A Comparison of Micromechanical Models for the Homogenization of Microheterogeneous Elastic Composites
The structural analyses of stresses, strains and deformations by mathematical means and mechanical considerations demand for constitutive models, which set the mathematical mapping between the different physical fields. The constitutive properties of many materials like metals or plastics can be represented well by phenomenological models that do not explicitly concern about the underlying microscopical structure. Nevertheless, all solid matter shows a discrete texture if it is regarded on a sufficiently small lengthscale. In the vast field of composite materials solely phenomenological models need a sophisticated formulation and demand for elaborate experimental data in order to identify the rather high number of constituting parameters. Hence, micromechanical approaches have more and more moved into the focus of material modelling. Their central task is to deduce and obtain large scale properties from numerical analyses of the small scale structure followed by the application of averaging procedures to the computed small scale fields. Thereby, the level, on which the constitutive formulation is a purely phenomenological one, is pushed towards a lower scale. Since several years, the growth of computational power has lead to the propagation of micromechanically based constitutive approaches.
KeywordsDisplacement Field Representative Volume Element Homogeneous Boundary Condition Fibre Shape Micromechanical Approach
The financial support of the DFG (Deutsche Forschungsgemeinschaft) under contract Ma 1186/4 is gratefully acknowledged for the second author.
- 1.Aboudi J (1991) Mechanics of composite materials. A unified micromechanical approach. Elsevier, AmsterdamGoogle Scholar
- 4.Altenbach H, Altenbach J, Rikards R (1996) Einführung in die Mechanik der Laminat- und Sandwichtragwerke. Deutscher Verlag für Grundstoffindustrie, StuttgartGoogle Scholar
- 7.Gerlach S (2003) Modellbildung und Parameteridentifikation viskoelastischer Faserverbundstrukturen. PhD Thesis, University of Kassel, KasselGoogle Scholar
- 8.Gerlach S, Matzenmiller A (2004) Comp Mat Sci 29:282–300Google Scholar
- 10.Kurnatowski B (2009) Zweiskalensimulation von mikroheterogenen Strukturen aus spröden Faserverbundwerkstoffen. PhD Thesis, University of Kassel, KasselGoogle Scholar
- 11.Matzenmiller A, Gerlach S (2001) Determination of effective material functions for linear viscoelastic fibrous composites with micromechanical models. In: Wall WA et al (eds) Trends computational structural mechanics. International conference, May 20–23, 2001 Lake Constance Austria/Germany, CIMNE, Barcelona, Spain, 2001Google Scholar
- 12.Matzenmiller A, Gerlach S (2002) Micromechanical modeling of viscoelastic fiber–matrix bond in composites. In: Mang HA (ed) Proceedings of the fifth world congress on computational mechanics. Vienna University of Technology, AustriaGoogle Scholar
- 13.Matzenmiller A, Gerlach S (2006) Comp Part B 37:1117–1264Google Scholar
- 15.Matzenmiller A, Köster B (2007) IJSS 44:2244–2268Google Scholar
- 16.Matzenmiller A, Köster B (2008) Proc Appl Math Mech 7:4080025–4080026Google Scholar
- 18.Nayfeh AH (1973) Perturbation methods. Pure and applied mathematics, A Wiley-Interscience series of texts, Monographs and tracts. Wiley, New YorkGoogle Scholar