各向异性载荷分配的离散断裂模型
Discrete Fracture Model with Anisotropic Load Sharing
摘要：
本文提出了一种用各向异性应力传递函数模拟单元间相互作用的二维断裂模型。各向异性的宏观性质的样品的影响是明确的，通过插值之间的几个极限情况下的负载分配。此外，临界应力和分布的破坏雪崩的数值得到的各向异性参数$α$的不同值和作为相互作用指数$γ$的函数。从数值结果中，可以肯定地得出结论，各向异性不会改变2D中的交叉点$γ_c=2$。因此，在无限系统尺寸的限制下，局部和全局负载分配之间的交叉值$γ_c=2$与各向同性情况下获得的交叉值相同。然而，在有限系统的情况下，对于$γ\le2$，全局载荷分配行为非常缓慢地接近。
英文摘要：
A two-dimensional fracture model where the interaction among elements is modeled by an anisotropic stress-transfer function is presented. The influence of anisotropy on the macroscopic properties of the samples is clarified, by interpolating between several limiting cases of load sharing. Furthermore, the critical stress and the distribution of failure avalanches are obtained numerically for different values of the anisotropy parameter $α$ and as a function of the interaction exponent $γ$. From numerical results, one can certainly conclude that the anisotropy does not change the crossover point $γ_c=2$ in 2D. Hence, in the limit of infinite system size, the crossover value $γ_c=2$ between local and global load sharing is the same as the one obtained in the isotropic case. In the case of finite systems, however, for $γ\le2$, the global load sharing behavior is approached very slowly.
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