Abstract
The object of analysis is continuum modelling of compositeswith a deterministic space-varying (nonperiodic) material microstructure. The aim of the paper is to propose a new modelling method which makes it possible to describe response of a composite by means of PDEs with smooth (averaged) coefficients. In contrast to the known asymptotic homogenization theory the proposed approach leads to model equations describing phenomena depending on the microstructure size. The presented paper summarizes new results obtained in Poland during the last decade. Instead of limit passage with the microstructure size to zero the idea of the method is strictly related to the concept of tolerance relation and tolerance parameter as a certain upper bound for negligibles. That is why the proposed approach is referred to as tolerance modelling method.
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Woźniak, C., Rychlewska, J. (2010). On the Mathematical Modelling of Functionally Graded Composites with a Determistinic Microstructure. In: Albers, B. (eds) Continuous Media with Microstructure. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11445-8_11
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DOI: https://doi.org/10.1007/978-3-642-11445-8_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11444-1
Online ISBN: 978-3-642-11445-8
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