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Treatment of near-incompressibility in meshfree and immersed-particle methods

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Abstract

We propose new projection methods for treating near-incompressibility in small and large deformation elasticity and plasticity within the framework of particle and meshfree methods. Using the \(\overline{\mathbf {B}}\) and \(\overline{\mathbf {F}}\) techniques as our point of departure, we develop projection methods for the conforming reproducing kernel method and the immersed-particle or material point-like methods. The methods are based on the projection of the dilatational part of the appropriate measure of deformation onto lower-dimensional approximation spaces, according to the traditional \(\overline{\mathbf {B}}\) and \(\overline{\mathbf {F}}\) approaches, but tailored to meshfree and particle methods. The presented numerical examples exhibit reduced stress oscillations and are free of volumetric locking and hourglassing phenomena.

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Acknowledgements

The support of this work by Sandia National Laboratories via the Laboratory Directed Research and Development (LDRD) program, the Doctoral Study Program (DSP) and to University of California, San Diego, under Contract Agreement 1655264 is greatly acknowledged. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

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Authors and Affiliations

  1. School of Engineering, Brown University, 184 Hope Street, Providence, RI, 02912, USA

    Georgios Moutsanidis & Yuri Bazilevs

  2. Engineering Sciences Center, Sandia National Laboratories, P. O. Box 5800, Albuquerque, NM, 87185, USA

    Jacob J. Koester & Michael R. Tupek

  3. Department of Structural Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0085, USA

    Jiun-Shyan Chen

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  1. Georgios Moutsanidis
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Correspondence to Georgios Moutsanidis.

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Moutsanidis, G., Koester, J.J., Tupek, M.R. et al. Treatment of near-incompressibility in meshfree and immersed-particle methods. Comp. Part. Mech. 7, 309–327 (2020). https://doi.org/10.1007/s40571-019-00238-z

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