A semi‐implicit material point method based on fractional‐step method for saturated soil

Kularathna, Shyamini; Liang, Weijian; Zhao, T. C.; Chandra, Bodhinanda; Zhao, Jidong; Soga, Kenichi

doi:10.1002/nag.3207

Cited by 51 publications

(31 citation statements)

References 57 publications

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“…The MPM‐DEM multiscale framework comprises two simulation components: the macroscopic MPM solver handling the motion and deformation of the continuum body, and the mesoscopic DEM solver providing mechanical material responses based on particle‐scale solutions. In particular, two popular open‐source codes, CB‐Geo MPM 38,39 and YADE 40 are employed for the MPM and DEM solvers, respectively.…”

Section: High‐efficiency Parallel Scheme and Its Implementation For C...mentioning

confidence: 99%

Scalable three‐dimensional hybrid continuum‐discrete multiscale modeling of granular media

Liang

Zhao

et al. 2022

Numerical Meth Engineering

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This study presents a scalable three‐dimensional (3D) multiscale framework for continuum‐discrete modeling of granular materials. The proposed framework features rigorous coupling of a continuum‐based material point method (MPM) and a discrete approach discrete element method (DEM) to enable cross‐scale modeling of boundary value problems pertaining to granular media. It employs MPM to solve the governing equations of a macroscopic continuum domain for a boundary value problem that may undergo large deformation. The required loading‐path‐dependent constitutive responses at each material point of the MPM are provided by a DEM solution based on grain‐scale contact‐based discrete simulations that receive macroscopic information at the specific material point as boundary conditions. This hierarchical coupling enables direct dialogs between the macro and micro scales of granular media while fully harnessing the predictive advantages of both MPM and DEM at the two scales. An effective, scalable parallel scheme is further developed, based on the flat message passing interface (MPI) model, to address the computational cost of the proposed framework for 3D large‐scale simulations. We demonstrate that the proposed parallel scheme may offer up to 32X and 40X speedup in strong and weak scaling tests, respectively, significantly empowering the numerical performance and predictive capability of the proposed framework. The 3D parallelized multiscale framework is validated by an element test and a column collapse problem, before being applied to simulate the intrusion of a solid object. The multiscale simulation successfully captures the characteristic response of intrusion as postulated by the modified Archimedes' law theory. The progressive development of the stagnant zone during the intrusion is further examined from a cross‐scale perspective.

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Section: High‐efficiency Parallel Scheme and Its Implementation For C...mentioning

confidence: 99%

Scalable three‐dimensional hybrid continuum‐discrete multiscale modeling of granular media

Liang

Zhao

et al. 2022

Numerical Meth Engineering

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“…However, previous implicit MPMs have so far mainly been developed for the analysis of single-phase problems. For two-phase applications, most coupled MPMs adopt explicit time integration, although a very few instances of semi-implicit and fully implicit schemes have recently begun to emerge in the literature [48,49]. To obtain better computational efficiency with respect to explicit algorithms (especially for long-lasting consolidation problems) and enable accurate MPM modelling both of slow and fast dynamic problems, this paper for the first time proposes a fully implicit coupled MPM using a complete three-field (i.e., u-p-U) formulation.…”

Section: Introductionmentioning

confidence: 99%

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

Zheng

Pisanò

Hicks

2022

Engineering with Computers

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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.

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“…This technique was also applied by Pastor et al [46] for coupled analysis in saturated soil problems, and extended later by Li et al [31], being worth mentioning the works of White and Borja [59] and Mira et al [33]. In the geotechnical field, fractional step techniques have been proposed within several meshfree techniques such as the SPH formulations proposed by Blanc and Pastor [4] and the MPM ones proposed by Kularathna et al [26].…”

Section: Introductionmentioning

confidence: 99%

Stabilized explicit $$u-p_w$$ solution in soil dynamic problems near the undrained-incompressible limit

et al. 2022

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Traditionally, Biot’s formulation is employed to model the behavior of saturated soils. The $$u-p_w$$ u - p w (solid displacement–pore water pressure) formulation can be considered as the standard one, since involves a good computational performance together with excellent accuracy for slow and moderate speed phenomena. Dynamic processes can be studied even if the acceleration of the water is neglected, what occurs in the undrained limit. It is well-known that $$u-p_w$$ u - p w formulation might display instabilities in the undrained-incompressible limit. Several techniques have been proposed to overcome this issue, principally within an implicit time integration scheme for small strains. In this paper, a robust implementation of the divergence of the momentum equation technique is presented for an explicit $$u-p_w$$ u - p w approach within the framework of optimal transportation meshfree scheme at finite strain. Several examples are provided in order to assess the good performance of the proposed methodology.

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A semi‐implicit material point method based on fractional‐step method for saturated soil

Cited by 51 publications

References 57 publications

Scalable three‐dimensional hybrid continuum‐discrete multiscale modeling of granular media

Scalable three‐dimensional hybrid continuum‐discrete multiscale modeling of granular media

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

Stabilized explicit $$u-p_w$$ solution in soil dynamic problems near the undrained-incompressible limit

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