2011/05/21 by Andrej Cherkaev, Cherkaev, Andrej · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1105.4302
openalex publication_date 2011/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe a new type of three material microstructures which we call wheel\nassemblages, that correspond to extremal conductivity and extremal bulk modulus\nfor a composite made of two materials and an ideal material. The exact lower\nbounds for effective conductivity and matching laminates was found in\n(Cherkaev, 2009) and for anisotropic composites, in (Cherkaev, Zhang, 2011).\nHere, we show different optimal structures that generalize the classical\nHashin-Shtrikman coated spheres (circles). They consist of circular inclusions\nwhich contain a solid central circle (hub) and radial spikes in a surrounding\nannulus, and (for larger volume fractions of the best material) an annulus\nfilled with it. The same wheel assemblages are optimal for the pair of dual\nproblems of minimal conductivity (resistivity) of a composite made from two\nmaterials and an ideal conductor (insulator), in the problem of maximal\neffective bulk modulus of elastic composites made from two linear elastic\nmaterial and void, and the dual minimum problem.\n