An anisotropic hardening description is proposed on the basis of the generalized isotropic hardening(GIH) rule. The key concept of the GIH rule is that any proper stress state inside or on a yield surface can be the homologic center of isotropic hardening. The center of isotropically hardening homology was selected at the stress state of reverse loading event. The anisotropic description of GIH postulates (1) discrete formation of the normalized homologue stress, and (2) simultaneous occurrence of GIH for both yield and reference surfaces.
As a result, yielding in the field of reverse loading can be completely modeled. The proposed model incorporates a very simple hardening function, only dependent on the size ratio between the yield surface and the reference surface. For verification, three sets of triaxial test results obtained from drained and undrained tests on overconsolidated clays and $K_0$ consolidated clays were evaluated. Consequently, it was determined that the proposed model can represent any plastic deformation in reverse loading.
The finite element solution to a nonlinear problem is typically achieved by Newton's method in which a sequence of linear problem is solved. In order to preserve the accuracy of the solution, implicit stress integration technique by the generalized trapezoidal rule was employed in the proposed anisotropic hardening constitutive equation. Furthermore, the tangent moduli was obtained by consistent linearization procedures relevant to the stress integration algorithm for the quadratic rate of asymptotic convergence. Through examples, it was verified that the stress integration is accurately performed and the asymptotic quadratic convergence rate is preserved.
Finally, a full scale problem of undrained excavation and a reverse loaded soil-structure system are analyzed. In the excavation example, plastic straining of overconsolidated state and various construction sequences could be predicted using the proposed constitutive model. Hence the displacement of excavated wall was predicted well. In the soil-structure system, the hysterisis loop of force-displacement relationships was evaluated. Consequently, it was shown that the proposed anisotropic hardening model can be applied to the nonlinear dynamic finite element analysis in the time domain.
