论文标题
形状记忆合金中微观结构的几何线性弹性模型的能量缩放定律
Energy scaling laws for geometrically linear elasticity models for microstructures in shape memory alloys
论文作者
论文摘要
我们考虑在平面几何线性弹性的背景下进行奇异扰动的两孔问题，以模拟奥氏体基质中的矩形马氏体核。我们根据问题参数得出最小能量的缩放状态，该参数代表了核的{shape}，这两个阶段的弹性模量的商，表面能量常数和两个martensensitic变体的体积分数。我们确定了几种不同的缩放制度，这些缩放模式由参数中的指数或对数校正来区分，我们具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.
