Energy scaling laws for geometrically linear elasticity models for microstructures in shape memory alloys
Energy scaling laws for geometrically linear elasticity models for microstructures in shape memory alloys
复制标题
形状记忆合金微结构几何线弹性模型的能量标度定律
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
B. Zwicknagl
中科院分区：
文献类型：
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作者：
S. Conti;Johannes Diermeier;D. Melching;B. Zwicknagl
我们在平面几何线性弹性背景下考虑奇异摄动双井问题，以模拟奥氏体基体中的矩形马氏体核。我们根据问题参数推导了最小能量的标度范围，这些参数代表核的{形状}、两相弹性模量的商、表面能常数以及两种马氏体变体的体积分数。我们确定了几种不同的缩放机制，这些缩放机制可以通过参数中的指数或通过对数校正来区分，我们有匹配的上限和下限。
We consider a singularly-perturbed two-well problem in the context of planar geometrically linear elasticity to model a rectangular martensitic nucleus in an austenitic matrix. We derive the scaling regimes for the minimal energy in terms of the problem parameters, which represent the {shape} of the nucleus, the quotient of the elastic moduli of the two phases, the surface energy constant, and the volume fraction of the two martensitic variants. We identify several different scaling regimes, which are distinguished either by the exponents in the parameters, or by logarithmic corrections, for which we have matching upper and lower bounds.
影响因子：
3
作者：
H. Knüpfer;R. V. Kohn;F. Otto
通讯作者：
F. Otto