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Hedgehogs, Spirals, etc.

These structures are hybrids of coated spheres and matrix laminates. The properties hedgehog structure is obtained using the effective medium theory but the material in the spherical inclusions is a laminate from infinitesimal thin layers oriented along the radius and (may be) with variable volume fraction of materials in these layers. The spiral structures deal with inclined layers instead.

In these settings, the properties are represented by tensor instead of scalar, but the elements of this tensor depend only on radius. This allows separation of variable in the problem analogous to 15. The resulting ODE allows either analytical or numerical solution, depending of the assumed dependence of volume fractions on radius.

Andre Cherkaev