An inquiry into the spin of a deforming body.

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  • スピンについての一考察
  • スピン ニ ツイテ ノ イチコウサツ

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Abstract

The conventional form of constitutive equations of solids is substantially and critically studied with the motivation that the τ-γ relation of a kinematically hardening plastic body subjected to simple shearing was found recently to be in the shape of a sine-curve in the range of large strain. It is concluded that the rate-type constitutive equation should take the form Σ^^(▽)=D^^:Γ^^(▽), and not the conventional form Σ^^(◯)=D^^:Γ, where Σ=stress, Γ=strain, super-▽ denotes the objective rate and super-◯ denotes the Jaumann-rate. The objective rates should be those with the spins of the principal axes of the corresponding physical quantities, not with the continuum spin ωc=(1/2)(L-LT), as in the Jaumann rate. Several other fundamental and important propositions are presented.

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