Possibilities and limitations of the sequential kinematic method for simulating evolutionary plasticity problems

Abstract

Evolutionary plasticity processes, such as ploughing and penetrating, widely exist in many geotechnical engineering applications. The simulation of these processes poses considerable challenges due to the occurrence of large deformation, unsteady nature of the material free surface, and inherent coupling between mechanical response and material geometries. This paper explores the possibility of simulating the first-order response of these processes by using sequential kinematic method (SKM) in combination with simple deformation mechanism. The mechanism consists of rigid elements separated by velocity discontinuities. Computations based on the kinematic approach of limit analysis are sequentially performed to evaluate the most likely deformation mode and update material geometries. An r-adaptive kinematic formulation is used that captures versatile velocity fields by optimizing the geometries of simple kinematic mechanism. The modelling methodology is studied in detail for two archetypal evolutionary plasticity problems: wedge ploughing Tresca material and cylinder penetrating undrained clay. The numerical results obtained by using the SKM are compared against existing analytical and numerical solutions, as well as experimental evidence. The paper demonstrates that evolutionary plasticity problems can be simulated in a conceptually simple way using SKM and highlights the potential pitfalls of this technique.