Research Article| June 01, 1977 A kinematic model of preferred orientation DAVID G. WILLIS DAVID G. WILLIS 1Geophysics Department, Stanford University, Stanford, California 94305 Search for other works by this author on: GSW Google Scholar Author and Article Information DAVID G. WILLIS 1Geophysics Department, Stanford University, Stanford, California 94305 Publisher: Geological Society of America First Online: 01 Jun 2017 Online ISSN: 1943-2674 Print ISSN: 0016-7606 Geological Society of America GSA Bulletin (1977) 88 (6): 883–894. https://doi.org/10.1130/0016-7606(1977)88<883:AKMOPO>2.0.CO;2 Article history First Online: 01 Jun 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation DAVID G. WILLIS; A kinematic model of preferred orientation. GSA Bulletin 1977;; 88 (6): 883–894. doi: https://doi.org/10.1130/0016-7606(1977)88<883:AKMOPO>2.0.CO;2 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGSA Bulletin Search Advanced Search Abstract Kinematic models of mineral grain behavior during deformation have been provided by G. B. Jeffery's study of rigid ellipsoids in a viscous fluid and A. March's analysis of deformable rods and plates. In this paper, a more general kinematic model is presented which is applicable to arbitrarily shaped grains.The simple premise of a constant linear relationship between the angular velocity of a mineral grain and the macroscopic strain rate of its surrounding material leads to the linear model. A further premise involving certain kinematic properties of the volume of deforming material displaced by an embedded mineral grain leads to a special form of the linear model called the displacement model; this model provides specific equations describing the motion of an individual mineral grain of arbitrary shape.The displacement model coincides with Jeffery's and March's models in the special cases of ellipsoids and of ideally slender needles or ideally thin plates, respectively. In addition, the displacement model is in good agreement with experimental measurements of the motions of rigid bodies of various shapes suspended in a slowly flowing viscous fluid.Using the displacement model for a particular class of grain shapes, it is possible to compute the preferred orientation diagrams resulting from an arbitrarily given strain history. Several sequences of such diagrams are presented showing the development of preferred orientation for different shapes and strains. These diagrams have the property that they depend not only upon the grain shape, but also upon the strain history. This is in contrast to March's solutions, which depend solely upon the finite strain ellipsoid and are otherwise independent of the strain history.The specific properties of the preferred orientations produced by the displacement model can be tested against observations of naturally occurring mineral orientations. In order to be significant, however, such observations will require simultaneous measurements of both grain shapes and grain orientations, a task which has apparently been attempted only by W. A. Duffield. His results are reviewed and are shown to be in agreement with the displacement model in the area studied. This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.