A Simple Criterion for the Existence of Rank-One Connections between Martensitic Wells
A Simple Criterion for the Existence of Rank-One Connections between Martensitic Wells
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马氏体井之间存在一级连接的简单判据
DOI：
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发表时间：
1999
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通讯作者：
A. Forclaz
中科院分区：
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作者：
A. Forclaz
我们证明了当3×3对称正定U和V具有相同的本征值时，若两个井SO(3)U和SO(3)V是秩一连通的，则deT(U−V)=0是充要条件，这一结果在高维是不成立的。利用这个判据和Gurtin的一个结果，得到了孪晶面和剪切矢量的公式，从而给出了出现所谓的复合孪晶的一个极其简单的条件。作为例证，我们将我们的结果应用于立方到单斜晶系的转变。
We show that for the two wells SO(3) U and SO(3) V to be rank-one connected, where the 3 × 3 symmetric positive definite U and V have the same eigenvalues, it is necessary and sufficient that det(U − V) = 0, a result that does not hold in higher dimensions. Using this criterion and a result of Gurtin, formulae for the twinning plane and the shearing vector are obtained, which yield an extremely simple condition for the occurrence of so-called compound twins. As an illustration, we apply our results to the cubic-to-monoclinic transition.