Implicit and explicit procedures for the yield vertex non-coaxial theory

The yield vertex non-coaxial model is different from classical elastoplastic models, in that there is an additional plastic strain rate tangential to yield surfaces, as well as the plastic strain rate normal to yield surfaces, when orientations of principal stress change. This feature raises concerns on its finite element implementations. In nonlinear finite element numerical iterations, a large tangential plastic strain rate is likely to make the trial total strain rate direct inside a yield surface, which entails convergence difficulty. Some modifications are introduced on the non-coaxial model itself to make numerical convergence easier in the work published in Yang and Yu (2010) [20]. This paper is an extension of the previous work. Instead of modifying the non-coaxial model itself, this paper concerns the use of finite element explicit procedure, which is suitable for highly discontinuous problems. The simulations of shallow foundation load-settlement responses indicate that the finite element explicit procedure, assisted with a robust and explicit automatic substepping integration scheme of the non-coaxial model, does not encounter numerical difficulty. In addition, the overall trends of implicit and explicit simulations are similar.