縞状滑り線発生荷重の確率変動理論

Abstract

This paper presents a theory on the imperfect bifurcation behavior at the emergence of parallel shear bands on uniform materials, and that of the statistical variation of the strength of these materials which often is governed by this emergence. It is shown by means of the group-theoretic bifurcation theory that the emergence can be explained as a symmetry-breaking bifurcation if the underlying symmetry is exploited to model the local uniformity of materials. The mechanism of the stochastic variation of uniform materials can be modeled in the theory of bifurcation by ascribing such variation to the stochastic variation of initial imperfections among them, which turns into the variation of the strength through imperfect bifurcation. Further, with these imperfections modeled to be normally-distributed multi-variate random variables, the probability density functions of the critical load (strength) are derived.