An adaptive generalized interpolation material point method for simulating elastoplastic materials

Gao, Ming; Tampubolon, Andre Pradhana; Jiang, Chenfanfu; Sifakis, Eftychios

doi:10.1145/3130800.3130879

Cited by 60 publications

(43 citation statements)

References 47 publications

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“…Chiang et al [CDH*09] proposed a GPU acceleration scheme for the Generalized Interpolation Material Point Method (GIMP) [BK04] with careful management of memory bandwidth. In computer graphics, Gao et al [GTJS17] achieved low‐level performance gain using a vectorized interpolation weight computation scheme for GIMP. Explicit MPM can also be combined with semi‐implicit fluid solvers to couple particles with imcompressible fluids [GTH*18].…”

Section: Related Workmentioning

confidence: 99%

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A Temporally Adaptive Material Point Method with Regional Time Stepping

Fang

et al. 2018

Computer Graphics Forum

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Spatially and temporally adaptive algorithms can substantially improve the computational efficiency of many numerical schemes in computational mechanics and physics‐based animation. Recently, a crucial need for temporal adaptivity in the Material Point Method (MPM) is emerging due to the potentially substantial variation of material stiffness and velocities in multi‐material scenes. In this work, we propose a novel temporally adaptive symplectic Euler scheme for MPM with regional time stepping (RTS), where different time steps are used in different regions. We design a time stepping scheduler operating at the granularity of small blocks to maintain a natural consistency with the hybrid particle/grid nature of MPM. Our method utilizes the Sparse Paged Grid (SPGrid) data structure and simultaneously offers high efficiency and notable ease of implementation with a practical multi‐threaded particle‐grid transfer strategy. We demonstrate the efficacy of our asynchronous MPM method on various examples including elastic objects, granular media, and fluids.

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Section: Related Workmentioning

confidence: 99%

“…St. Venant‐Kirchhoff Hyperelasticity . The St. Venant‐Kirchhoff hyperelasticity model combined with the logarithm Hencky strain measure has been mostly used for granular media [KGP*16, TGK*17] and elastoplastic flow [GTJS17] in graphics. Note that plasticity does not contribute to the pressure wave.…”

Section: Time Step Restrictionmentioning

confidence: 99%

A Temporally Adaptive Material Point Method with Regional Time Stepping

Fang

et al. 2018

Computer Graphics Forum

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“…More recently, Tampubolon et al [TGK*17] proposed an MPM approach for simulating porous sand and water mixtures. Gao et al [GTJS17] gave a generalized interpolating MPM method for elastoplastic materials, in which the specific region of interest is adaptively refined. Predominantly used for simulating solids, MPM is seldom used to model fluids or interactions of multiple fluids and solids.…”

Section: Previous Workmentioning

confidence: 99%

“…There are different options for the shape function, e.g. uniform GIMP [ZCL16], B‐spline interpolation [SSJ*14, SKB08] and adaptive GIMP [GTJS17]. For simplicity, we use uniform GIMP, defined as:…”

Section: Mpm Simulation Of Fluids and Solidsmentioning

confidence: 99%

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MPM simulation of interacting fluids and solids

Yan

Chen

et al. 2018

Computer Graphics Forum

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The material point method (MPM) has attracted increasing attention from the graphics community, as it combines the strengths of both particle‐ and grid‐based solvers. Like the smoothed particle hydrodynamics (SPH) scheme, MPM uses particles to discretize the simulation domain and represent the fundamental unknowns. This makes it insensitive to geometric and topological changes, and readily parallelizable on a GPU. Like grid‐based solvers, MPM uses a background mesh for calculating spatial derivatives, providing more accurate and more stable results than a purely particle‐based scheme. MPM has been very successful in simulating both fluid flow and solid deformation, but less so in dealing with multiple fluids and solids, where the dynamic fluid‐solid interaction poses a major challenge. To address this shortcoming of MPM, we propose a new set of mathematical and computational schemes which enable efficient and robust fluid‐solid interaction within the MPM framework. These versatile schemes support simulation of both multiphase flow and fully‐coupled solid‐fluid systems. A series of examples is presented to demonstrate their capabilities and performance in the presence of various interacting fluids and solids, including multiphase flow, fluid‐solid interaction, and dissolution.

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Mapped material point method for large deformation problems with sharp gradients and its application to soil‐structure interactions

Zhao,

Li,

Jiang

et al. 2024

Num Anal Meth Geomechanics

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The material point method (MPM) is often applied to large deformation problems that involve sharp gradients in the solution field. Representative examples in geomechanics are interactions between soils and various “structures” such as foundations, penetrometers, and machines, where the displacement fields exhibit sharp gradients around the soil‐structure interfaces. Such sharp gradients should be captured properly in the MPM discretization to ensure that the numerical solution is sufficiently accurate. In the MPM literature, several types of locally refined discretizations have been developed and used for this purpose. However, these local refinement schemes are not only quite complicated but also restricted to certain types of basis functions or update schemes. In this work, we propose a new MPM formulation, called the mapped MPM, that can efficiently capture sharp gradients with a uniform background grid compatible with every standard MPM basis function and scheme. The mapped MPM is built on the method of auxiliary mapping that reparameterizes the given problem in a different domain whereby sharp gradients become much smoother. Because the reparameterized problem is free of undesirably sharp gradients, it can be well solved with the standard MPM ingredients including a uniform background grid. We verify and demonstrate the mapped MPM through several numerical examples, with particular attention to soil‐structure interaction problems.

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An adaptive generalized interpolation material point method for simulating elastoplastic materials

Cited by 60 publications

References 47 publications

A Temporally Adaptive Material Point Method with Regional Time Stepping

A Temporally Adaptive Material Point Method with Regional Time Stepping

MPM simulation of interacting fluids and solids

Mapped material point method for large deformation problems with sharp gradients and its application to soil‐structure interactions

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