A fast algorithm for finding the first intersection with a non-convex yield surface

A major task in the numerical modelling of soils using complex elastoplastic material models is stress updating. This paper proposes a fast and robust numerical algorithm for locating the first intersection between a non-convex yield surface and an elastic trial stress path. The intersection problem is cast into a problem of finding the smallest positive root of a nonlinear function. Such a function may have multiple roots within the interval of interest. The method is based on the modified Steffensen method, with important modifications to address the issues arising from the non-convexity. Numerical examples demonstrate that the proposed M² Steffensen method is indeed computationally efficient and robust.