Dasgupta Ratul, Hentschel H George E, Procaccia Itamar
Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Feb;87(2):022810. doi: 10.1103/PhysRevE.87.022810. Epub 2013 Feb 19.
In recent research it was found that the fundamental shear-localizing instability of amorphous solids under external strain, which eventually results in a shear band and failure, consists of a highly correlated array of Eshelby quadrupoles all having the same orientation and some density ρ. In this paper we calculate analytically the energy E(ρ,γ) associated with such highly correlated structures as a function of the density ρ and the external strain γ. We show that for strains smaller than a characteristic strain γ(Y) the total strain energy initially increases as the quadrupole density increases, but that for strains larger than γ(Y) the energy monotonically decreases with quadrupole density. We identify γ(Y) as the yield strain. Its value, derived from values of the qudrupole strength based on the atomistic model, agrees with that from the computed stress-strain curves and broadly with experimental results.
在最近的研究中发现，非晶态固体在外部应变下的基本剪切局部化不稳定性最终会导致剪切带和破坏，它由一系列高度相关的埃舍尔比四极子组成，所有四极子都具有相同的取向和一定的密度ρ。在本文中，我们解析计算了与这种高度相关结构相关的能量E(ρ,γ)，它是密度ρ和外部应变γ的函数。我们表明，对于小于特征应变γ(Y)的应变，总应变能最初随着四极子密度的增加而增加，但对于大于γ(Y)的应变，能量随四极子密度单调递减。我们将γ(Y)确定为屈服应变。其值基于原子模型从四极子强度值推导得出，与计算得到的应力-应变曲线的值一致，并且与实验结果大致相符。
