{"product_id":"composite-materials-properties-as-influenced-by-phase-geometry-von-lauge-fuglsang-nielsen","title":"Composite Materials","description":"In the past ?ve decades considerable attention has been devoted to comp- ite materials. A number of expressions have been suggested by which mac- scopic properties can be predicted when the properties, geometry, and volume concentrations of the constituent components are known. Many expressions are purely empirical or semi-theoretical. Others, however, are theoretically well founded such as the exact results from the following classical boundary studies: Bounds for the elastic moduli of composites made of perfectly coherent homogeneous, isotropic linear elastic phases have been developed by Paul [1] and Hansen [2] for unrestricted phase geometry and by Hashin and Shtrikman [3] for phase geometries, which cause macroscopic homogeneity and isotropy. The composites dealt with in this book are of the latter type. For two speci?c situations (later referred to), Hashin [4] and Hill [5] derived exact - lutionsforthebulkmodulusofsuchmaterials.Hashinconsideredtheso-called Composite Spheres Assemblage (CSA) consisting of tightly packed congruent composite elements made of spherical particles embedded in concentric - trix shells. Hill considered materials in which both phases have identical shear moduli. In the ?eld of predicting the elastic moduli of homogeneous isotropic c- posite materials in general the exact Hashin and Hill solutions are of th- retical interest mainly. Only a few real composites have the geometry de?ned by Hashin or the sti?ness distribution assumed by Hill. The enormous sign- icance, however, of the Hashin\/Hill solutions is that they represent bounds which must not be violated by sti?ness predicted by any new theory claiming to consider geometries in general.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783642063671\"\u003e\u003ch3\u003eProperties as Influenced by Phase Geometry\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783540243854\"\u003e\u003ch3\u003eProperties as Influenced by Phase Geometry\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783642063671","offer_id":39424866779229,"sku":"9783642063671","price":106.99,"currency_code":"EUR","in_stock":true},{"title":"Hardcover - 9783540243854","offer_id":51074632518,"sku":"9783540243854","price":106.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/bd424c7d-7e5d-4202-b27b-c001333dca6c.jpg?v=1775192565","url":"https:\/\/shop.autorenwelt.de\/en\/products\/composite-materials-properties-as-influenced-by-phase-geometry-von-lauge-fuglsang-nielsen","provider":"Autorenwelt Shop","version":"1.0","type":"link"}