Associated and Non‐Associated Aspects of the Constitutive Laws for Coupled Elastic/Plastic Materials

Previous analyses are amplified to demonstrate that when the constitutive equations for geo‐materials, in which the elastic moduli depend on the plastic strain, are derived from basic thermo‐mechanical principles, the resulting rate forms of the equations have a symmetric stiffness matrix (tensor). This result is at odds with existing analyses, which have concluded that these matrices should be non‐symmetric. The consequences of these results for stability, bifurcation, and shear band formation are discussed.