Application of kinetic damping in dynamic material point method for static problems

Material point method (MPM) is widely used in geotechnical engineering, owing to its powerful capability of modelling large deformation problems. But the static equilibrium problems involving very large deformation and material non-linearity can be difficult to solve using the quasi-static MPM, because of numerical difficulties with convergence in iterative procedure. An alternative method is the dynamic relaxation (DR) method, which converts the static problem to a dynamic one by considering the virtual masses and artificial damping. This paper presents a method to solve static problems using dynamic MPM with DR technique. An energy ratio and a force ratio are defined to recognize the static equilibrium state from dynamic process first. Then the kinetic damping as an DR technique is introduced into the dynamic MPM for the first time. Finally, two numerical examples are presented to illustrate the convenience and efficiency of the kinetic damping in dynamic MPM for static problems.