Incorporation of Microfield Distortion into Rapid Effective Property Design  

Oleh:

Zohdi, T.I.

Jenis: Article from Journal - ilmiah internasional
Dalam koleksi: Mathematics and Mechanics of Solids vol. 7 no. 3 (Jun. 2002), page 237–254.
Topik: Inverse problems; irregular heterogeneous microstructure
Fulltext: 237MMS73.pdf (334.28KB)

Isi artikel

It is advantageous to use analytical effective property approximations during the initial stages of the design and development of new multiphase solids. Materials of this class are typified by microscopic second-phase particles suspended in a binding matrix. Such approximate methods are ideal since they require minimal computational effort, thus allowing one to perform rapid analyses for large numbers of multiphase solid combinations controlling parameters like the volume fractions and phase contrasts. Afterwards, when the number of feasible microstructural design combinations has been sufficiently narrowed down, one can perform further in-depth studies, applying computationally intensive numerical simulations, or more involved laboratory tests, to a reduced set of design alternatives. However, a limitation of approximate methods is that they do not provide much quantifiable information about the internal stress and strain fields in the material. Clearly, during material design development, when selecting micro-additives, information about the changes in the otherwise (relatively) smooth internal fields, corresponding to the matrix material alone, would be valuable to characterize a new multiphase material’s performance. With regard to materials possessing microstructures described by particles suspended in a binding matrix, one obvious quantity of interest is the microfield distortion, defined as the difference between the fields produced when heterogeneities are present and fields produced when the heterogeneities are absent. Consistent with the use of computationally inexpensive effective property approximations, such information would be attractive, especially if it involved no extra intensive numerical simulations. Accordingly, in this work an exact expression is derived for the microfield distortion, solely in terms of the external loading, property mismatches and volume fractions. Examples are given illustrating use of the expression in a design setting whereby second-phase additives are sought which deliver desired effective responses, while simultaneously obeying microfield distortion constraints.

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