A study on determination of application limits of bimodulus calculation using spherical stress tensor method

Abstract

For materials with different moduli in tension and compression, according to the features of spherical stress tensor, the new method (spherical stress tensor method (SSTM)) by judging the sign of the mean stress to determine elasticity modulus in tension or compression was put forward. Based on ANSYS, the analysis and calculation module of bimodulus materials were developed. In order to determine the application limits of spherical stress tensor method for plane stress state, referring to constitutive relation of Ambartsumyan, it could be improved by SSTM and the new constitutive model was obtained. It was set up that the relative error of principal strain between the new and Ambartsumyan model was less than 10%. Finally, the application limits of SSTM in plane stress problems are obtained by taking the relative error limits of principal strain as a judgment rule. The application limits for this method have certain limitations, but their advantage is that the flexibility matrix is not forced to be symmetric.