TY - JOUR
T1 - Microstructures minimizing the energy of a two phase elastic composite in two space dimensions. I
T2 - The confocal ellipse construction
AU - Grabovsky, Yury
AU - Kohn, Robert V.
N1 - Funding Information:
The work of R. V. K. was partially supported by AR0 contracDt AAL NSF grantsD MS-9404376 andD MS-9402763.
PY - 1995/6
Y1 - 1995/6
N2 - For modeling coherent phase transformations and for applications to structural optimization, it is of interest to identify microstructures with minimal energy or maximal stiffness. We present a new and appealingly simple class of extremal microstructures, which we call the confocal ellipse construction, for the case of a two-dimensional elastic composite made from two isotropic elastic materials. When the macroscopic stress and strain are isotropic, our construction reduces to the well-known "coated sphere" microstructure.
AB - For modeling coherent phase transformations and for applications to structural optimization, it is of interest to identify microstructures with minimal energy or maximal stiffness. We present a new and appealingly simple class of extremal microstructures, which we call the confocal ellipse construction, for the case of a two-dimensional elastic composite made from two isotropic elastic materials. When the macroscopic stress and strain are isotropic, our construction reduces to the well-known "coated sphere" microstructure.
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U2 - 10.1016/0022-5096(95)00016-C
DO - 10.1016/0022-5096(95)00016-C
M3 - Article
AN - SCOPUS:0029322810
SN - 0022-5096
VL - 43
SP - 933
EP - 947
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
IS - 6
ER -