Engineering Transactions, 64, 4, pp. 581–587, 2016

On the Static Nature of Minimal Kinematic Boundary Conditions for Computational Homogenisation

Marek WOJCIECHOWSKI
Technical University of Lódź
Poland

Marek LEFIK
Technical University of Lódź
Poland

In the paper, the concept of minimal kinematic boundary conditions (MKBC) for computational homogenisation is considered. In the presented approach, the strain averaging equation is applied to the microscopic representative volume element (RVE) via Lagrange multipliers, which are, in turn, interpreted as macroscopic stresses. It is shown that this formulation fulfil automatically Hill-Mandel macrohomogeneity condition. Also, it is demonstrated, that MKBCs are in fact static, Neumann kind boundary conditions. As a consequence the effective parameters computed with this approach are lower bounds of the true effective values. Numerical analysis illustrating these results is also provided.
Keywords: RVE; minimal kinematic boundary conditions; MKBC; computational homogenisation
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