基于朗道理论的形状记忆合金及复合结构的非线性热弹性动力学分析与控制

项目名称： 基于朗道理论的形状记忆合金及复合结构的非线性热弹性动力学分析与控制

项目编号： No.10872062

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 金属学与金属工艺

项目作者： 王林翔

作者单位： 杭州电子科技大学

项目金额： 32万元

中文摘要： 形状记忆合金独特的记忆效应和超弹性归因于材料内的马氏体相变和重定向，它使得相关结构的 热弹性动力学分析与控制变得非常复杂与困难。本项目针对含记忆效应的热弹性动力学问题，在细观尺度上根据朗道相变理论构造具有多个局部极小值的自由能函数来刻画不同的晶相，使之能描述马氏体相变和重定向。在宏观尺度上，根据非平衡热力学理论，构建非凸的热弹性耦合本构关系来模拟材料的滞回效应，并考虑松弛效应及本构关系对温度的依赖性。据此，将记忆合金及相关复合结构的动力学表述成一个非线性的热弹性耦合动力学问题。将由相变导致的记忆效应和超弹性、多晶材料中的次滞回效应等各种特性，都归结为一个非线性热弹性动力系统的响应。对相关结构的动力学进行数值分析，对模型进行简化、降阶。对滞回效应采用微分方程进行模拟，采用非线性反馈对其进行线性化处理，并对其进行控制。同时在细观尺度上，用同样的非线性热弹性动力学系统，来对马氏体相变的过程进行模拟，以对细观层状结构进行模拟。本项目的技术路线和研究成果，对其他智能材料中的滞回效应，同样具有适应性。

中文关键词： 马氏体相变；朗道理论；热弹性；滞回曲线；复合结构

英文摘要： The martensite transformations and variant re-orientations in shape memory alloys are responsible for its unique properties such as shape memory and pseduoelastic effects. On the other side, the transformations and re-orientations make the analysis and control of shape memory structures very complicated. In the present project,the Landau theory is employed to model the thermoelastic dynamics with phase transformations in shape memory alloy structures. A methodology for analysis and control of composite structures with shape memory alloys is developed. At mesoscale, a non-convex free energy function is constructed with each of its local equilibriums can be used to characterize one of the phases and variants involved in transformations. The constitutive laws of the materials are obtained by using the non-equlibirium thermodynamical equilibrium conditions. The hysteretic dynamics of the shape memory alloys is treated as nonlinear thermoelastic one. The hysteresis loops, pseduoelasticity, and sub-hysteresis-loops are all regarded as the outputs of the coupled nonlinear thermoelastic problem. Model reduction isemployed to approximate the dynamics by using an ordinary differential equation system.Feedback linearization strategy is introduced to construct a related linear system forcontrol purpose. At mesoscale, the laminated structures in the shape memory alloys arealso modeled by following the coupled nonlinear thermoelasitc approach. The strategyproposed in the current project can also be employed for the investigations offerroelectric, ferromagnetic materials and structures.

英文关键词： Martensite; transformation;thermoelastic; Landau theory;hysteresis;composite structures