Bifurcations in finite element models with a non-associated flow law

A numerical approach to bifurcation problems in soil mechanics is described. After locating the bifurcation point by a combination of an incremental-iterative loading procedure and an eigenvalue analysis of the tangent stiffness matrix, the solution is continued on the localization path by a suitable combination of the fundamental solution and the eigenvector belonging to the lowest eigenvalue. The procedures are applied in a bifurcation analysis of a cohesionless soil in a biaxial testing device. The results suggest that a diffuse bifurcation mode with a short wavelength is encountered whereupon a shear band gradually develops. The inclination angle of the shear band compares well with analytical formulae and with empirical data.