固有状態と多価条件の関連

概要

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Hill reformulates classical specification of plastic response in metal by introducing generalized variables, where the measures of stress are sets of the loading magnitudes, and the measures of strain rate are generated by work-conjugacy. The work hardening h_G in generalized variable is constructed in association with the original one. Eigenstates are defined as the state where h_G vanishes and they involve the state of simultaneous stationarity of generalized stress. The eigenstates are classified into latent eigenstate and active one. In the former the generalized stress rate vector is perpendicular to the normal of yield surface in generalized stress space, and the latter is named for the simultaneous stationarity of generalized stress. However, the eigenstates are given a priori without any explanation relevant to multiplicity. Therefore, doubt remains whether they satisfy solution multiplicity or not. Then, in this paper the doubt is examined from the view point of solution multiplicity. It is found that the latent eigenstate cannot satisfy the multiplicity criterion except for the case where the nominal stress is used as the generalized stress. Furthermore, in general, the active eigenstate cannot be realized. We propose here load instability instead of the active eigenstate.
一般社団法人日本機械学会の論文
1999-04-25