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SUMMARY:Multi-scale methods and the determination of Representative Volume
 s in Solid - Prof Harm Askes (University of Sheffield)
DTSTART:20070216T150000Z
DTEND:20070216T160000Z
UID:TALK6396@talks.cam.ac.uk
CONTACT:Nami Norman
DESCRIPTION:In many processes of engineering mechanics the various scales 
 of observation interact with one another. For instance\, in crack propagat
 ion problems the macroscopic geometry and boundary conditions influences t
 he microscopic dissipation processes at the crack tip and vice versa. Anot
 her example concerns the dispersive propagation of waves through microstru
 ctured media\, where every wave number propagates with a distinct velocity
  related to the characteristic size of the microstructure. In order to cap
 ture the material and structural behaviour properly\, all relevant scales 
 must be taken into account\, for instance by means of multi-scale methods.
 \n\nOn of the methods to perform a multi-scale analysis is to assign a mic
 roscopic unit cell to every macroscopic material point. The macroscopic ma
 terial behaviour is then evaluated not by means of a macroscopic constitut
 ive relation but instead by solving a microscopic boundary value problem o
 n the unit cell. This unit cell is often denoted a "Representative Volume 
 Element" (RVE). In the talk\, the following three issues will be addressed
 :\n\n1. RVE determination The size of the RVE must be determined before it
  can be used in multi-scale\nanalysis. A simple statistical procedure has 
 been developed to quantify the RVE size\, while it also allows to verify t
 he existence of the RVE. The existence and size determination of RVEs will
  be addressed for elastic\, hardening and softening materials.\n\n2. Homog
 enisation Once the issue of RVE size determination is dealt with\, its eff
 ects on the macroscopic response can be considered. To this end\, so-calle
 d micro-macro transitions must be made\, i.e. the microscopic RVE response
  must be homogenised in order to obtain the corresponding macroscopic cont
 inuum response. Two homogenisation schemes will be treated\, leading to a 
 classical continuum and a continuum enriched with higher-order strain grad
 ients\, respectively. For the latter\, the relation between RVE size and t
 he macroscopic intrinsic length scale will be treated in detail.\n\n3. Mul
 ti-scale analysis of quasi-brittle materials Finally\, a multi-scale analy
 sis framework will be presented. Whereas elastic analysis is relatively st
 raightforward\, problems arise in case the material\nexhibits softening. A
 s it turns out\, the two scales cannot be considered entirely separated an
 ymore. To overcome this\, a novel multi-scale scheme will be suggested in 
 which the competing influences of microscopic size effect and macroscopic 
 softening are balanced by a volume coupling of\nmacro-scale and micro-scal
 e.\n
LOCATION:Engineering Department - LR6
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