Analysis of slip planes in three-dimensional solids

Abstract Three-dimensional solids in which displacement jumps develop across planes are analysed. Critical to such analysis is the identification of the correct orientation of the discontinuity plane. To do this, strain softening continuum relationships are examined for the limit case of a strong (displacement) discontinuity, which then yields a localisation condition for the introduction of a displacement jump. A numerical procedure is proposed to correctly orientate the discontinuity plane in space. For the Von Mises and Drucker–Prager yield criteria, traction–displacement relationships are developed and implemented by embedding the slip planes in conventional solid finite elements. This makes the analysis ideal for large, three-dimensional calculations. The performance of the developed discrete constitutive models and that of the embedded discontinuity elements in three-dimensions are scrutinised, with special attention paid to mesh objectivity and volumetric locking.