An eigenvalue analysis of nonassociated plasticity

Boundary value problems with operators that are not self-adjoint are a direct consequence of the use a nonassociated plasticity model. As a result, the material stiffness matrix, and therefore also, the ensuing structural stiffness matrix become nonsymmetric, and complex eigenvalues are possible. In practice, however, these are not encountered for the structural stiffness matrix. We present a mathematical analysis of the eigenvalues characterizing the elasto-plastic material stiffness matrix with a Drucker-Prager yield function, for orthotropic and isotropic materials. We confine ourselves to plane-strain and stress conditions. All possible stress distributions are considered showing possible complex eigenvalues in case of orthotropy but none for isotropy. Finally, a numerical analysis is performed to gain insight into the eigenvalues of the structural stiffness matrix. © 1999 Elsevier Science Ltd. All rights reserved.