کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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796905 | 1467145 | 2008 | 12 صفحه PDF | دانلود رایگان |
In the last two decades, the problem of computing the elastic energy of phase transforming materials has been studied by a variety of research groups. Due to the non-quasiconvexity of the underlying multi-well landscape, different relaxation methods have been used in order to estimate the quasiconvex envelope of the energy density, for which no explicit expression is known at present.This paper combines a recently developed lamination bound for monocrystalline shape memory alloys which relies on martensitic twinned microstructures with the work of Smyshlyaev and Willis [1998a. A ‘non-local’ variational approach to the elastic energy minimization of martensitic polycrystals. Proc. R. Soc. London A 454, 1573–1613]. As a result, a lamination upper bound for n-variant polycrystalline martensitic materials is obtained.The lamination bound is then compared with Reuß- and Taylor-type estimates. While, for given volume fractions, good agreement of lamination upper and convexification lower bounds is obtained, a comparison using energy-minimizing volume fractions computed from the various bounds yields larger differences. Finally, we also investigate the influence of the polycrystal's texture. For a strong ellipsoidal texture, we observe even better agreement of upper and lower bounds than for the case of isotropic statistics.
Journal: Journal of the Mechanics and Physics of Solids - Volume 56, Issue 9, September 2008, Pages 2832–2843