主 办：爆炸科学与技术国家重点实验室
安全与防护协同创新中心
报告题目：源自教学的经典力学问题新探索
报告人：刘彬 教授
清华大学
时间：2020年10月21日上午10:00
报告人简介：
. 刘彬，男，清华大学工程力学系教授，主要从事固体力学的理论和计算研究，研究兴趣包括超大规模多尺度多物理场计算方法，断裂力学和复合材料力学。在国际期刊上共发表SCI论文130余篇，英文书章3篇。现为国际SCI期刊《International Journal of Plasticity》和《Journal of Computational and Theoretical Nanoscience》编委及《力学学报》副主编，曾获国家杰出青年科学基金，国家自然科学二等奖，中国力学学会青年科技奖，教育部新世纪人才计划，德国洪堡奖学金。
报告摘要：
Many materials are anisotropic. However, there is no widely accepted measure for characterizing the degree of elastic anisotropy. Here, assuming that the limiting case of extreme anisotropy should possess a positive semidefinite stiffness matrix, we propose three criteria to evaluate measures of anisotropy and show that the existing measures in the literature do not satisfy all of the proposed criteria.We then introduce a new measure of anisotropy based on the maximum strain energy ratio that is universally applicable to all material systems. The proposed measure is helpful for understanding the properties and behaviors of materials. Furthermore, this measure can be easily generalized to situations involving multiple fields and nonlinearity.
The J-integral based criterion is widely used in elastic-plastic fracture mechanics. However, it is not rigorously applicable when plastic unloading appears during crack propagation. One difficulty is that the energy density with plastic unloading in the J-integral cannot be defined unambiguously. In this paper, we alternatively start from the analysis on the power balance, and propose a surface-forming energy release rate (ERR), which represents the energy available for separating the crack surfaces during the crack propagation and excludes the loading-mode-dependent plastic dissipation. Therefore the surface-forming ERR based fracture criterion has wider applicability, including elastic-plastic crack propagation problems. Several formulae are derived for calculating the surface-forming ERR, and the definition of the energy density or work density is avoided. For any fracture behaviours, the surface-forming ERR is proven to be path-independent. The physical meanings and applicability of the proposed surface-forming ERR, the local ERR, the traditional global ERR, and J-integral are compared and discussed.
