Hao Shengwang, Yang Hang, Liang Xiangzhou
School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao 066004, China.
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Science, Beijing 100190, China.
Materials (Basel). 2017 May 9;10(5):515. doi: 10.3390/ma10050515.
This paper presents a spring-fiber bundle model used to describe the failure process induced by energy release in heterogeneous materials. The conditions that induce catastrophic failure are determined by geometric conditions and energy equilibrium. It is revealed that the relative rates of deformation of, and damage to the fiber bundle with respect to the boundary controlling displacement ₀ exhibit universal power law behavior near the catastrophic point, with a critical exponent of -1/2. The proportion of the rate of response with respect to acceleration exhibits a linear relationship with increasing displacement in the vicinity of the catastrophic point. This allows for the prediction of catastrophic failure immediately prior to failure by extrapolating the trajectory of this relationship as it asymptotes to zero. Monte Carlo simulations are completed and these two critical scaling laws are confirmed.
本文提出了一种弹簧纤维束模型，用于描述非均质材料中能量释放引起的破坏过程。引发灾难性破坏的条件由几何条件和能量平衡决定。研究表明，纤维束相对于边界控制位移₀的变形和损伤相对速率在灾难性点附近呈现普遍的幂律行为，临界指数为-1/2。响应速率相对于加速度的比例在灾难性点附近随位移增加呈现线性关系。这使得通过外推该关系趋近于零的轨迹，能够在破坏即将发生之前预测灾难性破坏。完成了蒙特卡罗模拟并证实了这两个临界标度律。
