On the modeling of equilibrium twin interfaces in a single-crystalline magnetic shape memory alloy sample. I: theoretical formulation
On the modeling of equilibrium twin interfaces in a single-crystalline magnetic shape memory alloy sample. I: theoretical formulation
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DOI：
10.1007/s00161-013-0319-4
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发表时间：
2014-07
影响因子：
2.6
通讯作者：
Jiong Wang;P. Steinmann
中科院分区：
文献类型：
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作者：
Jiong Wang;P. Steinmann
本文提出一种变分方法来研究单晶磁性形状记忆合金(MSMA)样品在外力和磁场作用下的响应。特别是推导了一些准则来模拟样品中孪晶界面的(准静态)运动。通过考虑相容条件，发现两个马氏体变异体之间的孪晶界面是具有给定法向量的平面。采用变分方法，建立了整个磁力系统的总能量泛函。通过计算总能量泛函对自变量的变化，可以得到内变量的平衡方程和演化规律。通过进一步考虑总能量泛函相对于变量分布的变化，可以推导出孪生界面运动的一些判据。通过建立平衡方程、内部变量的演化规律和孪生界面运动准则，建立了电流模型的控制系统。为了验证调节系统的有效性，在一定的简化条件下，构造了一些解析结果，可以用来模拟MSMA样品的磁力响应。
In this paper, a variational approach is proposed to study the response of a single-crystalline magnetic shape memory alloy (MSMA) sample subject to external forces and magnetic fields. Especially, some criteria are derived to model the (quasi-static) movements of twin interfaces in the sample. By considering the compatibility condition, twin interfaces between two martensite variants are found to be flat planes with given normal vectors. To adopt the variational method, a total energy functional for the whole magneto-mechanical system is proposed. By calculating the variations of the total energy functional with respect to the independent variables, the equilibrium equations and the evolution laws for the internal variables can be derived. By further considering the variation of the total energy functional with respect to the variant distribution, some criteria for twin interface movements can be derived. The governing system of the current model is then formulated by composing the equilibrium equations, the evolution laws for the internal variables and the twin interface movement criteria. To show the validity of the governing system, some analytical results are constructed under certain simplified conditions, which can be used to simulate the magneto-mechanical response of the MSMA sample.