elastic, Materials, Microstructure, Microstructure sensitive design, plastic


Materials microstructure is considered to be a design variable in the methodology called microstructure sensitive design (MSD). Based upon existing homogenization relations, relating the first-order representation of microstructure (the local state distribution function) to elastic and yield properties, the paper describes the construction of properties closures. These establish the theoretically-possible combinations of properties achievable by the set of all possible microstructures, which is called the microstructure hull. Exemplary homogenization relations are shown to be, typically, hypersurfaces (often hyperplanes) in the Fourier space in which the microstructure hull resides. All points lying on (or to one side of) the hypersurface, that also intersects the microstructure hull, represent microstructures that are predicted to have the same property (or property bound). It follows that intersections of several hypersurfaces (representing several properties), with the microstructure hull, represent allowable combinations of properties. From these intersections, combined properties closures have been constructed using conventional methods of linear programming. The primary example chosen is the cubic–orthorhombic Cu–Ni alloy system; for this case the elastic properties reside in a three-dimensional subspace of the infinite dimensional microstructure hull, and therefore a graphical depiction of the problem is convenient.

Original Publication Citation

International Journal of Plasticity 2 (24) 1577-162

Document Type

Peer-Reviewed Article

Publication Date


Permanent URL


Elsevier Ltd.




Ira A. Fulton College of Engineering and Technology


Mechanical Engineering