作为湿砂岩杆非线性共振响应中慢动力学机制的晶粒间缺陷的应变诱导动力学
Strain-induced kinetics of intergrain defects as the mechanism of slow dynamics in the nonlinear resonant response of humid sandstone bars
摘要：
提出了一种封闭形式的描述，解释砂岩杆纵向共振实验中表现出的非线性和慢动力学效应。随着纵向非线性位移的快速子系统，我们研究了应变依赖的慢子系统的破碎的晶粒间和层间的内聚键。我们表明，即使是最简单的，但现象学上正确的相互反馈的建模阐明了主要的实验结果典型的砂岩酒吧，即：（i）滞后行为的共振曲线上的上升和下降的斜坡，（ii）线性软化的共振频率的增加驱动水平，以及（iii）在样品被高应变调节后，在低动态应变下谐振频率的逐渐恢复（增加）。为了再现砂岩颗粒结构的高度非线性弹性特征，采用了一种真实的非微扰形式的应变势能。在我们的理论中，与实验观察到的峰值应变历史的记忆相关的慢动力学归因于应变引起的动力学变化的浓度破裂的晶粒间和层间的粘性债券造成的净滞后效应的弹性杨氏模量。最后，我们解释了如何增强滞后现象起源于平衡浓度的增加，是由于水饱和破裂的凝聚力债券。
英文摘要：
A closed-form description is proposed to explain nonlinear and slow dynamics effects exhibited by sandstone bars in longitudinal resonance experiments. Along with the fast subsystem of longitudinal nonlinear displacements we examine the strain-dependent slow subsystem of broken intergrain and interlamina cohesive bonds. We show that even the simplest but phenomenologically correct modelling of their mutual feedback elucidates the main experimental findings typical for forced longitudinal oscillations of sandstone bars, namely, (i) hysteretic behavior of a resonance curve on both its up- and down-slopes, (ii) linear softening of resonant frequency with increase of driving level, and (iii) gradual recovery (increase) of resonant frequency at low dynamical strains after the sample was conditioned by high strains. In order to reproduce the highly nonlinear elastic features of sandstone grained structure a realistic non-perturbative form of strain potential energy was adopted. In our theory slow dynamics associated with the experimentally observed memory of peak strain history is attributed to strain-induced kinetic changes in concentration of ruptured inter-grain and inter-lamina cohesive bonds causing a net hysteretic effect on the elastic Young's modulus. Finally, we explain how enhancement of hysteretic phenomena originates from an increase in equilibrium concentration of ruptured cohesive bonds that are due to water saturation.
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