IGA-MPM: The Isogeometric Material Point Method

Moutsanidis, Georgios; Long, Christopher C.; Bazilevs, Yuri

doi:10.1016/j.cma.2020.113346

IGA-MPM: The Isogeometric Material Point Method

Journal Article · Sat Aug 22 00:00:00 EDT 2020 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2020.113346· OSTI ID:1711396

^[1]; ^[2]; Bazilevs, Yuri ^[3]

Stony Brook Univ., NY (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Brown Univ., Providence, RI (United States)

In this work, we propose the use of Isogeometric Analysis (IGA) within the context of the Material Point Method (MPM), and refer to the approach as IGA-MPM. We use the idea of IGA, and its instantiation based on Non-Uniform Rational B-Splines (NURBS), to build higher-order accurate and smooth approximation for MPM. Higher-order smoothness yields a continuous representation of the strain rate, and, as a result, prevents jumps in the stress and other history variables as the material points cross the element boundaries. Furthermore, NURBS can exactly represent all conic sections and the corresponding symmetries in the solution, which may be important in some applications. Several numerical examples of increasing complexity are presented, and show the ability of IGA-MPM to eliminate the well known cell-crossing instability of the conventional MPM. In addition, the examples presented demonstrate improved accuracy, convergence, and symmetry preservation of IGA-MPM compared to the conventional MPM, both for rectilinear and curved geometries.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE; USDOE National Nuclear Security Administration (NNSA). Office of Defense Nuclear Nonproliferation R&D (NA-22)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1711396

Alternate ID(s):: OSTI ID: 1809310

Report Number(s):: LA-UR--20-23322

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 372; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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42 ENGINEERING
Cell-Crossing Instability
Isogeometric Analysis
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