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On the Hill's Fundamental Equation for Quasihomogeneous Materials
Author(s) -
Kafka V.
Publication year - 1983
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19830630302
Subject(s) - basis (linear algebra) , mathematics , meaning (existential) , calculus (dental) , mathematical analysis , epistemology , philosophy , geometry , medicine , dentistry
The well known Hill's equation (1) that is of fundamental meaning for the analysis of quasihomogeneous materials, is discussed and proved on the basis of assumptions that describe the macroscopic behaviour of these materials, i.e. on the basis of their definition. It is shown that an analogous equation where the volume averages are meant not in the composite but in one material constituent only, is not valid.