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Overcoming volumetric locking in material point methods.

Coombs, W.M. and Charlton, T.J. and Cortis, M. and Augarde, C.E. (2018) 'Overcoming volumetric locking in material point methods.', Computer methods in applied mechanics and engineering., 333 . pp. 1-21.


Material point methods suffer from volumetric locking when modelling near incompressible materials due to the combination of a low-order computational mesh and large numbers of material points per element. Large numbers of material points per element are required to reduce integration errors due to non-optimum placement of integration points. This restricts the ability of current material point methods in modelling realistic material behaviour. This paper presents for the first time a method to overcome finite deformation volumetric locking in standard and generalised interpolation material point methods for near-incompressible non-linear solid mechanics. The method does not place any restriction on the form of constitutive model used and is straightforward to implement into existing implicit material point method codes. The performance of the method is demonstrated on a number of two and three-dimensional examples and its correct implementation confirmed through convergence studies towards analytical solutions and obtaining the correct order of convergence within the global Newton–Raphson equilibrium iterations. In particular, the proposed formulation has been shown to remove the over-stiff volumetric behaviour of conventional material point methods and reduce stress oscillations. It is straightforward to extend this approach to other material point methods and the presented formulation can be incorporated into all existing material point methods available in the literature.

Item Type:Article
Additional Information:Figure data available from
Keywords:Material point method, Volumetric locking, Elasto-Plasticity, Finite deformation mechanics, Generalised interpolation
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Publisher statement:This article is available under the terms of the Creative Commons Attribution License (CC BY). You may copy and distribute the article, create extracts, abstracts and new works from the article, alter and revise the article, text or data mine the article and otherwise reuse the article commercially (including reuse and/or resale of the article) without permission from Elsevier. You must give appropriate credit to the original work, together with a link to the formal publication through the relevant DOI and a link to the Creative Commons user license above. You must indicate if any changes are made but not in any way that suggests the licensor endorses you or your use of the work.
Date accepted:07 January 2018
Date deposited:09 January 2018
Date of first online publication:16 January 2018
Date first made open access:06 February 2018

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