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CATEGORIES:Engineering Department Structures Research Seminar
s
SUMMARY:Multi-scale methods and the determination of Repre
sentative Volumes in Solid - Prof Harm Askes (Univ
ersity of Sheffield)
DTSTART;TZID=Europe/London:20070216T150000
DTEND;TZID=Europe/London:20070216T160000
UID:TALK6396AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/6396
DESCRIPTION:In many processes of engineering mechanics the var
ious scales of observation interact with one anoth
er. For instance\, in crack propagation problems t
he macroscopic geometry and boundary conditions in
fluences the microscopic dissipation processes at
the crack tip and vice versa. Another example conc
erns the dispersive propagation of waves through m
icrostructured media\, where every wave number pro
pagates with a distinct velocity related to the ch
aracteristic size of the microstructure. In order
to capture the material and structural behaviour p
roperly\, all relevant scales must be taken into a
ccount\, for instance by means of multi-scale meth
ods.\n\nOn of the methods to perform a multi-scale
analysis is to assign a microscopic unit cell to
every macroscopic material point. The macroscopic
material behaviour is then evaluated not by means
of a macroscopic constitutive 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 tal
k\, the following three issues will be addressed:\
n\n1. RVE determination The size of the RVE must b
e determined before it can be used in multi-scale\
nanalysis. A simple statistical procedure has been
developed to quantify the RVE size\, while it als
o allows to verify the existence of the RVE. The e
xistence and size determination of RVEs will be ad
dressed for elastic\, hardening and softening mate
rials.\n\n2. Homogenisation Once the issue of RVE
size determination is dealt with\, its effects on
the macroscopic response can be considered. To thi
s end\, so-called micro-macro transitions must be
made\, i.e. the microscopic RVE response must be h
omogenised in order to obtain the corresponding ma
croscopic continuum response. Two homogenisation s
chemes will be treated\, leading to a classical co
ntinuum and a continuum enriched with higher-order
strain gradients\, respectively. For the latter\,
the relation between RVE size and the macroscopic
intrinsic length scale will be treated in detail.
\n\n3. Multi-scale analysis of quasi-brittle mater
ials Finally\, a multi-scale analysis framework wi
ll be presented. Whereas elastic analysis is relat
ively straightforward\, problems arise in case the
material\nexhibits softening. As it turns out\, t
he two scales cannot be considered entirely separa
ted anymore. To overcome this\, a novel multi-scal
e scheme will be suggested in which the competing
influences of microscopic size effect and macrosco
pic softening are balanced by a volume coupling of
\nmacro-scale and micro-scale.\n
LOCATION:Engineering Department - LR6
CONTACT:Nami Norman
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