含孔洞的形状记忆合金模型
A model for shape memory alloys with the possibility of voids
摘要：
本文研究了金属形状记忆合金热力演化的数学模型。我们的方法的主要新颖之处在于，我们包括这些材料在相变过程中表现出空隙的可能性。事实上，在工程论文中最近已经证明，当混合物由粉末的聚集产生时，可能会出现空隙。因此，混合物的组成以这种方式变化（在热或机械作用下）：马氏体和奥氏体相互转化，而空隙体积分数则发生变化。因此，这方面的贡献的第一个目标是状态的PDE系统捕捉所有这些建模方面，然后建立相关的初始边值问题的适定性。
英文摘要：
The paper is devoted to the study of a mathematical model for the thermomechanical evolution of metallic shape memory alloys. The main novelty of our approach consists in the fact that we include the possibility for these materials to exhibit voids during the phase change process. Indeed, in the engineering paper has been recently proved that voids may appear when the mixture is produced by the aggregations of powder. Hence, the composition of the mixture varies (under either thermal or mechanical actions) in this way: the martensites and the austenite transform into one another whereas the voids volume fraction evolves. The first goal of this contribution is hence to state a PDE system capturing all these modelling aspects in order then to establish the well-posedness of the associated initial-boundary value problem.
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