On the calculation of energy-minimizing phase fractions in shape memory alloys
On the calculation of energy-minimizing phase fractions in shape memory alloys
复制标题
形状记忆合金能量最小化相分数的计算
DOI：
10.1016/j.cma.2007.01.001
复制
发表时间：
2007
影响因子：
7.2
通讯作者：
K. Hackl
中科院分区：
文献类型：
--
作者：
R. Heinen;K. Hackl
多相材料（如形状记忆合金）的建模通常会导致非准凸能量。这样的公式会引起微观结构的发展，因此不适合立即计算材料的行为。为了避免这个问题，许多模型使用凸Reuß下界作为松弛自由能的估计。为了评价这一估计的质量，最近的文献通过分层构造了上界，在许多例子中上界和下界有很小的差异。在这项工作中，我们比较了关于能量最优相分数的层压上界和凸化下界，以及两种方法产生的全局最小能量和总应力。讨论了两种边界下所得结果的异同。
Modeling of multi-phase materials such as shape memory alloys usually leads to non-quasi-convex energies. Such formulations give rise to the development of microstructure and are therefore not suitable for immediate computation of the material behavior. To circumvent this problem, many models make use of the convex Reuß lower bound as an estimate of the relaxed free energy. To evaluate the quality of this estimate, upper bounds have been constructed by lamination in recent literature showing a small difference of upper and lower bounds in many examples. In this work, we compare upper bounds by lamination and lower bounds by convexification regarding the energy-optimal phase fractions as well as the globally minimized energies and the overall stresses resulting from the two approaches. Similarities and differences of the results obtained with both bounds are discussed.