On the essential concept of objectivity in plasticity analysis

Abstract

For judging whether two stresses maintain objectivity between different frames, appropriate criterion needs to be used. The criterion, c^*_u= c_u・Q: Σ^*= Q^T・Σ・Q has been normally used, but it was found that it did not have the ability to judge the essence of objectivity. Getting over the deadlock for judging quality of objectivity, the comparison of stress values is indispensable between frames under an identical stress tensor. As a result of examining the difference of stress values, the essential criterion for objectivity σ^C_pq=σ^B_pq+D^Mσ^B_pq, Dσ^C_pq=Dσ^B_pq was given. It is shown that Jaumann stress increments D^Jσ_pq is not recognized as an objectivity stress increment. Even in such an environment, there are some proposals that D^Jσ_pq should be replaced instead of Dσ_pq in constitutive equations. Then, the spin included in D^Jσ_pq gives stress a fluctuation depending on the induced spin, which was presented in this manuscript.