Abstract
Numerical simulations, which include spacial descretization, difine the controlling domain of descrete elements, according to each characteristics of methods. Finite Element Method uses nodes and elements to define their controlling domains, whereas particle based methods use the interpolation functions. Particles based methods usually updates its geometric position, while they continue to use the same interpolation function through the whole simulation process. In particle based methods, separations due to numerical algorithms often occur when the intensive streches act on the materials, not because materials reaches its criteria of separation but because the distance from neigbor particles exceeds the interpolation radius.
The same difficulty has been discussed over the Material Point Method. Although original MPM, which generates numerical noise when crossing numerical grids, does not consider a controlling domain, GIMP method, which considers the change of controlling domain in axial direction, has been proposed to overcome the problems. More recentry, CPDI method, which considers the whole change of controlling domain, has been proposed. In this paper the author focuses on CPDI method and newly propeses the three dimensional formulation of CPDI method and applies it to the large deformation problem of geomaterials.
