| Abstract: | Grain boundaries and axial surfaces of folds are geological examples of thin transition zones, which can be modelled mathematically as surfaces of discontinuity. Here we consider coherent boundaries, across which no material lines are ever discontinuous, but deformation gradients and particle velocities can be so. A discontinuity in particle velocity requires that a coherent boundary propagate (migrate) through the material.The geometry and kinematics of coherent boundaries were studied by Hadamard (1903) and reviewed by Truesdell and Toupin (1960). Here, we rederive their results in a geological context, using modern notation and simple coordinates. We conclude that velocity gradient, stretching and spin can all be discontinuous. Applied to ideal kink bands in non-dilatant foliated materials, the theory predicts that kink boundaries rotate through the material at exactly the rate needed to maintain fold symmetry. In a polycrystalline aggregate, easily migrating coherent grain boundaries are mechanically analogous to slippery incoherent boundaries: both kinds support little shear stress. |
