Sarmah Ritupan, Ananthakrishna G
Materials Research Centre, Indian Institute of Science, Bangalore 560012, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 2):056208. doi: 10.1103/PhysRevE.86.056208. Epub 2012 Nov 13.
We investigate the possibility of projecting low-dimensional chaos from spatiotemporal dynamics of a model for a kind of plastic instability observed under constant strain rate deformation conditions. We first discuss the relationship between the spatiotemporal patterns of the model reflected in the nature of dislocation bands and the nature of stress serrations. We show that at low applied strain rates, there is a one-to-one correspondence with the randomly nucleated isolated bursts of mobile dislocation density and the stress drops. We then show that the model equations are spatiotemporally chaotic by demonstrating the number of positive Lyapunov exponents and Lyapunov dimension scale with the system size at low and high strain rates. Using a modified algorithm for calculating correlation dimension density, we show that the stress-strain signals at low applied strain rates corresponding to spatially uncorrelated dislocation bands exhibit features of low-dimensional chaos. This is made quantitative by demonstrating that the model equations can be approximately reduced to space-independent model equations for the average dislocation densities, which is known to be low-dimensionally chaotic. However, the scaling regime for the correlation dimension shrinks with increasing applied strain rate due to increasing propensity for propagation of the dislocation bands.
我们研究了从一种在恒定应变速率变形条件下观察到的塑性失稳模型的时空动力学中投影低维混沌的可能性。我们首先讨论了在位错带性质中反映出的模型时空模式与应力锯齿性质之间的关系。我们表明，在低施加应变速率下，随机成核的移动位错密度的孤立突发与应力下降之间存在一一对应关系。然后，我们通过展示在低应变速率和高应变速率下正李雅普诺夫指数的数量和李雅普诺夫维数随系统大小的变化，表明模型方程是时空混沌的。使用一种改进的算法来计算关联维数密度，我们表明在低施加应变速率下对应于空间不相关位错带的应力 - 应变信号呈现出低维混沌的特征。通过证明模型方程可以近似简化为平均位错密度的与空间无关的模型方程（已知该方程是低维混沌的），这一点得到了量化。然而，由于位错带传播倾向的增加，关联维数的标度范围随着施加应变速率的增加而缩小。
