Vol. 4, No. 3, 2009

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ISSN: 1559-3959
Design of crack-resistant two-dimensional periodic cellular materials

Fabian Lipperman, Michael Ryvkin and Moshe B. Fuchs

Vol. 4 (2009), No. 3, 441–457
Abstract

The resistance to macrocrack propagation in two-dimensional periodic cellular materials subjected to uniaxial remote stresses is improved by redistributing the material of the solid phase. The materials are represented by beam lattices with regular triangular or hexagonal patterns. The purpose of the design is to minimize the maximum tensile stress for all possible crack locations allowed by the material microstructure. Two design cases are considered. In the cell design case material is redistributed between the otherwise uniform elements of the repetitive cell. In the element design case the shape of identical elements is optimized. The analysis of such infinite trellis with an arbitrary macroscopic crack is enabled by an efficient exact structural analysis approach. It is shown that the fracture toughness of the triangular layout can be significantly increased by redistribution of the material between the elements with uniform cross sections while for the case of hexagonal lattice the effect is achieved mainly by using identical elements with variable thickness distribution.

Keywords
fracture toughness, honeycombs, design, discrete Fourier transform
Milestones
Received: 5 March 2008
Revised: 7 December 2008
Accepted: 14 January 2009
Published: 8 June 2009
Authors
Fabian Lipperman
School of Mechanical Engineering
Tel Aviv University
Ramat Aviv 69978
Israel
Michael Ryvkin
School of Mechanical Engineering
Tel Aviv University
Ramat Aviv 69978
Israel
http://www.eng.tau.ac.il/~arikr/
Moshe B. Fuchs
School of Mechanical Engineering
Tel Aviv University
Ramat Aviv 69978
Israel