A note on formulas for localized failure of frictional materials in compression and biaxial loading modes

The paper investigates aspects of the localization analysis of frictional m aterials. We derive closed formulas and diagrams for the inclination angle of critical discontinuity surfaces which develop in homogeneous compression and biaxial loading tests. The localization analysis is based on a Drucker -Prager-type elastoplastic hardening model for non-associated plastic flow at small strains, which we represent in spectral form. For this type of con stitutive model, general analytical formulas for the so-called critical har dening modulus and the inclination angle of critical discontinuity surfaces are derived for the plane strain case. The subsequent treatment then speci alizes these formulas for the analysis of compression and biaxial loading m odes. The key contribution here is a detailed analysis of plane strain defo rmation modes where the localized failure occurs after subsequent plastic f low. The derived formulas and diagrams can be applied to the checking of an accompanying localization analysis of frictional materials in finite-eleme nt computations. Copyright (C) 2001 John Wiley & Sons, Ltd.