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= cu・Q: Σ*= QT・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 σCpq=σBpq+DMσBpq, DσCpq=DσBpq was given. It is shown that Jaumann stress increments DJσpq is not recognized as an objectivity stress increment. Even in such an environment, there are some proposals that DJσpq should be replaced instead of Dσpq in constitutive equations. Then, the spin included in DJσpq gives stress a fluctuation depending on the induced spin, which was presented in this manuscript.

Keywords

• plasiticity
• spin
• spin tensor
• objectivity