Elasto-plasticity model in structural optimization of composite materials with periodic microstructures

Authors:
Ronald H. W. Hoppe;Svetozara I. Petrova
Affiliations:
Institute of Mathematics, University of Augsburg, D-86159 Augsburg, Germany and Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA;Institute of Mathematics, University of Augsburg, D-86159 Augsburg, Germany and Institute for Parallel Processing, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
Venue:
Mathematics and Computers in Simulation
Year:
2007

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Abstract

The paper deals with a structural optimization of composite materials with periodic microstructures invoking an elasto-plasticity model with the von Mises yield criterion. Closest-point return mapping algorithms within the incremental finite element method are applied for the numerical solution of the problem. The latter iterative schemes are computationally effective, robust and stable, and have recently become the most popular means for numerical implementation of elasto-plastic models. The homogenized elasto-plastic equation is considered as an equality constraint in the structural optimization problem. Numerical experiments for the computation of the homogenized coefficients involving adaptive finite element discretizations of the three-dimensional periodicity microcell are presented.