Material-point method analysis of bending in elastic beams

The aim of this paper is to test different types of spatial interpolation for the materialpoint method. The interpolations include quadratic elements and cubic splines. A brief introduction to the material-point method is given. Simple liner-elastic problems are tested, including the classical cantilevered beam problem. As shown in the paper, the use of negative shape functions is not consistent with the material-point method in its current form, necessitating other types of interpolation such as cubic splines in order to obtain smoother representations of field quantities. It is shown that the smoother field representation using the cubic splines yields a physically more realistic behaviour for impact problems than the traditional linear interpolation.