The exploration of nonlinear elasticity and its efficient parameterization for crystalline materials
The exploration of nonlinear elasticity and its efficient parameterization for crystalline materials
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DOI：
10.1016/j.jmps.2017.06.009
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发表时间：
2017-10
影响因子：
5.3
通讯作者：
John C. Thomas;Anton Van der Ven
中科院分区：
文献类型：
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作者：
John C. Thomas;Anton Van der Ven
分析固态相变过程中可能发生的非常大的相干应变的传统方法是在线性弹性中建立的，并且依赖于无穷小的应变度量。尽管如此，有许多技术上重要的例子，其中多相混合物的失配应变在其合成和/或应用期间非常大。在本文中，我们提出了一个框架，用于构建应变能表达式和应力应变关系超过线弹性极限的结晶固体。这种方法利用群论的概念，以最大限度地减少自由参数的应变能表达式和量的第一原理训练数据所需的参数化应变能模型是不变的所有晶体对称性。在这个框架内，应变能和弹性刚度可以被描述为高精度的一组传统的的自适应有限应变度量，我们定义独立的晶体对称性。作为一个例子，我们使用第一性原理的电子结构数据parameterized应变能多项式，并利用它们来探索的应变能表面的HCP锆和镁，以及几个重要的Zr-H和Mg-Nd相，是已知的沉淀连贯内的HCP矩阵的锆和镁。
Conventional approaches to analyzing the very large coherency strains that can occur during solid-state phase transformations are founded in linear elasticity and rely on infinitesimal strain metrics. Despite this, there are many technologically important examples where misfit strains of multi-phase mixtures are very large during their synthesis and/or application. In this paper, we present a framework for constructing strain-energy expressions and stress-strain relationships beyond the linear-elastic limit for crystalline solids. This approach utilizes group theoretical concepts to minimize both the number of free parameters in the strain-energy expression and amount of first-principles training data required to parameterize strain-energy models that are invariant to all crystal symmetries. Within this framework, the strain-energy and elastic stiffness can be described to high accuracy in terms of a set of conventional symmetry-adapted finite strain metrics that we define independent of crystal symmetry. As an illustration, we use first-principles electronic structure data to parameterize strain energy polynomials and employ them to explore the strain-energy surfaces of HCP Zr and Mg, as well as several important Zr-H and Mg-Nd phases that are known to precipitate coherently within the HCP matrices of Zr and Mg.