The analytical understanding of microstructures arising in martensitic phase transitions relies usually on the study of stress-free interfaces between different variants of martensite. However, in the literature there are experimental observations of non stress-free junctions between martensitic plates, where the compatibility theory fails to be predictive. In this work, we focus on $V_{II}$ junctions, which are non stress-free interfaces between different martensitic variants experimentally observed in Ti74Nb23Al3. We first motivate the formation of some non stress-free junctions by studying the two well problem under suitable boundary conditions. We then give a mathematical characterisation of $V_{II}$ junctions within the theory of elasto-plasticity, and show that for deformation gradients as in Ti74Nb23Al3 our characterisation agrees with experimental results. Furthermore, we are able to prove that, under suitable hypotheses that are verified in the study of Ti74Nb23Al3, $V_{II}$ junctions are strict weak local minimisers of a simplified energy functional for martensitic transformations in the context of elasto-plasticity.

中文翻译：

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在马氏体板之间的非无应力连接处

对马氏体相变中出现的微观结构的分析理解通常依赖于对不同马氏体变体之间的无应力界面的研究。然而，在文献中有对马氏体板之间的非无应力连接的实验观察，其中相容性理论无法预测。在这项工作中，我们专注于 $V_{II}$ 结，这是在 Ti74Nb23Al3 中实验观察到的不同马氏体变体之间的非无应力界面。我们首先通过在合适的边界条件下研究两井问题来激发一些非无应力结的形成。然后我们在弹塑性理论中给出了 $V_{II}$ 连接点的数学特征，并表明对于 Ti74Nb23Al3 中的变形梯度，我们的表征与实验结果一致。此外，我们能够证明，在 Ti74Nb23Al3 研究中得到验证的适当假设下，$V_{II}$ 结是弹塑性背景下马氏体转变的简化能量泛函的严格弱局部极小值。