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Shear localization is a damage mechanism characterized by the concentration of plastic deformation within thin bands of materials, often observed as a precursor to failure in metals. In this study, we present a three-dimensional explicit finite element formulation with embedded weak discontinuities for the treatment of shear localization under dynamic loading conditions. In this formulation, the onset of localization is detected via a material stability analysis suitable for rate-sensitive materials, and the continuity of propagating shear bands is ensured using a global tracking strategy involving a heat-conduction type boundary value problem, solved for a scalar level set function over themore » global domain of the problem. In addition, we propose a modified quadrature rule that is used to compute the contribution of an individual element to the global finite element arrays, taking into account the position of the embedded shear band within that element.« less