Material stability analysis based on the local and global elasto-plastic tangent operators

TLDR: In this paper, the second-order work criterion is used to investigate bifurcation in geomaterials with the help of the second order work criterion and the analysis is extended to boundary value problems in quasi-static conditions, by considering the finite element stiffness matrix.

Abstract: The present paper investigates bifurcation in geomaterials with the help of the second-order work criterion. The approach applies mainly to non associated materials such as soils. The analysis usually performed at the material point level is extended to quasi-static boundary value problems, by considering the finite element stiffness matrix. The first part of the paper reminds some results obtained at the material point level. The bifurcation domain is presented in the 3D principal stress space as well as 3D cones of unstable loading directions for an incrementally nonlinear constitutive model. In the second part, the analysis is extended to boundary value problems in quasi-static conditions. Non-linear finite element computations are performed and the global tangent stiffness matrix is analyzed. For several examples the eigenvector associated with the first vanishing eigenvalue of the symmetrical part of the stiffness matrix gives an accurate estimation of the failure mode even for non homogeneous boundary value problems.