A method using freedom and constraint topologies to synthesize and analyze the microstructure of a material with a desired thermal expansion coefficient. The method includes identifying tab kinematics of a design space sector that will produce a desired bulk material property, selecting a freedom space that contains a desired tab motion identified from the tab kinematics identified, selecting flexible constraint elements from within a complementary constraint space of the freedom space selected, and selecting actuation elements from within an actuation space generated from a system generated from the flexible constraint element selection.
FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
 The United States Government has rights in this invention pursuant to Contract No. DE-AC52-07NA27344 between the United States Department of Energy and Lawrence Livermore National Security, LLC for the operation of Lawrence Livermore National Laboratory.