基于一类非局部宏-微观损伤模型的裂纹模拟

结合近场动力学和统一相场理论的基本思想, 最近提出了一类非局部宏-微观损伤模型, 为固体裂纹扩展模拟提供了新途径. 本文在此基础上改进了微观损伤准则, 并给出损伤的$\bar{\lambda}-\ell$语言以刻画固体破坏过程中位移场的不连续程度. 在改进模型中, 首先根据两物质点(即物质点对)之间的变形量, 基于相对临界伸长量的历史最大超越程度, 给出表征物质键性能退化的微细观损伤. 进而, 对影响域内的物质键损伤进行空间局部加权平均, 获得宏观拓扑损伤. 通过引入能量退化函数, 建立基于能量的损伤与宏观拓扑损伤之间的关系, 由此将其嵌入连续损伤力学基本框架, 形成了问题求解的基本方程. 该模型是一类非局部化模型, 可采用有限单元法进行离散求解, 避免了经典局部损伤力学所面临的网格敏感性问题. 文中, 进一步将其应用于具有强非线性回弹特性的裂纹扩展模拟问题. 实例分析表明, 本文方法不仅可以把握裂纹扩展模式, 而且能够定量刻画裂纹扩展过程中的载荷-变形关系. 最后指出了需要进一步研究的问题. 

CRACKING SIMULATION BASED ON A NONLOCAL MACRO-MESO-SCALE DAMAGE MODEL1)

Inspired by peridynamics and the unified phase-field model, a new nonlocal macro-meso-scale consistent damage model has been proposed recently, which provides a new method for the numerical simulation of crack propagation. In the present paper, the criterion for meso-scale damage in this model is modified, and a $\bar{\lambda}-\ell $ damage language is proposed to depict the displacement discontinuity in a cracked solid. In the modified model, the meso-scale damage characterizing the performance degradation of bond between two material points (namely a material point pair), is firstly determined according to the maximum exceedance of deformation of the point pair in terms of the critical elongation quantity during loading history. Then, by the weighted averaging over the meso-scale damage of material point pairs in the influence domain, the macro-scale topologic damage is obtained. Further, by advocating the energetic degradation function, the energy-based damage can be connected to the topologic damage, and in turn can be inserted into the framework of continuum damage mechanics such that governing equations are readily established. The proposed method is a nonlocal model, and it can be numerically implemented by the finite element discretization, where the problem of mesh size sensitivity that occurs in the classical continuum damage mechanics model is circumvented. The modified model is applied to crack modeling problems involving strong nonlinear snap-back property. Examples are studied, showing that the proposed method can not only characterize the crack patterns, but also capture quantitatively the load-deformation curves. The problems to be studied in the future are also discussed.