A Sharp-Interface Limit for a Two-Well Problem in Geometrically Linear Elasticity
A Sharp-Interface Limit for a Two-Well Problem in Geometrically Linear Elasticity
复制标题
几何线弹性二井问题的锐界面极限
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
B. Schweizer
中科院分区：
文献类型：
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作者：
S. Conti;B. Schweizer
在固-固相变理论中，弹性体的变形是通过一个含有非凸能量密度和奇异摄动的泛函来确定的。我们研究
在线性化的情况下，框架无差异性要求W只依赖于Δ u的对称部分。电势W是非负的并且在两个威尔斯阱上消失，即，对于d = 2，在矩阵空间的两条直线上。我们确定，对于d = 2，Gamma极限I 0 = Γ-lim → 0 I。极限I 0 [u]仅对于几乎处处满足W（u）=0且在u有跳跃的地方有尖锐界面的变形u是有限的。对于这些u，I 0 [u]等于表面能量密度界面上的线积分。
AbstractIn the theory of solid-solid phase transitions the deformation of an elastic body is determined via a functional containing a nonconvex energy density and a singular perturbation. We study
Frame indifference, within a linearized setting, requires that W depends only on the symmetric part of ∇u. The potential W is nonnegative and vanishes on two wells, i.e., for d = 2, on two lines in the space of matrices.We determine, for d = 2, the Gamma limit I0 = Γ− lim ɛ→0Iɛ. The limit I0[u] is finite only for deformations u that fulfill W(∇u)=0 almost everywhere and have sharp interfaces where ∇u has jumps. For these u, I0[u] equals the line integral over the interfaces of a surface energy density.