MPMSolver#

MPMSolver 实现了 Material Point Method (MPM，物质点法)，用于仿真各种材料，包括弹性固体、颗粒材料、流体和相变。

概述#

MPM 结合了：

Lagrangian particles (拉格朗日粒子): Track material points (追踪物质点)
Eulerian grid (欧拉网格): Solve momentum equations (求解动量方程)
Particle-grid transfers (粒子-网格传输): MLS-MPM for stability (MLS-MPM 用于稳定性)

支持的材料#

Material	Description
`MPM.Elastic`	Neo-Hookean elasticity (Neo-Hookean 弹性)
`MPM.ElastoPlastic`	Plasticity with yield (带屈服的塑性)
`MPM.Sand`	Drucker-Prager granular (Drucker-Prager 颗粒材料)
`MPM.Snow`	Snow plasticity (雪的塑性)
`MPM.Liquid`	Weakly compressible fluid (弱可压缩流体)
`MPM.Muscle`	Active muscle material (主动肌肉材料)

使用方法#

import genesis as gs

gs.init()
scene = gs.Scene(
    mpm_options=gs.options.MPMOptions(
        dt=1e-4,
        lower_bound=(-1, -1, 0),
        upper_bound=(1, 1, 2),
        grid_density=64,
    ),
)

# Add MPM entity
soft_box = scene.add_entity(
    gs.morphs.Box(pos=(0, 0, 0.5), size=(0.2, 0.2, 0.2)),
    material=gs.materials.MPM.Elastic(
        E=1e5,      # Young's modulus (杨氏模量)
        nu=0.3,     # Poisson's ratio (泊松比)
        rho=1000,   # Density (密度)
    ),
)

scene.build()

for i in range(1000):
    scene.step()

配置#

MPMOptions 中的关键选项：

Option	Type	Description
`dt`	float	Internal timestep (内部时间步长)
`lower_bound`	tuple	Grid lower corner (网格下角)
`upper_bound`	tuple	Grid upper corner (网格上角)
`grid_density`	int	Grid cells per unit (每单位网格单元数)
`particle_size`	float	Particle spacing (粒子间距)

网格设置#

MPM 需要一个背景网格进行计算：

mpm_options = gs.options.MPMOptions(
    lower_bound=(-2, -2, 0),   # Grid min (网格最小值)
    upper_bound=(2, 2, 4),     # Grid max (网格最大值)
    grid_density=128,          # Resolution (分辨率)
)

材料参数#

弹性材料#

material = gs.materials.MPM.Elastic(
    E=1e5,       # Young's modulus (Pa) (杨氏模量)
    nu=0.3,      # Poisson's ratio (泊松比)
    rho=1000,    # Density (kg/m^3) (密度)
)

颗粒材料 (Sand)#

material = gs.materials.MPM.Sand(
    E=1e6,
    nu=0.2,
    rho=1500,
    friction_angle=30,  # degrees (摩擦角，单位：度)
)

另请参阅#