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Building proper behavior into mathematical models for shape memory alloys

机译:构建适当的行为进入形状记忆合金的数学模型

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Many mathematical models currently used for modeling shape memory alloy behavior in a control setting make use of an internal variable that has the interpretation of being the phase fraction of either austenite or martensite. Recently, more detailed models have been introduced that further discriminate phase species. These models seem to be pitched at the correct level for implementation in FEM based design protocols in that they are sufficiently detailed to accurately reflect much of the underlying physics, without having to track individual events at the microscale. In order for these models to enjoy reliable predictive status, it is necessary that conditions be built into them that ensure proper qualitative behavior for all processes to which the model will be applied. We discuss how the constitutive functions which enter into these models (such as the phase fraction envelope curves) can be validated to ensure proper behavior in general processes.
机译:目前用于在控制设置中建模形状记忆合金行为的许多数学模型利用内部变量,该变量具有解释是奥氏体或马氏体的相位分数。最近,已经介绍了更详细的模型,进一步辨别相阶段。这些模型似乎在基于FEM的设计协议中实现的正确水平,因为它们足以准确地反映出大部分地下物理学,而不必在微尺度追踪各个事件。为了使这些模型享受可靠的预测状态,必须建立一个条件,以确保适用模型的所有进程的正确定性行为。我们讨论如何验证进入这些模型(例如相位分数包络曲线)的本构函数,以确保一般过程中的正确行为。

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