On the Scaling of the Cubic-to-Tetragonal Phase Transformation with Displacement Boundary Conditions

IF 1.8 3区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

Journal of Elasticity Pub Date : 2024-07-02 DOI:10.1007/s10659-024-10075-8

Angkana Rüland, Antonio Tribuzio

引用次数: 0

Abstract

We provide (upper and lower) scaling bounds for a singular perturbation model for the cubic-to-tetragonal phase transformation with (partial) displacement boundary data. We illustrate that the order of lamination of the affine displacement data determines the complexity of the microstructure. As in (Rüland and Tribuzio in ESAIM Control Optim. Calc. Var. 29:68, 2023) we heavily exploit careful Fourier space localization methods in distinguishing between the different lamination orders in the data.

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关于带有位移边界条件的立方到四方相变的规模问题

我们为具有（部分）位移边界数据的立方到四方相变奇异扰动模型提供了（上、下）缩放边界。我们说明，仿射位移数据的层序决定了微观结构的复杂性。正如（Rüland 和 Tribuzio 在 ESAIM Control Optim. Calc. Var. 29:68, 2023 中）一样，我们在区分数据中的不同层序时大量利用了细致的傅立叶空间定位方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Elasticity 工程技术-材料科学：综合

CiteScore

3.70

自引率

15.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Elasticity was founded in 1971 by Marvin Stippes (1922-1979), with its main purpose being to report original and significant discoveries in elasticity. The Journal has broadened in scope over the years to include original contributions in the physical and mathematical science of solids. The areas of rational mechanics, mechanics of materials, including theories of soft materials, biomechanics, and engineering sciences that contribute to fundamental advancements in understanding and predicting the complex behavior of solids are particularly welcomed. The role of elasticity in all such behavior is well recognized and reporting significant discoveries in elasticity remains important to the Journal, as is its relation to thermal and mass transport, electromagnetism, and chemical reactions. Fundamental research that applies the concepts of physics and elements of applied mathematical science is of particular interest. Original research contributions will appear as either full research papers or research notes. Well-documented historical essays and reviews also are welcomed. Materials that will prove effective in teaching will appear as classroom notes. Computational and/or experimental investigations that emphasize relationships to the modeling of the novel physical behavior of solids at all scales are of interest. Guidance principles for content are to be found in the current interests of the Editorial Board.