The Discussion About the Identification of the Anand Model Parameters and Two Alternative Identification Methods

Abstract

Abstract The Anand model is a unified viscoplastic model, which is widely employed to describe the solder material deformation. The parameters in the Anand model for a certain material are usually identified by using the classical method based on two algebraic equations derived from the original differential equation of the Anand model. However, the second algebraic equation describing the relationship between the stress and inelastic strain is obtained with some terms about the unsteady value of internal variable neglected. But the effects induced by the omission of some unsteady terms on the effectiveness of classical method are not researched comprehensively. Therefore, in this paper, the effects of the omitted terms on the accuracy of the classical method are discussed. The inelastic deformation for the material which the second algebraic equation cannot describe due to the omission of unsteady terms is presented. The precondition for obtaining accurate results from the second algebraic equation is given out. Two criteria used to judge the effectiveness of the second algebraic equation are derived. To reduce the error related to the second algebraic equation of the classical method for some materials, two alternative identification methods are proposed. By combining the step of solving differential equation and genetic algorithm, the parameters in the Anand model originally identified by the second algebraic equation are determined in the processes of the two proposed methods. The effectiveness of the two alternative methods is presented by identifying the material Anand parameters where the classical method cannot be applied.