(a)加权平均后的结点失效方向
(a)Node failure direction afterweighted average
(b)单元内断裂
(b)Rupture in elements
(c) 单元间断裂
(c)Rupture between elements
图2 裂纹生成方式
Fig.2Crack formation way
当裂纹被引入之后，单元的损伤状态变量由于裂纹的形成而被恢复为初始值。理想的情况是只有垂直于裂纹的方向上的单元损伤被恢复为零，但是若有网格更新而生成了额外的新单元，则所有失效单元的状态变量全部初始化为零。
3 数值算例
假设冲击物为准脆性材料，被冲击物强度很高，冲击速度100m/s，计算模型的各项参数如表1所示，图3(a)给出计算用初始的网格剖分。图3(b)-(f)给出了准脆性材料冲击物裂纹开始产生及扩展的过程。由图可见，裂纹从接触处开始产生，随着时步的增加，裂纹扩展，由小的裂纹慢慢扩展成大的裂缝，接下来会有离散子块产生。
表1 准脆性材料冲击模型参数
|
|
ρ（kg/m3）
密度
|
E(GPa)
弹性模量
|
Ν
泊松比
|
ft(MPa)
抗拉强度
|
Gf(J/m2)
断裂能
|
p0
罚系数
|
|
冲击物
|
2340
|
26
|
0.18
|
3.15
|
3.0e+2
|
10e+9
|
|
被冲击物
|
3.0e+4
|
210
|
0.3
|
1.0e+14
|
3.0e+12
|
10e+9
|
the parameters of quasibrittle material impact model
table1 
(a) (b)
 
(c)(d)
 
(e)(f)
图3 准脆性冲击问题裂纹产生及扩展图
Fig3 cracking and extension figures of quasi brittle material impact problem
(a)初始网格剖分 (b)裂纹开始产生(c)裂纹扩展 (d)- (f)开始产生较大的裂缝
(a) Initial mesh (b) Began to crack (c)crack propagation (d)-(f) Began to produce larger crack
4 结论
基于有限元动力问题中心差分算法，给出用于模拟冲击载荷作用下准脆性连续体多重破裂问题的可离散有限元法，针对准脆性材料的结构可以分裂、破碎的特点，建议采用不建立刚度矩阵的中心差分法求解。在准脆性材料只产生裂纹但没有达到破碎分离和不研究二次破碎问题时，线性小变形理论也还是可以采用的。但是为了描述分离子块的运动、碰撞及二次破碎问题，由于小块一般均有大位移、大转动，应该采用有限变形理论。由数值计算，我们发觉裂纹的发生、发展以及破裂现象对网格剖分是敏感的，但是只要网格剖分的足够密，裂纹的的发展趋势大致相同。
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