Boundary Conditions in a Multiscale Homogenization Procedure

Abstract:

This paper is concerned with a second-order multiscale computational homogenization scheme for heterogeneous materials at small strains. A special attention is directed to the macro-micro transition and the application of the generalized periodic boundary conditions on the representative volume element at the microlevel. For discretization at the macrolevel the C¹ plane strain triangular finite element based on the strain gradient theory is derived, while the standard C⁰ quadrilateral finite element is used on the RVE. The implementation of a microfluctuation integral condition has been performed using several numerical integration techniques. Finally, a numerical example of a pure bending problem is given to illustrate the efficiency and accuracy of the proposed multiscale homogenization approach.

• Periodical: Key Engineering Materials (Volumes 577-578)
• Pages: 297-300
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.577-578.297
• Online since: September 2013
• Authors: Tomislav Lesičar, Zdenko Tonković, Jurica Sorić
• Keywords: C¹ Finite Element, Generalized Periodic Boundary Conditions, Heterogeneous Materials, Microfluctuations Integral Condition, Multiscale, Second-Order Computational Homogenization

References

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[5] Lesičar T., Tonković Z., Sorić J., submitted to the journal Comp. Mech., (2013)