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On the implementation of a material point‐based arc‐length method

Gavin, Nathan; Pretti, Giuliano; Coombs, William; Brigham, John; Augarde, Charles

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Nathan Gavin
PGR Student Doctor of Philosophy

John Brigham


Summary: The material point method is a versatile technique which can be used to solve various types of solid mechanics problems, especially those involving large deformations. However, the capability of the material point method to track a load‐displacement response can deteriorate once a limit point, such as snap‐through or snap‐back, in the response is encountered. One way of overcoming this is to use path following techniques, such as an arc‐length method. This technique is well established in finite element analysis but not within any material point method formulation. This paper provides for the first time an arc‐length controlled implicit, quasi‐static material point method. The modifications to the standard arc‐length scheme to allow for the stable execution of an arc‐length solver within the material point method are detailed. The capability of the material point‐based arc‐length method is demonstrated through a number of problems, which include linear elastic, non‐linear elastic, linear elastic‐perfectly plastic and linear elastic‐plastic softening material behaviour under large deformations. The techniques presented in this paper are essential for arc‐length techniques to be applied effectively to the material point method and the combination of these techniques makes the method suitable for new problems that cannot be solved with existing implicit material point approaches.


Gavin, N., Pretti, G., Coombs, W., Brigham, J., & Augarde, C. (2024). On the implementation of a material point‐based arc‐length method. International Journal for Numerical Methods in Engineering, 125(9), Article e7438.

Journal Article Type Article
Acceptance Date Jan 13, 2024
Online Publication Date Feb 6, 2024
Publication Date May 15, 2024
Deposit Date Jan 15, 2024
Publicly Available Date Feb 7, 2024
Journal International Journal for Numerical Methods in Engineering
Print ISSN 0029-5981
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 125
Issue 9
Article Number e7438
Keywords arc‐length methods, snap‐through, large deformation mechanics, elastoplasticity, material point method
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