A microscopically motivated constitutive model for shape memory alloys: Formulation, analysis and computations
A microscopically motivated constitutive model for shape memory alloys: Formulation, analysis and computations
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形状记忆合金的微观驱动本构模型：公式、分析和计算
DOI：
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发表时间：
2016
期刊：
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通讯作者：
P. Sedlák
中科院分区：
文献类型：
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作者：
M. Frost;B. Benesová;P. Sedlák
我们提出了一个三维本构模型的NiTi多晶形状记忆合金表现出三个固相（奥氏体，R相，马氏体）之间的转换。“完整的建模序列”包括制定建模假设，模型的建设，数学分析和数值实现和验证。也就是说，通过制定微观力学启发的建模假设，我们专注于描述的耗散机制：这种描述的一种改进形式，使我们的模型特别适用于复杂的加载路径。然后，我们将模型嵌入到所谓的能量框架（扩展到我们的情况），同时利用通过所谓的耗散距离描述耗散机制。我们证明了我们的模型的能量解的存在性向后欧拉计划。然后，这是实现到有限元软件，并与实验相比，数值模拟。
We present a three-dimensional constitutive model for NiTi polycrystalline shape memory alloys exhibiting transformations between three solid phases (austenite, R-phase, martensite). The ‘full modelling sequence’ comprised of formulation of modelling assumptions, construction of the model, mathematical analysis and numerical implementation and validation is presented. Namely, by formulating micromechanics-inspired modelling assumptions we concentrate on describing the dissipation mechanism: a refined form of this description makes our model especially useful for complex loading paths. We then embed the model into the so-called energetic framework (extended to our case) while taking advantage of describing the dissipation mechanism through the so-called dissipation distance. We prove the existence of energetic solutions to our model by a backward Euler scheme. This is then implemented into finite element software, and numerical simulations compared with experiments are also presented.