Abstract Shape Memory Alloys (SMAs) have the main interesting property to recover an inelastic strain induced by martensitic transformation. The initial shape can be recovered directly after unloading or with the application of an additional heating. Iron-based SMAs (Fe-SMAs) are characterized by a high coupling between phase transformation and plastic slip at low temperatures under small stress levels. Thermomechanical constitutive models describing such coupling developed based on small-strains are not suitable for higher loading levels. This motivates the proposed development of a finite-strain constitutive model for Fe-SMAs considering thermomechanical coupling between phase transformation and plastic slip, and by extending the small-strain model within a finite-strain thermodynamical framework in order to describe large strains mainly induced by plastic hardening in Fe-SMA material point. The model here has two internal variables (volume fraction of martensite and the accumulative plastic strain). It is based on the assumption of the local multiplicative split of the deformation gradient into elastic and inelastic parts with a total Lagrangian formulation. The inelastic deformation gradient splits also into a transformation and a plastic parts. The developed model is implemented into the commercial software Matlab. The results obtained for thermomechanical loadings are discussed and, a good agreement with experimental results is also observed.

中文翻译：

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考虑相变和塑性滑移耦合的铁基形状记忆合金的有限应变热机械行为模型

摘要 形状记忆合金 (SMA) 具有恢复由马氏体转变引起的非弹性应变的主要有趣特性。初始形状可以在卸载后直接恢复或通过额外加热恢复。铁基 SMA (Fe-SMA) 的特点是相变和塑性滑移在低温和小应力水平下的高度耦合。基于小应变开发的描述这种耦合的热机械本构模型不适用于更高的负载水平。这激发了考虑相变和塑性滑移之间热机械耦合的 Fe-SMA 有限应变本构模型的拟议开发，并通过在有限应变热力学框架内扩展小应变模型来描述主要由 Fe-SMA 材料点的塑性硬化引起的大应变。这里的模型有两个内部变量（马氏体的体积分数和累积塑性应变）。它基于变形梯度局部乘法分裂为弹性和非弹性部分的假设，具有总拉格朗日公式。非弹性变形梯度也分为变形部分和塑性部分。开发的模型在商业软件 Matlab 中实现。讨论了热机械载荷获得的结果，并且还观察到与实验结果的良好一致性。这里的模型有两个内部变量（马氏体的体积分数和累积塑性应变）。它基于变形梯度局部乘法分裂为弹性和非弹性部分的假设，具有总拉格朗日公式。非弹性变形梯度也分为变形部分和塑性部分。开发的模型在商业软件 Matlab 中实现。讨论了热机械载荷获得的结果，并且还观察到与实验结果的良好一致性。这里的模型有两个内部变量（马氏体的体积分数和累积塑性应变）。它基于变形梯度局部乘法分裂为弹性和非弹性部分的假设，具有总拉格朗日公式。非弹性变形梯度也分为变形部分和塑性部分。开发的模型在商业软件 Matlab 中实现。讨论了热机械载荷获得的结果，并且还观察到与实验结果的良好一致性。非弹性变形梯度也分为变形部分和塑性部分。开发的模型在商业软件 Matlab 中实现。讨论了热机械载荷获得的结果，并且还观察到与实验结果的良好一致性。非弹性变形梯度也分为变形部分和塑性部分。开发的模型在商业软件 Matlab 中实现。讨论了热机械载荷获得的结果，并且还观察到与实验结果的良好一致性。