Material-point Method for Geotechnical Engineering.

The focus of the PhD project is the generalized interpolation material-point (GIMP) method applied to geotechnical problems. The GIMP method is a new numerical method for modelling dynamic problems involving large strains and displacements. The physical domain is discretized into a set of sub-domains. The material properties and any state variables are referred to so-called material points placed at the centre coordinates of these sub-domains. The governing equations are solved on a background grid. The mapping between the material points and the grid is performed using interpolation functions, obtained by integrating nodal shape functions associated with the grid nodes over particle characteristic functions associated with the material points.

This dual description has the advantage that mesh entanglement is avoided, as the mesh does not carry any physical properties and can be reset at each time step. Furthermore, convection issues associated with pure Eulerian methods are avoided as the material points are tracked in time.

The PhD work presents an extension to very large strain problems by obtaining the GIMP interpolation functions by numerical integration of the particle characteristic functions over the volume of the material points in the deformed configuration. The method is applied to geotechnical problems, including the dynamic behaviour of landslides and cone penetration test.

It is concluded that the new method provides a tool for studying problems involving large strains, where the application of finite element of finite difference schemes is problematic.