Multiscale modelling of fracture…

(1)

Multiscale modelling of fracture…

 

Stéphane Bordas & Pierre Kerfriden 

University of Luxembourg and Cardiff University

Saarland University, 20140131

Workshop Multiscale Simulations

(2)

M

A

M

Institute of Mechanics

& Advanced Materials

I

the group… November 2012

thank you 

Application to Si-wafer splitting

Mechanical splitting of a wafer

(3)

Research directions

• Model reduction methods for fracture/

cutting

• homogenisation (FE^2, …)

• algebraic model reduction (e.g. POD)

!

• Advanced discretization methods

• XFEM

• Meshfree

(4)

M

_{Institute of Mechanics}

A

M

I

Institute of Mechanics and Advanced Materials

bordasS@cardiff.ac.uk

Engineering & Medical Mul/scale Problems -‐ fracture & cu8ng

[Allix, Kerfriden, Gosselet 2010]

Discretise

0.125 mm 50 mm

100 plies

(5)

M

A

M

I

Practical advanced early-stage design simulations

Discretise

0.125 mm 50 mm

100 plies

(6)

M

A

M

I

Surgical simulation (real time)

Discretise

0.125 mm 50 mm

100 plies

(7)

M

A

M

I

Surgical simulation (real time)

‣ Reduce the problem size while maintaining accuracy in solving very large multiscale mechanics problems

Discretise

0.125 mm 50 mm

100 plies

(8)

http://www.researcherid.com/rid/A-1858-2009

I M

A

M

Facilitate the transi/on from CAD to analysis for fracture sim.

eXtended

FEM/BEM Meshless

CAD / Analysis

Advanced discretisations to alleviate the mesh burden

Element technology Isogeometric Analysis Boundary Elements Ambient Space FEM

Isogeometric Boundary Element Analysis

(9)

Outline

➢ Introduction: Multiscale methods for Fracture ➢ Adaptive multiscale method

▪ Strategy

▪ Fine scale problem ▪ Coarse scale problem

• FE2 _method

• Adaptive mesh refinement

▪ Coupling fine and coarse discretisations ▪ Results

• L-shape problem

(10)

erro

r

Coarse Element size

Discre

tizatio

n erro r

Homogenisation error

Critical level of error

Error control in multiscale modelling

(11)

Multiscale methods for Fracture

▪ Concurrent ▪ Non-concurrent

Damage zone is modelled by a macroscopic cohesive crack that homogenises the failure zone. V.P. Nguyen 2012 l L L/l >1 L l L/l >>1

(12)

➢Strategy:

• control the coarse scale discretization error

Mesh refinement _{Hybrid method}

• control the modelling error

FE2 FE2 FE2+ Domain

Decomposition Method

(13)

➢Microscale problem: ▪Orthotropic grains ! ! ! ▪Cohesive interface

(14)

➢Macroscale problem: ▪ FE2 Method

Based on averaging theorem (computational homogenisation)

!

▪Adaptive mesh refinement

Error estimation by Zienkiewicz-Zhu-type recovery technique

Mesh refinement

RVE

(15)

▪ The FE2 Method

RVE time step, i

Macroscale problem

Iteration, j

RVE problem

Iteration, k

❖ Shortcoming of the FE2_{Method :}

Lack of scale separation

RVE cannot be found in the softening regime

! !

(16)

• Error estimation by Zienkiewicz-Zhu-type

recovery technique

➢Coarse scale Adaptive mesh refinement

Element to refine Refined mesh

•Convergence criterion:

Coarse Scale: Adaptive mesh refinement

Error$due$to$the$ discre-sa-on$of$

neglected$$$ ⌦

(17)

⌦c

What is the solution for the FE2

shortcoming:

“Hybrid Multiscale Method”

•FE2 for non-critical region

(hierarchical multiscale)

!

•Domain decomposition for critical region (concurrent multiscale)

Fine-Coarse scales Coupling 

Critical region

FE2

(18)

(19)

(20)

Results: uni-axial tension

(21)

Results: uni-axial tension

(22)

Results: uni-axial tension

(23)

Results: uni-axial tension

(24)

Results: uni-axial tension

(25)

Results: uni-axial tension

(26)

An adaptive multiscale method was developed for discrete fracture in polycrystalline materials:

!

• _{An unstructured mesh is used for the coarse scale}

problem

!

• A local arc-length was used to control crack speed in the

fully resolved region.

!

• A recovery based error indicator was employed to limit

discretization error at each time step.

(27)

Perspectives

• coarsening once the crack is open

• molecular dynamics at the fine scale

! ! ! !

• real-life problems! :)

• coupling with algebraic model reduction

(POD)

(28)

(29)

(30)

(31)

(32)

Demos

• http://www.youtube.com/watch?

v=90NAq76mVmQ

• Solder joint durability

• http://www.youtube.com/watch?

v=Ri96Wv6zBNU

• http://www.youtube.com/watch?

v=1g3Pe_9XN9I

(33)

(34)

Multiscale modelling of fracture…