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SUMMARY:A Hierarchical  Multiscale Model for Evolving Discontinuities in H
 eterogeneous Solids - Prof Ekkehard Ramm (University of Stuttgart)
DTSTART:20080125T150000Z
DTEND:20080125T160000Z
UID:TALK8391@talks.cam.ac.uk
CONTACT:Nami Norman
DESCRIPTION:The present study is motivated by the fact that homogenization
  concepts may fail because the scale separation law for different scales d
 oes not hold. This violation may exist already in the initial stage or may
  evolve during material deterioration. A typical example is a long range l
 ocalized failure by distinct cracks. \nFor this situation the material beh
 aviour of heterogeneous solids on a small scale is projected onto the larg
 e or structural scale. We employ a hierarchical two-scale model derived fr
 om on a stringent variational concept. It belongs to the superposition bas
 ed methods with an additive split of the solution u into the large scale 
 ū and small scale part ú. One focus of the present formulation is to all
 ow for locality of the small scale solution within the large scale element
 s resulting in an efficient solution strategy. At the same time the small 
 scale information exchange over the large scale boundaries is achieved by 
 employing conventional Domain Decomposition concepts and satisfying the re
 lated interface constraints.\nIn the current stage of the project the inel
 astic behaviour of quasi-brittle materials is modeled by continuum damage 
 mechanics in a smeared fashion as well as by the cohesive zone theory for 
 a discrete failure. For the discretization of distinct cracks and material
  interfaces we apply an extended finite element model (X-FEM) which is sup
 ported by level set techniques. It turns out that the X-FEM enhanced small
  scale solution ú can be perfectly combined with the multi-scale solution
  scheme.\nFor the time being most of the work is done in a two-dimensional
  setting\; we are currently in the stage to extend the formulation to thre
 e-dimensional problems as well.\n
LOCATION:Engineering Department - LR6
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