通常材料在不同載荷下，其失穩(wěn)應(yīng)力和失穩(wěn)模式并不相同。比如，材料在靜水壓作用下，其失穩(wěn)壓強(qiáng)可以達(dá)到100 GPa左右，而在單純剪切下，材料在很低的應(yīng)力載荷下（通常在100~200 MPa）產(chǎn)生失穩(wěn)剪切變形。傳統(tǒng)的材料失穩(wěn)準(zhǔn)則例如最大剪切應(yīng)力（Tresca準(zhǔn)則）或者能量準(zhǔn)則（von Mises準(zhǔn)則）只能描述材料的塑性失穩(wěn)變形，并不能描述材料的相變失穩(wěn)。因此需要構(gòu)建任意載荷下材料失穩(wěn)的連續(xù)介質(zhì)模型，為材料的失效分析提供理論支持，為材料強(qiáng)度的精準(zhǔn)設(shè)計(jì)提供理論指導(dǎo)。

來(lái)自華東理工大學(xué)的陳浩講師和其博士導(dǎo)師美國(guó)愛(ài)荷華州立大學(xué)航空航天工程和機(jī)械工程系的Valery I. Levitas教授團(tuán)隊(duì)，以及材料學(xué)院的Duane D. Johnson教授團(tuán)隊(duì)合作，采用第一性原理計(jì)算得到了單晶硅材料在任意載荷下的失穩(wěn)應(yīng)力，擬合了提出的大變形彈性理論，發(fā)現(xiàn)該彈性理論可以精確給出硅材料任意載荷下的失穩(wěn)應(yīng)力。該研究為在連續(xù)介質(zhì)框架下研究精確模擬材料在任意載荷下的失穩(wěn)條件提供了理論基礎(chǔ)，由于不同載荷可以導(dǎo)致不同的失穩(wěn)模式，比如剪切應(yīng)力下發(fā)生塑性變形，而在正應(yīng)力下發(fā)生相變。因此該模型為連續(xù)介質(zhì)力學(xué)提供了模擬任意載荷下導(dǎo)致不同失效模式的可能性。 該文近期發(fā)表于npj Computational Materials6:115 (2020)，英文標(biāo)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.

責(zé)任編輯：xj

原文標(biāo)題：npj: 材料任意載荷下失穩(wěn)條件—從第一性原理到連續(xù)介質(zhì)力學(xué)

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