Explicit phase diagram for a one-dimensional blister model

被引:0
作者
Chmaycem, G. [1 ,2 ]
Jazar, M. [1 ]
Monneau, R. [2 ]
机构
[1] Lebanese Univ, LaMA Liban, POB 37, Tripoli, Lebanon
[2] Univ Paris Est, CERMICS, Ecole Ponts ParisTech, 6 & 8 Ave Blaise Pascal, F-77455 Champs Sur Marne 2, Marne La Vallee, France
来源
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2017年 / 97卷 / 02期
关键词
Blister; thin film; fracture; delamination; buckling; Foppl-von Karman; variational model; classification of global minimizers; phase diagram; nonlinear elasticity; obstacle problem; non interpenetration condition; THIN-FILMS; DELAMINATION;
D O I
10.1002/zamm.201500226
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider a thin film bonded to a substrate. The film acquires a residual stress upon cooling due to the mismatch of the thermal expansion coefficients between the film and the substrate. The film tends to lift off the substrate once this residual stress is compressive and large enough. In this work, this phenomenon is described by a simplified one-dimensional variational model. We minimize an energy and study its global minimizers. This problem depends on three parameters: the length of the film, its elasticity and the temperature. Our main result consists of describing a phase diagram, that depends on those parameters, in order to identify three types of global minimizers: a blister, a fully delaminated blister and a trivial solution (without any delamination). Moreover, we prove various qualitative results describing the shape of the blisters and allowing us to identify the smallest blister that may appear. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
引用
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页码:202 / 216
页数:15
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