非均匀脆性介质损伤演化的一维准静态线性失稳及其发展

One-dimension damage evolution instability and its growth of heterogeneous brittle material under quasi-static loading

非均匀脆性介质的局部化转变及其发展是非均匀介质通向灾变破坏的一个重要途径,对于均匀场失稳及其发展的认识是理解局部化触发灾变破坏的根本。本文通过微扰分析方法,基于损伤演化方程,分析了非均匀脆性介质的均匀场在微小扰动下的线性失稳问题,指出一维弹脆性系统的损伤演化最大应力点后可能发生失稳。基于分区平均场近似和弹脆性模型分析了系统发生一部分加载另一部分卸载的非均匀演化问题,结果表明均匀场发生这种非均匀转变并继续发展的状态是可以存在的。而发生这种分叉失稳后,系统中出现部分弹性卸载和部分继续损伤的非均匀性会进一步发展和增强。

The uncertainty of both localization transition and its growth are a key factor leading to the uncertainty of catastrophic rupture.In this paper,instabilities in heterogeneous material are investigated for one-dimensional state under quasi-static loadings by using a perturbation approach.The interests of present paper focused in particular on the onset and growth of localization.The perturbation analysis indicated that the instability might be occur after peak stress point.Base on local-mean-field approximation and the elastic and statistical brittle（ESB） model,it is demonstrated that the state that one part unloads elastically but the other part is loaded could appear if the system is loaded by controlling the boundary displacement.Moreover,the localization would grow with loading.These results can help to understand the mechanism of localization evolution inducing catastrophic rupture.