An implicit Generalised Interpolation Material Point Method for large deformation and gradient elasto-plasticity

Abstract

The ability to correctly capture large deformation behaviour in solids is important in many problems in geotechnical engineering such as slope failure or installation of foundations. The Material Point Method (MPM) is a computational method with particular suitability for modelling problems involving large deformations. In the MPM, a domain is modelled using a set of material points at which state variables are stored and tracked. These material points move through a fixed background grid upon which calculations take place with variables being mapped between the material points and the grid. This thesis sets out to develop the MPM as a method with potential for use in geotechnical problems.
Problems are encountered with the original MPM when material points cross between grid cells, and one solution to this is the Generalised Interpolation Material Point (GIMP) method, where material points are able to influence nodes beyond the currently occupied grid cell. Most development of the GIMP method has used an explicit approach, however there are a number of advantages of an implicit approach including larger load steps and improved error control. This thesis focuses on the development of a large deformation elasto-plastic implicit GIMP method. A way of calculating the deformation gradient consistent with the MPM is introduced and convergence is demonstrated using this method which has previously been frequently omitted from MPM research. An alternative way of updating material point domains using the stretch tensor is also proposed.
The MPM has a number of similarities to the FEM, and it is often suggested that FEM technologies are trivial to use with the MPM. The MPM can encounter localisations caused by shear banding and, to overcome this, a gradient plasticity approach previously implemented for the FEM is investigated with the GIMP method for the first time. The addition of gradient plasticity to the GIMP method introduces a length scale parameter which governs the width of these shear bands and removes the mesh dependency which is encountered with conventional approaches. It is shown that implementation is possible however, there are a number of problems that are present in the combination of the two methods which should not be overlooked in the future.