Lerner Edan
Institute for Theoretical Physics, Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, the Netherlands.
Phys Rev E. 2016 May;93(5):053004. doi: 10.1103/PhysRevE.93.053004. Epub 2016 May 16.
Nonlinear plastic modes (NPMs) are collective displacements that are indicative of imminent plastic instabilities in elastic solids. In this work we formulate the atomistic theory that describes the reversible evolution of NPMs and their associated stiffnesses under external deformations. The deformation dynamics of NPMs is compared to those of the analogous observables derived from atomistic linear elastic theory, namely, destabilizing eigenmodes of the dynamical matrix and their associated eigenvalues. The key result we present and explain is that the dynamics of NPMs and of destabilizing eigenmodes under external deformations follow different scaling laws with respect to the proximity to imminent instabilities. In particular, destabilizing modes vary with a singular rate, whereas NPMs exhibit no such singularity. As a result, NPMs converge much earlier than destabilizing eigenmodes to their common final form at plastic instabilities. This dynamical difference between NPMs and linear destabilizing eigenmodes underlines the usefulness of NPMs for predicting the locus and geometry of plastic instabilities, compared to their linear-elastic counterparts.
非线性塑性模式（NPMs）是集体位移，它表明弹性固体中即将发生塑性失稳。在这项工作中，我们阐述了原子理论，该理论描述了NPMs及其相关刚度在外部变形下的可逆演化。将NPMs的变形动力学与从原子线性弹性理论导出的类似可观测量的变形动力学进行比较，即动力学矩阵的失稳本征模式及其相关特征值。我们给出并解释的关键结果是，NPMs和失稳本征模式在外部变形下的动力学，相对于接近即将发生的失稳情况遵循不同的标度律。特别是，失稳模式以奇异速率变化，而NPMs没有这种奇异性。因此，在塑性失稳时，NPMs比失稳本征模式更早收敛到它们的共同最终形式。与线性弹性对应物相比，NPMs和线性失稳本征模式之间的这种动力学差异突出了NPMs在预测塑性失稳的位置和几何形状方面的有用性。
