﻿ 可破碎颗粒体在动力载荷下的耗能特性
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 力学学报  2015, Vol. 47 Issue (2): 252-259  DOI: 10.6052/0459-1879-14-145 0

### 引用本文 [复制中英文]

[复制中文]
Qi Yuan, Huang Junjie, Chen Mingxiang. ENERGY DISSIPATION CHARACTERISTICS OF CRUSHABLE GRANULES UNDER DYNAMIC EXCITATIONS[J]. Chinese Journal of Ship Research, 2015, 47(2): 252-259. DOI: 10.6052/0459-1879-14-145.
[复制英文]

### 文章历史

2014-05-23 收稿
2014-07-12 录用
2014–09-17 网络版发表

1 基本原理

1.1 颗粒体连接键

 图 1 颗粒体代替单个颗粒示意图(红线表示接触键,蓝线表示平行键) Fig. 1 Schematic picture of the repalcement of single particle by cluster.(Red line stands for contact bond, and blue line stands for paralleled bond)

1.2 破碎率

 ${B_{\rm{r}}} = \frac{{{N_{{\rm{br}}}}}}{{{N_{{\rm{ini}}}}}}$ (1)

1.3 能量

 ${E_{\rm{b}}} = \sum\limits_{t = 0}^t {\sum\limits_{p = 1}^{{N_p}} {\rm{ }} } {m_p}g{\rm{d }}{u_p}{\rm{d }}t$ (2)

 ${E_w} = \sum\limits_{t = 0}^t {\sum\limits_{w = 1}^{{N_w}} {\left( {{f_w}{\rm{d}}{u_w} + {t_w}{\rm{d}}{\theta _w}} \right)} } {\rm{ d}}t$ (3)

 ${E_k} = \frac{1}{2}\sum\limits_{p = 1}^{{N_p}} {\left( {{m_p}\dot u_p^2 + {I_p}\omega _p^2} \right)}$ (4)

 ${E_{\rm{s}}} = \frac{1}{2}\sum\limits_{c = 1}^{{N_{\rm{c}}}} {\left( {\frac{{f_{\rm{n}}^2}}{{{k_{\rm{n}}}}} + \frac{{f_{\rm{t}}^2}}{{{k_{\rm{t}}}}}} \right)}$ (5)

 ${E_{\rm{f}}} = \sum\limits_{t = 0}^t {\sum\limits_{c = 1}^{{N_{\rm{c}}}} {{f_{\rm{t}}}d{u_{{\rm{slip}}}}{\rm{d}}} } t$ (6)

 ${E_{\rm{d}}} = \sum\limits_{t = 0}^t {\sum\limits_{c = 1}^{{N_{\rm{c}}}} {\left[{\left( {{c_{\rm{n}}}{{\mathop u\limits^. }_{\rm{n}}}} \right){\rm{d}}{u_{\rm{n}}} + \left( {{c_{\rm{t}}}{{\mathop u\limits^. }_{\rm{t}}}} \right){\rm{d}}{u_{\rm{t}}}} \right]} } {\rm{d}}t$ (7)

 ${E_{{\rm{pb}}}} = \frac{1}{2}\sum\limits_{c = 1}^{{N_{{\rm{pb}}}}} {\left( {\frac{{f_{{\rm{pbn}}}^2}}{{{A_{{\rm{pb}}}}{k_{{\rm{pbn}}}}}} + \frac{{f_{{\rm{pbt}}}^2}}{{{A_{{\rm{pb}}}}{k_{{\rm{pbt}}}}}} + \frac{{t_{{\rm{pb}}}^2}}{{{I_{{\rm{pb}}}}{k_{{\rm{pbn}}}}}}} \right)}$ (8)

 ${E_{{\rm{br}}}} = \sum\limits_{{c_{{\rm{br}}}} = 1}^{{c_{{\rm{br}}}}} {E_{{\rm{bp}}}^{\max }{\rm{d}}{c_{{\rm{br}}}}}$ (9)

 ${E_w} = {E_{\rm{b}}} + {E_k} + {E_{\rm{s}}} + {E_{\rm{f}}} + {E_{\rm{d}}} + {E_{{\rm{pb}}}} + {E_{{\rm{br}}}}$ (10)
2 数值颗粒微观参数及动力载荷参数选取

 图 2 样本示意图 Fig. 2 2D computational model

 $\left. \begin{array}{l} {{\dot u}_x}\left( t \right) = \frac{{{v_p}}}{2}\sin \left( {{\alpha _p}t} \right),0 \le t \le T\\ {{\dot u}_y}\left( t \right) = {v_p}\sin \left( {{\alpha _p}t + \pi } \right),0 \le t \le T \end{array} \right\}$ (11)

3 结果和讨论

3.1 颗粒体破碎及系统耗能

 图 3 颗粒体破碎情况随时间变化示意图: 由(a)到(d)加载时间分别为0,1/4,3/4,1个周期, (e)到(h)为相应红圈区域放大图(颗粒间有效连接键由红线表示) Fig. 3 The progress of cluster breakage: the loading time of the snippets from (a) to (d) are 0,1/4,3/4,1 period, respectively; and the snippets from (e) to (f) are the zooming pictures of the area circled with red lines, vskip -1mm respectively (The red lines indicate the effective contact bonds)

 图 4 系统破碎率(a) 与竖向应力分量(b) 随时间变化曲线 Fig. 4 The cluster breakage ratio (a) and the vertical stress component (b) time histories

 图 5 外界输入能量(a) 以及内部消耗能量(b) 随时间变化示意图 Fig. 5 Input (a) and consumed (b) energy time histories
3.2 破碎对系统耗能的影响

 图 6 不同连接键强度下系统能量各组成部分随时间的变化(由(a) 到(d) 连接键强度分别为1.5, 2.0, 3.0, 5.0 kN) Fig. 6 Energy components time histories of different contact bond values (The bond strengths from (a) to (d) are 1.5, 2.0, 3.0, 5.0 kN, respectively)

 图 7 外界累计最大输入能量时连接键强度对能量耗散率和破碎率的影响 Fig. 7 The influence of contact bond value on energy dissipation ratio and cluster breakage ratio
3.3 循环载荷下破碎率和系统耗能的变化

 图 8 循环载荷下破碎率随时间的变化 Fig. 8 Cluster breakage ratio time history under cyclic loading
4 结 论

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ENERGY DISSIPATION CHARACTERISTICS OF CRUSHABLE GRANULES UNDER DYNAMIC EXCITATIONS
Qi Yuan, Huang Junjie, Chen Mingxiang
Department of Mechanical Engineering, Wuhan University, Wuhan 430072, China
Fund: This project was supported by The Hubei Provincial Key Laboratory of Safety for Structural and Geotechnical Engineering (HBKLCIV201207), the Young Faculty Research Grant atWuhan University (2042014KF0007), and The National Key Basic Research Development Program (973 Program) sub-project (2014CB046902).
Abstract: Using the discrete element method (DEM) with cluster, different degrees of particle crushing by setting various contact bond thresholds under external dynamic excitation are implemented, and their energy dissipation characteristics are also discussed. Numerical results indicate that the particle breakage ratio has a great influence on the energy dissipation ratio which is defined as consumed energy to the input energy. As the particle breakage ratio rises, which intensify the friction and the collision between particles, the energy dissipation ratio increases. Besides, most cluster disintegration happens on the early stage of cyclic loading. Gradually, the breakage rate slows down, and the energy dissipation ratio reduces.
Key words: discrete element method    particle breakage    breakage ratio    energy dissipation