Distributed Meshes : Fracture

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Distributed Meshes Fracture

• Matt Galloway
• Pembroke College

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Project Aims

• Data structures
• Store connectivity of a mesh
• Algorithms
• Perform fracture along element faces
• Packaged into a library of code
• Example applications
• Show how to use the library for simulation or
  animation

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Software Layers
Physics of Simulation Physical laws being
simulated Computation of vertex displacements
Vertex displacements Request for fracture
Adjacency information Cohesive elements
Mesh Geometry Responsible for maintaining
connectivity Representation of mesh topology
geometry
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Fracture Simulation

• Maintain connectivity
• Introduce cohesive elements

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Distributing a Mesh

• Splitting elements between sub-domains
• Which elements / vertices need to communicate?

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Programming Approach

• Object-oriented design
• C
• Templates
• Extension libraries
• Standard Template Library (STL)
• Boost
• Parallel programming
• Message Passing Interface (MPI)

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Previous Implementations

• Simple vertex element structures
• Connectivity between elements
• What should be stored explicitly?

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Implementation

• Distributed AdaPtive Triangulation Algorithms
  (DAPTA)
• Tetra4 element designed first
• Fracture algorithm implemented
• Element connectivity lists
• Parallel algorithms
• Domain decomposition
• Fracture by merging connectivity lists

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Element Connectivity Lists

• Method for tracking fracture
• Store the order in which elements are connected
  to an edge
• Breaking of the lists associated with the
  fractured face
• Splits the fracture algorithm into two steps
• Break element connectivity lists
• Check if any element connectivity lists are in
  two fragments
• In parallel, swap element connectivity lists
  which are on boundary of sub-domains and merge

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Element Connectivity Lists

• Step 1 Initial Mesh

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Element Connectivity Lists

• Step 2 Fracture between elements 2 and 3

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Element Connectivity Lists

• Step 3 Fracture between elements 1 and 6

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Element Connectivity Lists

• Step 4 Splitting the connectivity list

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Implementation

• Data Structures
• Vertex, Element, Mesh
• Element Connectivity List
• Custom made iterator
• Algorithms
• Load / export mesh
• Decomposition of a mesh
• Fracture in two stages using element connectivity
  lists

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Example Applications

• OpenGL mesh viewer
• Parallel mesh example
• Fracture example
• Simple Finite Element Analysis (FEA) physics
  model
• Fracture when force perpendicular to a face
  reaches threshold
• Cohesive elements dont store any information
  about the crack

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Example Applications Parallel

• Decomposing a large mesh into 6 sub-domains
• Fracture was performed on the individual
  sub-domains and after merging element
  connectivity lists, each sub-domain obtains the
  same mesh representation

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Example Applications FEA

• Simple FEA physics applied
• Spring-damper model
• Test model of mass on spring

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Example Applications Fracture
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Any Questions?

• Source code available fromhttp//dapta.sourcefor
  ge.net/http//www.sourceforge.net/projects/dapta