Programming Experience 2018
- Material Point Method -
Sebastian Koall
Software Architecture Group
Hasso Plattner Institute
University of Potsdam, Germany
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Introduction
- Abbreviation: MPM
- Simulating behavior of:
solids, fluids, gas
- Based on
Particle-In-Cell Method &
Finite Element Method
- Frozen: snow animation
- Short: tons of formulas
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MPM Overview
-
- Located in Euclidean grid with e cells (Elements)
- Grid has n nodes
(2D: n = (e + 1)²)
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Demo 1
```javascript {.ShowCode .Hidden}
let url = lively4url + '/doc/PX2018/project_2/elasticbodies.js';
lively.openComponentInWindow("lively-container").then(comp => comp.editFile("" + url));
```
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Demo 2
```javascript {.ShowCode .Hidden}
let url = lively4url + '/doc/PX2018/project_2/elasticbodies.js';
lively.openComponentInWindow("lively-container").then(comp => comp.editFile("" + url));
```
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Correct Result
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Related Work
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Processing Loop
- Preparation:
- Init particle mass, volume and force
- Init grid
- Loop:
- Particles to nodes
- Apply force to momtentum
- Nodes to particles
- Reset grid
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Step: Particles To Nodes
- Maps material points
to grid nodes
- Calculate node values:
- Create Lagrange grid
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Step: Nodes To Particles
- Map Lagrange grid to particles
- Calculate particle values:
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Shape Function
- Degree of influence of
nodes on particles
and vice versa
- Simple approach:
linear interpolation
- Transform into natural coordinates:
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Shape Function (Linear Interpolation)
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Step: Particles To Nodes - Details
- For each node of every element:
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Step: Nodes To Particles - Details
- For each node of every element:
- For every element:
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Outcomes & Learnings
- MPM is cool (when it works)
- Large number of MPM variables complicates the understanding
- Many MPM papers contain incomplete explanations
- Few code examples only complex systems
- Utilize proper language function when possible (requestAnimationFrame)
- Math.js has an inconvenient syntax
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Close Presentation
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# TODOs
- Alter speed
- Show parts of the animation canvas zoomed