STREAM FUNCTIONS AND COMPLEX POTENTIALS - IMPLICATIONS FOR DEVELOPMENT OF ROCK FABRIC AND THE CONTINUUM ASSUMPTION

Stream functions may be applied to study the development of ductile de formation patterns in rocks. It is demonstrated how to derive the stre am function and the associated complex potential from the velocity fie ld of any particular flow. Finite deformation patterns are subsequentl y modelled analytically from this mathematical description of flow. Ba sic examples discussed are rigid body translation, pure shear, and com posite flows due to simultaneous pure and simple shear. A general stre am function is obtained to describe the flow regime within a ductile d eformation zone deforming by homogeneous plane strain by superposed pu re and simple shear components. The deformation patterns are visualize d, using analytical methods only. The results are discussed in terms o f fabric formation. Progressive deformation in a simple continuum, mod elled here mathematically using principles of fluid mechanics, is comp ared with crystalline creep in rocks. The validity of the continuum as sumption is briefly outlined in view of recent experiments on particul ar synthetic, monocrystalline aggregates (octochloropropane, OCP) defo rmable at room conditions. This provides a method for testing how crys talline deformation compares with an isotropic continuum.