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Sills, saucer‐shaped sills, and cone sheets are fundamental magma conduits in many sedimentary basins worldwide. Models of their emplacement usually approximate the host rock properties as purely elastic and consider the plastic deformation to be negligible. However, many field observations suggest that inelastic damage and shear fracturing play a significant role during sill emplacement. Here we use a rigid plasticity approach, through limit analysis modeling, to study the conditions required for inelastic deformation of sill overburdens. Our models produce distinct shear failure structures that resemble intrusive bodies, such as cone sheets and saucer‐shaped sills. This suggests that shear damage greatly controls the transition from flat sill to inclined sheets. We derive an empirical scaling law of the critical overpressure required for shear failure of the sill's overburden. This scaling law allows to predict the critical sill diameter at which shear failure of the overburden occurs, which matches the diameters of natural saucer‐shaped intrusions' inner sills. A quantitative comparison between our shear failure model and the established sill's tensile propagation mechanism suggests that sills initially propagate as tensile fractures, until reaching a critical diameter at which shear failure of the overburden controls the subsequent emplacement of the magma. This comparison also allows us to predict, for the first time, the conditions of emplacement of both conical intrusions, saucer‐shaped intrusions, and large concordant sills. Beyond the application to sills, our study suggests that shear failure significantly controls the emplacement of igneous sheet intrusions in the Earth's brittle crust.

Strain localization is ubiquitous in geodynamics and occurs at all scales within the lithosphere. How the lithosphere accommodates deformation controls, for example, the structure of orogenic belts and the architecture of rifted margins. Understanding and predicting strain localization is therefore of major importance in geodynamics. While the deeper parts of the lithosphere effectively deform in a viscous manner, shallower levels are characterized by an elastoplastic rheological behavior. Herein we propose a fast and accurate way of solving problems that involve elastoplastic deformations based on the consistent linearization of the time‐discretized elastoplastic relation and the finite difference method. The models currently account for the pressure‐insensitive Von Mises and the pressure‐dependent Drucker‐Prager yield criteria. Consistent linearization allows for resolving strain localization at kilometer scale while providing optimal, that is, quadratic convergence of the force residual. We have validated our approach by a qualitative and quantitative comparison with results obtained using an independent code based on the finite element method. We also provide a consistent linearization for a viscoelastoplastic framework, and we demonstrate its ability to deliver exact partitioning between the viscous, the elastic, and the plastic strain components. The results of the study are fully reproducible, and the codes are available as a subset of M2Di MATLAB routines.

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