We present a numerical method to find specific composite microstructures with targeted effective properties. The effective properties that may be prescribed are quite diverse and include transport, mechanical, and electromagnetic properties, as well as properties associated with coupled phenomena, such as piezoelectric and thermoelectric coefficients. We formulated the target problem as an optimization problem. To illustrate our general target optimization technique, we have successfully found two-phase composite microstructures having specified effective electrical or thermal conductivities at fixed volume fractions. The method can also be used to design microstructures with multifunctional characteristics.
[1]
S. Vigdergauz.
Two-Dimensional Grained Composites of Extreme Rigidity
,
1994
.
[2]
Zvi Hashin,et al.
On elastic behaviour of fibre reinforced materials of arbitrary transverse phase geometry
,
1965
.
[3]
S. Torquato,et al.
Design of materials with extreme thermal expansion using a three-phase topology optimization method
,
1997
.
[4]
Narendra Karmarkar,et al.
A new polynomial-time algorithm for linear programming
,
1984,
Comb..
[5]
S. Shtrikman,et al.
A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials
,
1962
.