The Significance of Weak Interfaces for the Kinematics and Rheology of the Ductile Deformation of Earth Materials

Abstract The rheology of Earth's lithosphere under natural deformation conditions is of paramount importance for all tectonic processes and for addressing why plate tectonics emerged on Earth. Most continuum theories, extrapolations of experimental results to natural conditions, and numerical models assume that rheologically distinct elements comprising earth materials are perfectly bonded to each other. This assumption is inadequate in many situations and may lead to an unrealistically high estimate of the actual strength of earth materials. A micromechanical theory for weak interfaces is developed here for the viscous deformation of heterogeneous materials. The weak‐interface theory is validated against existing theoretical results and natural data and then applied to assess the rheology of two‐phase materials. Numerical calculations based on the weak‐interface theory confirm that weak interfaces between rigid porphyroclasts and the matrix were responsible for the porphyroclasts' shape‐preferred orientations observed in many crustal shear zones. Slippery interfaces can weaken the material so significantly that its bulk strength may fall below the Reuss average—long held to be the lower bound strength of a heterogeneous material. In a two‐phase mixture, the ultimate lower bound is when the second phase is made of rigid voids. The weak‐interface theory incorporates the effect of rheological discontinuities into homogenization methods to obtain the bulk rheology of Earth materials and offers a method for constructing anisotropic flow laws for plastic creep of polycrystalline materials undergoing intracrystalline dislocation creep and grain boundary sliding.