Finite element computations of yield vertex non-coaxial models

This paper concerns the issues on finite element numerical implementations of yield vertex non-coaxial models, and approaches to mitigate the numerical difficulties. According to the yield vertex non-coaxial theory, in addition to the plastic strain rate normal to a yield surface, the plastic strain rate tangential to a yield surface is generated by principal stress rotations. This tangential plastic strain rate can easily direct inside a yield surface, which becomes an elastic strain rate. This alternate occurrence of plastic and elastic strain rates makes numerical iterations difficult to converge in the presence of large principal stress rotations. As a result, the numerical applications of yield vertex models can be regarded as moderate discontinuous problems, similar to the use of contact elements with alternate closing and opening. Two approaches are presented in the paper to mitigate the non-convergence problem. The approach in the implicit finite element procedure is to choose appropriate model parameters to limit the amount of tangential plastic strain rate compared to the normal one. The other is to use the explicit finite element procedure, characterized with a large number of computational steps but without numerical iterations. The computation of load-settlement responses for a shallow foundation is used as an example to show the numerical difficulty of yield vertex models, and how the two approaches mitigate the difficulties.