Fully implicit, stabilised, three-field material point method for dynamic coupled problems

This study presents the formulation and implementation of a fully implicit stabilised Material Point Method (MPM) for dynamic problems in two-phase porous media. In particular, the proposed method is built on a three-field formulation of the governing conservation laws, which uses solid displacement...

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Bibliographic Details
Published in:Engineering with computers 2022-12, Vol.38 (6), p.5583-5602
Main Authors: Zheng, Xiangcou, Pisanò, Federico, Vardon, Philip J., Hicks, Michael A.
Format: Article
Language:English
Subjects:
Accuracy
CAE) and Design
Calculus of Variations and Optimal Control
Optimization
Classical Mechanics
Computer Science
Computer-Aided Engineering (CAD
Conservation laws
Control
Deformation
Fluid flow
Incompressible flow
Interpolation
Math. Applications in Chemistry
Mathematical and Computational Engineering
Original Article
Porous media
Shape functions
Systems Theory
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Summary:This study presents the formulation and implementation of a fully implicit stabilised Material Point Method (MPM) for dynamic problems in two-phase porous media. In particular, the proposed method is built on a three-field formulation of the governing conservation laws, which uses solid displacement, pore pressure and fluid displacement as primary variables ( u – p – U formulation). Stress oscillations associated with grid-crossing and pore pressure instabilities near the undrained/incompressible limit are mitigated by implementing enhanced shape functions according to the Generalised Interpolation Material Point (GIMP) method, as well as a patch recovery of pore pressures – from background nodes to material points – based on the same Moving Least Square Approximation (MLSA) approach investigated by Zheng et al. [ 1 ]. The accuracy and computational convenience of the proposed method are discussed with reference to several poroelastic verification examples, spanning different regimes of material deformation (small versus large) and dynamic motion (slow versus fast). The computational performance of the proposed method in combination with the PARDISO solver for the discrete linear system is also compared to explicit MPM modelling [ 1 ] in terms of accuracy, convergence rate, and computation time.
ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-022-01678-7