Axisymmetric form of the generalized interpolation material point method

This paper reformulates the axisymmetric form of the material point method (MPM) using generalized interpolation material point (GIMP) methods. The reformulation led to a need for new shape functions and gradients specific for axisymmetry that were not available before. The new shape functions differ most from planar shape functions near the origin where r = 0. A second purpose for this paper was to evaluate the consequences of axisymmetry on a variety MPM extensions that have been developed since the original work on axisymmetric MPM. These extensions included convected particle domain integration (CPDI), traction boundary conditions, explicit cracks, multimaterial mode MPM for contact, thermal conduction, and solvent diffusion. Some examples show that the axisymmetric shape functions work well and are especially crucial near the origin. One real-world example is given for modeling a cylinder-penetration problem. Finally, a check list for software development describes all tasks needed to convert 2D planar or 3D codes to include an option for axisymmetric MPM. Copyright (c) 2014 John Wiley & Sons, Ltd.