History




Independently
of this development scientists within the field of micromechanics have
developed their own theory concerning the mechanics of composites and structures,
often referred to as the theory of cellular solids. At Narvik Institute
of Technology, HiN, scientists from both these fields work closely together.
The local industri (Natech A/S) is also involved in this reseach activity
(at the moment one Natechemployee is a doctorand in this field).
Typical
problems
By using these theories we can determine locale and global (effective) properties of inhomogeneous structures which are too complex to be treated by conventional computational methods. 

The
theories make it possible to design material structures with optimal properties
with respect to weight, strength, stiffness, heat conductivity, electric
conductivity, magnetic permeability, viscosity etc.

(Graeme Milton 1992) 
The
discoveries so far even include isotropic materials with negative Poisson’s
ratio close to 1 (i.e. when the material is expanded in one direction
it will expand in the orthogonal direction as well in almost the same ratio).
Many of the structures illustrated on this page are socalled iterated structures. Concerning the recent developement of the mathematical theory of such structures e.g. BraidesLukkassen, 2000 , Lions, Lukkassen, Persson, Wall 2001 and LukkassenMilton, 2002 

Homogenization
theory in Narvik and Luleå



(Dag Lukkassen 1998 pdffile ). 
Activities
at HiN



Optimal
reiterated structure with respect to outofplane shear stiffness.

The
scientific staff at HiN doing research on homogenization and composites
has good connections with foreign research institutions within homogenization
theory, composites and cellular solids, such as Cambridge University, Moscow
State University, SISSA in Italy, Collège de France, Royal Institute
of Technology (KTH), Chalmers University, Lund University, New Dehli University.
Visiting
Research Scientists at HiN The research has been
financially supported by a number of institutions and enterprises, e.g.
the oil company ELF, Natech A/S, The Norwegian Research Council, Nordland
Fylke and the Ministry of Education and Research (KUF). 

(Lukkassen 1998). 
Further examples Below we give some further illustrations of physical problems which
can be analysed by the theory.


(Zeuthen
1997). For similar structures see also a publication in <<Nature>>
by R. Lakes 
(Dag Lukkassen 1996). 
The
''Lavrentiev phenomenon'':

Low
speed flow in porous media (Stokes flow) is an other example of physical
problem which can be analysed by using the homogenization method. In the
figure the structure is periodic. In the figure on the right side we show
the streamlines in one period. 
Numerical
computation by using ''Flow 3D'' (BangLukkassen 1999) 
Last Update: