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  • 1
    Electronic Resource
    Electronic Resource
    A comparison of homogenization and standard mechanics analyses for periodic porous composites (1992)
    Springer
    Computational mechanics 10 (1992), S. 73-95 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Composite material elastic behavior has been studied using many approaches, all of which are based on the concept of a Representative Volume Element (RVE). Most methods accurately estimate effective elastic properties when the ratio of the RVE size to the global structural dimensions, denoted here as ν, goes to zero. However, many composites are locally periodic with finite ν. The purpose of this paper was to compare homogenization and standard mechanics RVE based analyses for periodic porous composites with finite ν. Both methods were implemented using a displacement based finite element formulation. For one-dimensional analyses of composite bars the two methods were equivalent. Howver, for two- and three-dimensional analyses the methods were quite different due to the fact that the local RVE stress and strain state was not determined uniquely by the applied boundary conditions. For two-dimensional analyses of porous periodic composites the effective material properties predicted by standard mechanics approaches using multiple cell RVEs converged to the homogenization predictions using one cell. In addition, homogenization estimates of local strain energy density were within 30% of direct analyses while standard mechanics approaches generally differed from direct analyses by more than 70%. These results suggest that homogenization theory is preferable over standard mechanics of materials approaches for periodic composites even when the material is only locally periodic and ν is finite.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00369853
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  • 2
    Electronic Resource
    Electronic Resource
    Effective anisotropic elastic constants of bimaterial interphases: comparison between experimental and analytical techniques (1996)
    Springer
    Journal of materials science 7 (1996), S. 109-117 
    Details
    ISSN: 1573-4838
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: The effective elastic constants of a bimaterial composite were experimentally measured with the goal of validating the numerical predications of these constants made by homogenization theory. Secondly, solutions predicted by homogenization theory were compared to predictions made with more standard composite theories. Composite specimens consisting of titanium and epoxy were developed to mimic a porous titanium/tissue interphase. Tensile and shear tests (ASTM D3983) measured the stiffness along the porous coating/epoxy interphase (E L), across the interphase (E T) and in shear (G LT). No significant differences in moduli were found between the experimental measurements and predictions made with homogenization theory, nor between the experimental measurements and Hashin-Shtrikman estimates. Homogenization theory predicted results usually within 20% of Hashin-Shtrikman estimates, but typically more than 50% different from what is predicted by the rule of mixtures. However, homogenization theory allows calculation of anisotropic stiffness estimates and local strains, neither of which is possible using Hashin-Shtrikman estimates. With this experimental validation, the accuracy of homogenization theory for use in implant/tissue interface mechanics applications is confirmed. Since the composite interphase is anisotropic and more compliant in the transverse direction, with stiffness an order of magnitude lower across the interphase, local mechanics, tissue ingrowth and remodeling may be strongly directional dependent.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00058722
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  • 3
    Electronic Resource
    Electronic Resource
    Homogenization theory and digital imaging: A basis for studying the mechanics and design principles of bone tissue (1994)
    New York, NY [u.a.] : Wiley-Blackwell
    Biotechnology and Bioengineering 43 (1994), S. 586-596 
    Details
    ISSN: 0006-3592
    Keywords: homogenization theory ; digital imaging ; cortical bone ; trabecular bone ; osteocyte lacunae ; bone mechanics ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Bone tissue is a complex multilevel composite which has the ability to sense ad respond to its mechanical environment. It is believed that bone cells called osteocytes within the bone matrix sense the mechanical environment and determine whether structural alterations are needed. At present it is not known, however, how loads are transferred from the whole bone level to cells. A computational procedure combining representative volume element (RVE) based homogenization theory with digital imaging is proposed to estimate strains at various levels of bone structure. Bone tissue structural organization and RVE based analysis are briefly reviewed. The digital image based computational procedure was applied to estimate strains in individual trabeculae (first-level microstructure). Homogenization analysis of an idealized model was used to estimate strains at one level of bone structure around osteocyte lacunae (second-level trabecular microstructure). The results showed that strain at one level of bone structure is amplified to a broad range at the next microstructural level. In one case, a zeor-level tensile principal strain of 495 μE engendered strains ranging between -1000 and 7000 μE in individual trabeculae (first-level microstructure). Subsequently, a first-level tensile principal strains of 1325 μE within an inidividual trabecula engendered strains ranging between 782 and 2530 μE around osteocyte lacunae. Lacunar orientation was found to influence strains around osteocyte lacunae much more than lacunar ellipticity. In conclusion, the computational procedure combining homogenization theory with digital imaging can proveide estimates of cell level strains within whole bones. Such results may be used to bridge experimental studies of bone adaptation at the whole bone and cell culture level. © 1994 John Wiley & Sons, Inc.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bit.260430708
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    Paper (German National Licenses)
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