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The eXtended Bridging Scale Method (XBSM)

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The eXtended Bridging Scale 

Method (XBSM)

Pattabhi Ramaiah

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Motivation

The eXtended BSM for fracture

Adaptivity

Numerical Examples

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Bridging Scale Method

u = ū+ũ

Total displacement

Coarse scale solution

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XBSM Overview

Fine scale lattice ­  (111) atoms of FCC crystal

Coarse scale – VAC model with phantom node

Coupling – Displacement bc's.

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XBSM Overview

Fine scale lattice ­  (111) atoms of FCC crystal

Coarse scale – VAC model with phantom node

Coupling – Displacement bc's.

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Fine scale model : Lattice

LJ potential – to model atom­atom interactions

FCC unit lattice

(111) plane atoms

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Virtual Atom Cluster model

Each atom has the same environment

Possess 6 nearest neighbors

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Coarse scale model

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The total displacement 

The phantom node method

Cracked element = two overlapping elements

Theory ­ Hansbo & Hansbo (2004)

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Motivation

The eXtended BSM for fracture

Adaptivity

Numerical Examples

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Adaptivity

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Adaptive refining – convert the coarse scale region 

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Adaptivity

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Adaptive refining – convert the coarse scale region 

into fine scale region

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Motivation

The eXtended BSM for fracture

Adaptivity

Numerical Examples

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Example 1 : steps

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Example 1 : steps

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Example 1 : steps

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Example 1 : steps

Coarse scale mesh

Create VAC

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Example 1 : steps

Coarse scale mesh

Create VAC

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Example 1 : steps

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Example 1 : summary

 1       to      n

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Example 2 : initial BSM and XBSM

BSM

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Example 2 : BSM and XBSM – 18

th

 LS

BSM

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Example 2 : BSM and XBSM – 18

th

 LS

BSM

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Example 2 : BSM and XBSM – 24

th

 LS

BSM

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Example 2 : BSM and XBSM – 24

th

 LS

BSM

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Example 2 : Comparison – 18

th

 & 24

th

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Example 2 : Comparison – 18

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 & 24

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18

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 LS

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Collaboration

Timon Rabczuk

Robert Gracie

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Références

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