Fast computation of first-order elastic–plastic closures for polycrystalline cubic-orthorhombic microstructures

In recent papers, we have described a rigorous mathematical procedure for delineating the first-order elastic–plastic closures for polycrystalline microstructures where the crystallographic texture (also called the Orientation Distribution Function or the ODF) was assumed to be the main variable influencing the effective properties. These closures were based on elementary bounding theories, and delineate the complete set of theoretically feasible combinations of effective properties in the selected material system. In this paper, we demonstrate certain key properties of these elastic–plastic closures for the class of cubic-orthorhombic textures that, in turn, facilitate a fast computation of these closures with drastically reduced computational effort. Using the novel methods described herein, we have computed and presented numerous examples of property atlases covering a broad range of cubic materials.