Smoothed Particle Hydrodynamics Techniques for the Physics Based - PowerPoint PPT Presentation

Smoothed Particle Hydrodynamics Techniques for the Physics Based Simulation of Fluids and Solids Elastic Solids Dan Jan Barbara Matthias Koschier Bender Solenthaler Teschner

Graphics Research - SPH Solver  Fluids  Low viscosity [Mueller 2003, Bender 2017]  High viscosity [Debrun 1996, Peer 15, Takahashi 15, Weiler 18]  Ferrofluids [Huang 2019]  Granular materials  Elastic solids [Solenthaler 2007, Peer 2018]  Plastic solids [Gerszewski 2009]  Rigid bodies [Gissler 2019] SPH for the Physics Based Simulation of Fluids and Solids – 2

[Peer et al., presented at Eurographics 2018] SPH for the Physics Based Simulation of Fluids and Solids – 3

[Peer et al., presented at Eurographics 2018] SPH for the Physics Based Simulation of Fluids and Solids – 4

Outline  Elastic force model  SPH implementation  Implicit formulation SPH for the Physics Based Simulation of Fluids and Solids – 5

Linear Elasticity  Continuum mechanics formulation Goal: Computation of forces from deformations, e.g. shear, compression, stretch Input: Current deformed object state, initial undeformed state Linearity: Forces depend linearly on object positions SPH for the Physics Based Simulation of Fluids and Solids – 6

Linear Elasticity – Force Computation  Initial position  Current position  Displacement  Deformation map  Deformation gradient  Strain  Stress  Force per volume SPH for the Physics Based Simulation of Fluids and Solids – 7

Linear Elasticity - Examples  Object translation by  Isotropic compression or stretch with  Rotation with SPH for the Physics Based Simulation of Fluids and Solids – 8

Linear Elasticity - Examples  Stress scales strain  Strain components are scaled differently with  Body force accelerates material from high to low deformation  Isotropic compression / stretch SPH for the Physics Based Simulation of Fluids and Solids – 9

Linear Elasticity - Discussion  Enables stable, efficient, simple implicit formulations  Cannot handle rotating objects  Cannot handle “large” deformations  Limited to incompressible elastic solids SPH for the Physics Based Simulation of Fluids and Solids – 10

Outline  Elastic force model  SPH implementation  Implicit formulation SPH for the Physics Based Simulation of Fluids and Solids – 11

Kernel Gradient Correction  Deformation gradient  SPH kernel gradient correction, e.g. [Bonet and Lok 1999]  First-order consistent deformation gradient SPH for the Physics Based Simulation of Fluids and Solids – 12

Corotated Formulation  Linear elasticity misinterprets rotations as deformations  Rotation is extracted from deformation gradient , e.g. polar decomposition or [Mueller 2016]  Reference configuration is rotated with the object  Kernel gradient with rotated reference configuration  Deformation map with rotated reference configuration SPH for the Physics Based Simulation of Fluids and Solids – 13

Corotated Formulation - Illustration SPH for the Physics Based Simulation of Fluids and Solids – 14

SPH Force Computation  Strain  Stress  Stress with alternative parameter formulation  Separation of shear and bulk stress  Force per volume [Ganzenmueller 2015] SPH for the Physics Based Simulation of Fluids and Solids – 15

Zero-Energy Modes [Ganzenmueller 2015]  Certain deformations do not result in forces  Compute correction forces for inconsistent states  For all vectors , the term should be zero  Penalty force minimizes SPH for the Physics Based Simulation of Fluids and Solids – 16

SPH for the Physics Based Simulation of Fluids and Solids – 17

Outline  Elastic force model  SPH implementation  Implicit formulation SPH for the Physics Based Simulation of Fluids and Solids – 18

Linear System  Explicit:  Implicit:  Position update:  Implicit:  Linear force formulation:  Linear system SPH for the Physics Based Simulation of Fluids and Solids – 19

Solver  Linear, symmetric system  Matrix-free solver implementation  See PPE solver  Iterative solvers, e.g. CG  Two iterations over particles and neighbors per iteration SPH for the Physics Based Simulation of Fluids and Solids – 20

Framework  Start:  Gravity, viscosity, … :  Elastic forces:  Zero-energy modes:  Pressure:  Velocity update:  Position update: SPH for the Physics Based Simulation of Fluids and Solids – 21

Pressure Projection  Handles self-collisions, preserves volume  Elastic forces preserve volume, but do not detect collisions  Boundary handling with other phases  Simply solve pressure for all particles of all interacting phases, e.g. elastic solids, rigid solids, fluids SPH for the Physics Based Simulation of Fluids and Solids – 22

[Peer et al., presented at Eurographics 2018] SPH for the Physics Based Simulation of Fluids and Solids – 23

[Peer et al., presented at Eurographics 2018] SPH for the Physics Based Simulation of Fluids and Solids – 24

[Peer et al., presented at Eurographics 2018] SPH for the Physics Based Simulation of Fluids and Solids – 25