Fast and efficient MPM solver for strain localization problems

Strain localization problems, i.e., shearbandings, have received a lot of interest, especially when strain softening is disregarded from the elasto-plastic consistution relationship. Indeed, reproducing correctly oriented shear bands without softening allows to overcome the mesh-depenency problem. Our work focuses on a Material Point Method (MPM) implementation of strain localization to i) study the behavior of shear bands in order to ii) assess the capabilities of this quite recent numerical method. To study strain localization and shear banding, we developped an efficient numercial Material Point Method (MPM) solver in Matlab, based on the Update Stress Last (USL) scheme enriched with the Generalized Interpolation Material Point (GIMP) variant, which fixes a major flaw of any MPM solver: the cell-crossing error due to discontinuous gradient of the basis functions. This home-made solver allows us to study strain localizations in either a fixed or continuously deforming continuum. The algorithm solves explicitly momentum equations in an updated lagrangian manner similarly to an explicit FEM solver. We therefore investigate the compression of an elasto-plastic domain under pure shear condition, thus reproducing the geometrical settings and pure shear conditions used in Duretz et al. (2018). Strain softening is disregarded since we do not want any mesh dependence within the solver. A Mohr-Coulomb yield criterion was selected and plasticity was computed by a return mapping algorithm, i.e., we did not use consistent tangent operator. Localization is triggered by a weaker circular inculsion in the center of the domain.. Preliminary results demonstrates the suitability of the MPM solver to reproduce the correct shearbanding behavior under compression, for both static and dynamic meshes. The higher the resolution, the more accurate are the shear bands. Naturally, this implies future implementations of the solver in a GPU-accelerated environment to increase the numerical resolution.

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Shear banding in elasto-plastic slumping process on a GPU: mechanical and hydromechanical MPM solver

10.5194/egusphere-egu21-15861 ◽

2021 ◽

Author(s):

Michel Jaboyedoff ◽

Emmanuel Wyser ◽

Yury Podladchikov

Keyword(s):

Liquid Phase ◽

High Resolution ◽

Strain Localization ◽

Mechanical Response ◽

Shear Banding ◽

Shear Bands ◽

Material Point ◽

Future Perspective ◽

Deformation Problem ◽

Rate Dependent

Strain localization plays an important role in the mechanical response of a slumping mass and defines the overall behaviour of such process. We study strain localization with the help of the Material Point Method (MPM), which is well-suited to simulate large deformation problem.We implemented both mechanical and hydromechanical (i.e., we assume fully saturated conditions of the material) MPM-based solvers within a rate-dependent formulation framework under a GPU architecture. We selected an explicit MPM formulation enriched with the Generalized Interpolation Material Point (GIMP) variant, which fixes a major flaw of MPM, i.e., the cell-crossing error. To avoid spurious oscillation of the pressure field (due to the use of low-order elements) for both solid and liquid phase, we used an element-based averaging technique. This minimizes volumetric locking problems. This numerical framework allows to study high-resolution two-dimensional elasto-plastic (i.e., Mohr-Coulomb plasticity) problems in an affordable amount of time. The solvers were written in a CUDA C environment on a single Nvidia GPU. We report a speed-up factor of 500 compared to a similar MATLAB implementation.Our results showcase a contribution of pore water pressures over shear banding. In particular, we report a significant influence of the liquid phase over the steady thickness of the shear bands and their location. Pore pressures add a viscous contribution to the elasto-plastic rheological model we choose, i.e., Mohr-Coulomb.As a future perspective, even high resolution could be achieved considering the extension of the actual implementation toward a multi-GPU solver using MPI.

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Simulating Ice-Structure Interaction With the Material Point Method

Volume 8: Polar and Arctic Sciences and Technology; Petroleum Technology ◽

10.1115/omae2017-61392 ◽

2017 ◽

Author(s):

Yaomei Wang ◽

Biye Yang ◽

Guiyong Zhang ◽

Yichen Jiang ◽

Zhi Zong

Keyword(s):

Yield Criterion ◽

Ice Sheet ◽

Material Point Method ◽

Friction Angle ◽

Complex Problem ◽

Material Point ◽

Point Method ◽

Structure Interaction ◽

Future Work ◽

Large Deformation Problems

The process of ice-structure interaction is a complex problem which is influenced by the properties of both ice and the structure. In this paper, the material point method (MPM) is introduced to simulate the interaction between an ice sheet and a cylinder structure. MPM is efficient in solving history dependent and large deformation problems and has shown advantage in hyper-velocity impact and landslide issues, etc.. The constitutive relation of ice is based on elasto-viscous-plastic model with the Drucker-Pragers yield criterion. Ice follows the Maxwell elasto-viscous model before the yield criterion is reached and fails when the plastic strain surpasses the failure strain. Meanwhile, the constitutive model used in this work considers the effect of the Young’s modulus, Poisson’s ratio, density, temperature, cohesive force and internal friction angle of ice. A series of simulations are conducted and the results are in accord with existing theories. According to the comparison, the influences of ice temperature and penetration speed of the structure on the global ice load are testified. The numerical tests have proven the feasibility of MPM in simulating the interaction between an ice sheet and a cylinder structure. Future work in ice-structure interaction problems with MPM is also discussed.

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A Hybrid Material Point Method for Frictional Contact with Diverse Materials

Proceedings of the ACM on Computer Graphics and Interactive Techniques ◽

10.1145/3340258 ◽

2019 ◽

Vol 2 (2) ◽

pp. 1-24 ◽

Cited By ~ 7

Author(s):

Xuchen Han ◽

Theodore F. Gast ◽

Qi Guo ◽

Stephanie Wang ◽

Chenfanfu Jiang ◽

...

Keyword(s):

Hybrid Material ◽

Frictional Contact ◽

Material Point Method ◽

Material Point ◽

Point Method

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Three-dimensional face stability analysis of shallow tunnels using numerical limit analysis and material point method

Tunnelling and Underground Space Technology ◽

10.1016/j.tust.2021.103904 ◽

2021 ◽

Vol 112 ◽

pp. 103904

Author(s):

Fabricio Fernández ◽

Jhonatan E.G. Rojas ◽

Eurípedes A. Vargas ◽

Raquel Q. Velloso ◽

Daniel Dias

Keyword(s):

Stability Analysis ◽

Limit Analysis ◽

Three Dimensional ◽

Material Point Method ◽

Material Point ◽

Point Method ◽

Face Stability ◽

Shallow Tunnels ◽

Dimensional Face

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A moving least squares material point method with displacement discontinuity and two-way rigid body coupling

ACM Transactions on Graphics ◽

10.1145/3197517.3201293 ◽

2018 ◽

Vol 37 (4) ◽

pp. 1-14 ◽

Cited By ~ 31

Author(s):

Yuanming Hu ◽

Yu Fang ◽

Ziheng Ge ◽

Ziyin Qu ◽

Yixin Zhu ◽

...

Keyword(s):

Rigid Body ◽

Least Squares ◽

Material Point Method ◽

Material Point ◽

Point Method ◽

Displacement Discontinuity ◽

Moving Least Squares

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Dam Breach Simulation with the Material Point Method

Computation ◽

10.3390/computation9020008 ◽

2021 ◽

Vol 9 (2) ◽

pp. 8

Author(s):

Chendi Cao ◽

Mitchell Neilsen

Keyword(s):

Material Point Method ◽

Mixture Theory ◽

Material Point ◽

Point Method ◽

Internal Erosion ◽

Dam Breach ◽

New Model ◽

Hencky Strain ◽

The Impact ◽

Soil And Water

Dam embankment breaches caused by overtopping or internal erosion can impact both life and property downstream. It is important to accurately predict the amount of erosion, peak discharge, and the resulting downstream flow. This paper presents a new model based on the material point method to simulate soil and water interaction and predict failure rate parameters. The model assumes that the dam consists of a homogeneous embankment constructed with cohesive soil, and water inflow is defined by a hydrograph using other readily available reach routing software. The model uses continuum mixture theory to describe each phase where each species individually obeys the conservation of mass and momentum. A two-grid material point method is used to discretize the governing equations. The Drucker–Prager plastic flow model, combined with a Hencky strain-based hyperelasticity model, is used to compute soil stress. Water is modeled as a weakly compressible fluid. Analysis of the model demonstrates the efficacy of our approach for existing examples of overtopping dam breach, dam failures, and collisions. Simulation results from our model are compared with a physical-based breach model, WinDAM C. The new model can capture water and soil interaction at a finer granularity than WinDAM C. The new model gradually removes the granular material during the breach process. The impact of material properties on the dam breach process is also analyzed.

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