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RVE computations with error control and adaptivity: the power of duality

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Abstract

The goal of computational homogenization is to obtain the macro-scale response, normally in terms of macro-scale stress for given macro-scale deformation, via RVE-computations. In this paper we investigate, in a systematic manner, the effects of Dirichlet and Neumann boundary conditions on the RVE. Adaptive computations are carried out with respect to, in particular, control of the error in the macro-scale stress tensor. This requires the corresponding dual solutions. As a new result, it is shown how the same dual solutions can be conveniently used in computing the algorithmic tangent stiffness tensor, thereby demonstrating the “power of duality”.

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Authors and Affiliations

  1. Department of Applied Mechanics, Chalmers University of Technology, 412 96, Goteborg, Sweden

    Fredrik Larsson & Kenneth Runesson

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  1. Fredrik Larsson
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  2. Kenneth Runesson
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Correspondence to Fredrik Larsson.

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Larsson, F., Runesson, K. RVE computations with error control and adaptivity: the power of duality. Comput Mech 39, 647–661 (2007). https://doi.org/10.1007/s00466-006-0108-z

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  • DOI: https://doi.org/10.1007/s00466-006-0108-z

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