We classify all exactly stress-free solutions to the cubic-to-trigonal phase transformation within the geometrically linearized theory of elasticity, showing that only simple laminates and crossing-twin structures can occur. In particular, we prove that although this transformation is closely related to the cubic-to-orthorhombic phase transformation, all its solutions are rigid. The argument relies on a combination of the Saint-Venant compatibility conditions together with the underlying nonlinear relations and non-convexity conditions satisfied by the strain components.

中文翻译：

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关于三次相变三角相变中出现的四井问题的刚度

我们在几何线性弹性理论中对立方到三角相变的所有完全无应力解决方案进行分类，表明只能出现简单的层压板和交叉孪晶结构。特别是，我们证明虽然这种转变与立方到正交相变密切相关，但它的所有解都是刚性的。该论点依赖于 Saint-Venant 相容性条件与应变分量满足的潜在非线性关系和非凸性条件的组合。