通常材料在不同載荷下，其失穩應力和失穩模式并不相同。比如，材料在靜水壓作用下，其失穩壓強可以達到100 GPa左右，而在單純剪切下，材料在很低的應力載荷下（通常在100~200 MPa）產生失穩剪切變形。傳統的材料失穩準則例如最大剪切應力（Tresca準則）或者能量準則（von Mises準則）只能描述材料的塑性失穩變形，并不能描述材料的相變失穩。因此需要構建任意載荷下材料失穩的連續介質模型，為材料的失效分析提供理論支持，為材料強度的精準設計提供理論指導。

來自華東理工大學的陳浩講師和其博士導師美國愛荷華州立大學航空航天工程和機械工程系的Valery I. Levitas教授團隊，以及材料學院的Duane D. Johnson教授團隊合作，采用第一性原理計算得到了單晶硅材料在任意載荷下的失穩應力，擬合了提出的大變形彈性理論，發現該彈性理論可以精確給出硅材料任意載荷下的失穩應力。該研究為在連續介質框架下研究精確模擬材料在任意載荷下的失穩條件提供了理論基礎，由于不同載荷可以導致不同的失穩模式，比如剪切應力下發生塑性變形，而在正應力下發生相變。因此該模型為連續介質力學提供了模擬任意載荷下導致不同失效模式的可能性。 該文近期發表于npj Computational Materials6:115 (2020)，英文標題與摘要如下。

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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原文標題：npj: 材料任意載荷下失穩條件—從第一性原理到連續介質力學

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