Three-dimensional stress state during dynamic shear rupture propagation along frictional interfaces in elastic plates

The state of stress in plates, where one geometric dimensions is much smaller than the others, is often assumed to be of plane stress. This assumption is justified by the fact that the out-of-plane stress components are zero on the free-surfaces of a plate to satisfy the boundary conditions, and have little chance to develop in the bulk, due to the small thickness of the plate. At the same time, it is known that the static stress field associated with cracks approximates plane-strain conditions in the near-crack tip. However, it is not clear how the pre-existing plane-stress field of a plate is modified by a propagating dynamic shear rupture. Here we study the particle velocities and stress fields of dynamic shear ruptures in mode II propagating along the predefined frictional interface of two plates of an elastic material, loaded in compression and shear, using three-dimensional finite element modeling. The numerical simulations show the rapid development of out-of-plane stresses in the interior of the specimen, between the free surfaces. The out-of-plane normal stress is characterized by an anti symmetric pattern with lobes of alternating polarity, in planes parallel to the free-surfaces. On the interface plane, the out-of-plane stress has a complex pattern exhibiting an initial sudden variation over the plane stress conditions followed by crisscrossing features, behind the rupture tip. This study shows how plane-stress conditions, defining the state of stress before rupture arrival, are suddenly altered during dynamic rupture propagation. The out-of-plane stress rapidly deviates from the free-surface condition and a state of equivalent plane-strain in the stress-changes field is attained at the rupture tip, while behind the rupture tip a fully three-dimensional stress state is established. The three-dimensional finite element simulations presented here help interpret and explain previous experiments of dynamic shear ruptures by showing the complex particle velocity and stress fields in the interior of the specimen and along the interface plane, which are currently not accessible to full-field experimental measurements.