Flow and finite deformation of surface elements in three dimensional homogeneous progressive deformations

Rocks are heterogeneous materials. Deformation structures and fabrics in the ductile lithosphere can result from the history of the three dimensional flow field, or the progressive deformation of some rheologically distinct elements embedded in the 3D flow field, or a combination of both. The flow and progressive deformation of a rheologically distinct element is generally non-steady even if the hosting 3D flow field is steady. Vorticity decomposition is the key to following the progressive history of the deformation of specific elements. A general theoretical background to the problem is presented. Flow and progressive deformation of surface (and layer-like) elements in 3D homogeneous flows are investigated specifically. Analytical procedures to calculate the sectional vorticity number and the sectional dilatancy number on a general section in a 3D flow field are introduced. The theoretical analysis is applied to various examples of sectional flow embedded in different types of 3D homogeneous and steady flow fields. Implications of this investigation for kinematic analysis of natural rock deformation are discussed. All types of material line histories are expected in sectional flows of layer-like elements. Shortened boudins can be formed in a single progressive deformation. In sequences of rocks with a well-developed transposition foliation common in large scale high-strain zones, each layer unit may have undergone a unique deformation history during its rotation to the final, shear zone boundary parallel orientation. In kinematic analysis of such areas, it is important to ascribe the correct kinematic significance to structural associations and fabrics.