npj: 单晶硅材料在任意载荷下的失稳应力

通常材料在不同载荷下，其失稳应力和失稳模式并不相同。比如，材料在静水压作用下，其失稳压强可以达到100 GPa左右，而在单纯剪切下，材料在很低的应力载荷下（通常在100~200 MPa）产生失稳剪切变形。传统的材料失稳准则例如最大剪切应力（Tresca准则）或者能量准则（von Mises准则）只能描述材料的塑性失稳变形，并不能描述材料的相变失稳。因此需要构建任意载荷下材料失稳的连续介质模型，为材料的失效分析提供理论支持，为材料强度的精准设计提供理论指导。

来自华东理工大学的陈浩讲师和其博士导师美国爱荷华州立大学航空航天工程和机械工程系的Valery I. Levitas教授团队，以及材料学院的Duane D. Johnson教授团队合作，采用第一性原理计算得到了单晶硅材料在任意载荷下的失稳应力，拟合了提出的大变形弹性理论，发现该弹性理论可以精确给出硅材料任意载荷下的失稳应力。该研究为在连续介质框架下研究精确模拟材料在任意载荷下的失稳条件提供了理论基础，由于不同载荷可以导致不同的失稳模式，比如剪切应力下发生塑性变形，而在正应力下发生相变。因此该模型为连续介质力学提供了模拟任意载荷下导致不同失效模式的可能性。   该文近期发表于npj Computational Materials 6: 115 (2020)，英文标题与摘要如下。  

Fifth-degree elastic energy for predictive continuum stress-strain relations and elastic instabilities under large strain and complex loading in silicon

Hao Chen, Nikolai A. Zarkevich, Valery I. Levitas, Duane D. Johnson & Xiancheng Zhang 

Materials under complex loading develop large strains and often phase transformation via an elastic instability, as observed in both simple and complex systems. Here, we represent a material (exemplified for Si I) under large Lagrangian strains within a continuum description by a 5^th-order elastic energy found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress-Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including the elastic instability driving the Si I→II phase transformation (PT) and the shear instabilities. PT conditions for Si I →II under action of cubic axial stresses are linear in Cauchy stresses in agreement with DFT predictions. Such continuum elastic energy permits study of elastic instabilities and orientational dependence leading to different PTs, slip, twinning, or fracture, providing a fundamental basis for continuum physics simulations of crystal behavior under extreme loading.

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原文标题：npj: 材料任意载荷下失稳条件—从第一性原理到连续介质力学

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