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.
修改评论