せん断帯解析に見られる解析構造の矛盾点

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Shear banding is considered as localized necking where multiple solutions can exist on the necking plane comprising the boundary between the shear band and its surroundings. Therefore, shear banding is identical with localized necking though it is investigated under plane strain. On the necking plane the discontinuity of velocity gradient can be permitted. Hill and Hutchinson [J. Mech. Phys. Solids, 23 (1975), 239-264] investigated shear band without considering the discontinuity, but their method is methodically equivalent to that which takes into account the discontinuity. In previously published analyses of shear banding, it is assumed that the regions separated by the necking plane keep contact each other during the onset of shear banding, and the equilibrium of forces is maintained on the plane. However, it is proven that this assumption cannot provide useful information for determining the deformation when shear banding begins to occur. Furthermore, the assumption does not allow the formation of a common boundary condition imposed on both regions separated by the necking plane. When shear banding occurs, the spin rate of the regions differs because of multiple solutions. The criterion for determining the occurrence of shear banding can be deduced by imposing a rigid spin to make the spin rates identical. It is found that this criterion agrees with one of the universal criteria obtained from considering the occurrence of multiple solutions under the common boundary condition on the surface of a body.
一般社団法人日本機械学会の論文
1997-09-25

せん断帯解析に見られる解析構造の矛盾点

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