = z direction = min elongation (min principle e) V. STRESS vs. STRAIN ELLIPSES A. Inversely related e.g., silly putty VI. COMPARISON OF 2 STRAIN PATHS - PURE SHEAR vs. SIMPLE SHEAR A. Pure shear - orientation of principal strain axes is constant (irrotational strain) e.g., silly putty B. Simple shear (shear zones) - Only one line maintains its original orientation and doesn't shorten or lengthen. Principal axes do rotate = rotational strain VI. DIFFICULTIES INVOLVED IN STRAIN ANALYSIS: A. Volume changes - e.g., metamorphism of shale produces volume changes e.g. shale - lower specific gravity = 2.5 - 2.6 metamorphism à schist - micas with s.g. = 2.8 - 3.2 1. Higher density, removal of pore spaces, new crystals B. Deformation of original coordinate system C. Strain path: 1. d1 à shortening + extension 2. d2 à shortening + elongation VII. WAYS OF ILLUSTRATING STRAIN: A. Finite strain ellipsoid 1. Principal strains = x, y, and z mutually perpendicular 2. xyz ¹ 0 3. x ³y ³ z 4. x = max prin. strain, z = min prin. strain 5. Special cases: a. If x = y > z -- pancake b. If x > y = z -- cigar shaped c. y =1, plane strain = all elong./short. going on x, z axes B. Flinn diagram - plots ratio of x/y against ratio y/z