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Keywords: multiscale, second-order continuum, computational homogenization, scale transition.

Summary

A wide range of materials produced by industry, as well as natural materials, are heterogeneous at a certain scale of observation. The macroscopic (equivalent) properties of a heterogeneous material should describe the essence of the microstructural response and they must be independent of its macrostructural loads and geometry. Traditionally, equivalent material properties have been obtained as a result of analytical or semi-analytical techniques. In recent years, a promising alternative approach has been developed, i.e. computational homogenization [1].

Computational homogenization does not require the constitutive response on the macro level to be known a priori and enables the incorporation of nonlinear geometric and material behaviour [2,1]. Kouznetsova [1] presented a second-order computational homogenization framework whereby all microstructural constituents are treated as classical continua and described by classical equilibrium and constitutive equations.

In this paper, the averaging method for this second-order scheme is extended to encompass not only periodic type boundary conditions for the Representative Volume Element (RVE) but also traction and displacement boundary conditions in a generalized manner. The key contribution of this paper is in the formulation of the scale transition equations coupling the microscopic and macroscopic variables and in the definition and enforcement of boundary conditions for the representative volume element.

The paper considers computational homogenization applied to three numerical examples in which attention is focussed on higher order effects, where the characteristic size of the microstructure is significant.

References

1: V.G. Kouznetsova, "Computational homogenization for the multi-scale analysis of multi-phase materials", PhD Eindhoven University of Technology, 2002.
2: F. Feyel, "Multiscale FE2 elastoviscoplastic analysis of composite structures", Computational Materials Science, 16, 344-354, 1999. doi:10.1016/S0927-0256(99)00077-4

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 85 PROCEEDINGS OF THE FIFTEENTH UK CONFERENCE OF THE ASSOCIATION OF COMPUTATIONAL MECHANICS IN ENGINEERING Edited by: B.H.V. Topping Paper 21 Scale Transition for Computational Homogenization L. Kaczmarczyk, C.J. Pearce and N. Bicanic Department of Civil Engineering, University of Glasgow, United Kingdom doi:10.4203/ccp.85.21 purchase the full-text of this paper Full Bibliographic Reference for this paper L. Kaczmarczyk, C.J. Pearce, N. Bicanic, "Scale Transition for Computational Homogenization", in B.H.V. Topping, (Editor), "Proceedings of the Fifteenth UK Conference of the Association of Computational Mechanics in Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 21, 2007. doi:10.4203/ccp.85.21 Keywords: multiscale, second-order continuum, computational homogenization, scale transition. Summary A wide range of materials produced by industry, as well as natural materials, are heterogeneous at a certain scale of observation. The macroscopic (equivalent) properties of a heterogeneous material should describe the essence of the microstructural response and they must be independent of its macrostructural loads and geometry. Traditionally, equivalent material properties have been obtained as a result of analytical or semi-analytical techniques. In recent years, a promising alternative approach has been developed, i.e. computational homogenization [1]. Computational homogenization does not require the constitutive response on the macro level to be known a priori and enables the incorporation of nonlinear geometric and material behaviour [2,1]. Kouznetsova [1] presented a second-order computational homogenization framework whereby all microstructural constituents are treated as classical continua and described by classical equilibrium and constitutive equations. In this paper, the averaging method for this second-order scheme is extended to encompass not only periodic type boundary conditions for the Representative Volume Element (RVE) but also traction and displacement boundary conditions in a generalized manner. The key contribution of this paper is in the formulation of the scale transition equations coupling the microscopic and macroscopic variables and in the definition and enforcement of boundary conditions for the representative volume element. The paper considers computational homogenization applied to three numerical examples in which attention is focussed on higher order effects, where the characteristic size of the microstructure is significant. References 1 V.G. Kouznetsova, "Computational homogenization for the multi-scale analysis of multi-phase materials", PhD Eindhoven University of Technology, 2002. 2 F. Feyel, "Multiscale FE2 elastoviscoplastic analysis of composite structures", Computational Materials Science, 16, 344-354, 1999. doi:10.1016/S0927-0256(99)00077-4 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £75 +P&P)
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