Implicit integration method of shape memory alloys constitutive model

Abstract

shape memory alloys, implicit stress integration, trial stress direction, large strain theory, governing parameter method Abstract. Shape memory alloys (SMA) material is widely used in many applications of interest where it is necessary to recover permanent strains. There are many constitutive models which describe that phenomenon. The SMA model described by Lagoudas in [1] and [2] is modified and implemented into the PAK software package [3]. Development of this model is motivated by previous papers of Lagoudas and Auricchio groups and it considers governing parameter method applied on phenomenological behavior of SMA materials. All variables are derived to depend on effective values of stress and strain and now we have only one scalar equation to solve in the integration point. Critical thermodynamic force is also modified to match new integration method. Integration is done for the deviatoric and mean stress using trial stress direction for each time step. Difference between the return mapping algorithm and the integration in the trial deviatoric stress direction can be neglected for nearly proportional loading [2]. The second case provide possibility to solve large strain problems in the similar manner, using the same constitutive model relations. One dimensional loaded examples of super-elasticity, shape memory and thermally induced phase transformation effect proposed by Lagoudas group are verified by modified governing parameter method using the PAK software. Several large strain examples are examined under uniaxial and non-proportional loading and the results are compared with the experimental results proposed in referenced papers.