Recent developments towards Isogeometric MPM
Keywords: MPM, IGA
Abstract: The numerical simulation of large strains plays an important role in the understanding of natural hazards such as landslides. Over the past decade, the Material Point Method (MPM) has been pioneered to simulate such large strain problems while avoiding mesh entanglement. This includes the proposal of various multiphase formulations to simulate solid-water interaction in porous media. The MPM traditionally employs linear shape functions (i.e., discontinuous derivatives at the nodes) which results in the generation of spurious high frequency noise in the strain profile when spatially integrating upon the mobile material points (i.e., integration points) that cross from one element to another (i.e., cell-crossing error). The goal of this research is to improve the stability of MPM and enable the simulation of complex geometries within the context of Isogeometric Analysis (IGA).
In this research, we will replace the traditional shape functions defined on the MPM mesh with another set of high order continuous basis functions commonly employed in IGA known as NURBS. The use of NURBS will allow seamless transition of material points from one element to another with no discontinuity in the derivatives, thus improving accuracy and eliminating instabilities due to the cell-crossing effect when simulating large deformations. A large strain benchmark problem of column response due to gravity and P-wave propagation will be adopted to investigate the efficacy of the proposed developments. Parametric analysis will be conducted using these two examples to investigate the rate of solution convergence, effect of element refinement, and number of material points. The IGA framework will also be used to showcase its ability in simulating complex geometries accurately. An example of a circular geometry compressing under gravity will be presented and compared with traditional MPM. Multipatch aspects of IGA and its ability to provide users with control over geometry characterization will be discussed with a simple example.
Submission Number: 4
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