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Stabilized material point methods for coupled large deformation and fluid flow in porous materials

机译：多孔材料中大变形与流体耦合的稳定材料点方法

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摘要

The material point method (MPM) has been increasingly used for the simulation of large-deformation processes in fluid-infiltrated porous materials. For undrained poromechanical problems, however, standard MPMs are numerically unstable because they use low-order interpolation functions that violate the inf-sup stability condition. In this work, we develop stabilized MPM formulations for dynamic and quasi-static poromechanics that permit the use of standard low-order interpolation functions notwithstanding the drainage condition. For the stabilization of both dynamic and quasi-static formulations, we utilize the polynomial pressure projection method whereby a stabilization term is augmented to the balance of mass. The stabilization term can be implemented with both the original and generalized interpolation material point (GIMP) methods, and it is compatible with existing time-integration methods. Here we use fully-implicit methods for both dynamic and quasi-static poromechanical problems, aided by a block-preconditioned Newton-Krylov solver. The stabilized MPMs are verified and investigated through several numerical examples under dynamic and quasi-static conditions. Results show that the proposed MPM formulations allow standard low-order interpolation functions to be used for both the solid displacement and pore pressure fields of poromechanical formulations, from undrained to drained conditions, and from dynamic to quasi-static conditions. (C) 2019 Elsevier B.V. All rights reserved.
机译：物质点方法（MPM）已越来越多地用于流体渗透多孔材料中大变形过程的模拟。但是，对于不排水的球体力学问题，标准的MPM在数值上是不稳定的，因为它们使用违反inf-sup稳定性条件的低阶插值函数。在这项工作中，我们为动态和准静态的风速力学开发了稳定的MPM公式，即使存在排水条件，该公式也允许使用标准的低阶插值函数。对于动态和准静态公式的稳定化，我们使用多项式压力投影方法，其中将稳定项扩展到质量平衡。稳定项可以使用原始和广义插值物质点（GIMP）方法来实现，并且与现有的时间积分方法兼容。在这里，我们使用完全隐式方法解决动态和准静态的杆件力学问题，并借助块预处理的Newton-Krylov求解器。通过在动态和准静态条件下的几个数值示例验证并研究了稳定的MPM。结果表明，所提出的MPM配方允许将标准低阶插值函数用于poromechanical配方的固体位移和孔隙压力场，从不排水到排水条件，从动态到准静态条件。 （C）2019 Elsevier B.V.保留所有权利。

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