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A conservation law consistent updated Lagrangian material point method for dynamic analysis

Pretti, G.; Coombs, W.M.; Augarde, C.E.; Sims, B.; Puigvert, M.M.; Gutierrez, J.A.R.

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Bradley Sims
PGR Student Doctor of Philosophy

M.M. Puigvert

J.A.R. Gutierrez


The Material Point Method (MPM) is well suited to modelling dynamic solid mechanics problems undergoing large deformations with non-linear, history dependent material behaviour. However, the vast majority of existing material point method implementations do not inherit conservation properties (momenta and energy) from their continuum formulations. This paper provides, for the first time, a dynamic updated Lagrangian material point method for elasto-plastic materials undergoing large deformation that guarantees momenta and energy conservation. Sources of energy dissipation during point-to-grid and grid-to-point mappings for FLuid Implicit Particle (FLIP) and Particle In Cell (PIC) approaches are clarified and a novel time-stepping approach is proposed based on an efficient approximation of the Courant-Friedrich-Lewy (CFL) condition. The formulation provided in this paper provides a platform for understanding the energy conservation nature of future/existing features of material point methods, such as contact approaches.

Journal Article Type Article
Acceptance Date Mar 15, 2023
Online Publication Date Mar 29, 2023
Publication Date Jul 15, 2023
Deposit Date Mar 16, 2023
Publicly Available Date Mar 30, 2023
Journal Journal of Computational Physics
Print ISSN 0021-9991
Electronic ISSN 1090-2716
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 485
Article Number 112075
Public URL


Journal Article (In Press, Journal Pre-proof) (6.1 Mb)

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Copyright Statement
In Press, Journal Pre-proof 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://

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