单斜I型马氏体的非层状组织
Non-laminate Microstructures in Monoclinic-I Martensite
摘要：
本文在几何线弹性力学的背景下研究了单斜Ⅰ马氏体（一种十二变量材料）的对称一秩凸包。我们构建了一套T3，这是（非平凡的）对称秩一凸包的三元组的两两不相容的菌株。此外，我们构造了一个五维连续T3，并证明了它与对称秩一凸包边界的相交是四维的。我们还指出，存在另一种具有不同性质的半凸包的单斜I马氏体，据我们所知，这种半凸包尚未在实验中观察到。我们的策略是将对称秩一凸锥的代数结构的理解与由菌株形成的凸多胞体的刻面结构的知识相结合。
英文摘要：
We study the symmetrised rank-one convex hull of monoclinic-I martensite (a twelve-variant material) in the context of geometrically-linear elasticity. We construct sets of T3s, which are (non-trivial) symmetrised rank-one convex hulls of three-tuples of pairwise incompatible strains. Moreover we construct a five-dimensional continuum of T3s and show that its intersection with the boundary of the symmetrised rank-one convex hull is four-dimensional. We also show that there is another kind of monoclinic-I martensite with qualitatively different semi-convex hulls which, so far as we know, has not been experimentally observed. Our strategy is to combine understanding of the algebraic structure of symmetrised rank-one convex cones with knowledge of the faceting structure of the convex polytope formed by the strains.
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