Are stylolitic surfaces inherently unstable surfaces? Insights from shape minimization considerations

Non-planar solid-fluid-solid interfaces under stress are very common in many materials, and particularly in the rocks of the Earth's crust. Such patterns are observed in many rocks in a wide range of spatial scales, from undulate grain boundaries at the micrometer scale, to stylolite dissolution interface at the meter scale. It is proposed here that these initially flat rock-fluid interfaces become rough by a morphological instability triggered by elastic stress. A model for the formation of stylolitic patterns at all scales is thus presented. It is shown that such instability is inherently present due to the uniaxial stress that promotes them, owing to the gain in the total elastic energy: the intrinsic elastic energy plus the work of the external forces. This is shown explicitly by solving the elastic problem in a linear stability analysis, and proved more generally without having resort to the computation of the elastic field.