Numerical simulation of martensitic phase transitions in shape memory alloys using an improved integration algorithm

The numerical simulation of structures made of shape memory materials is of increasing interest in different fields. Among others, the computation of pipe connectors or medical devices like endoscopic instruments and stents is a challenge. In such practical applications the pseudoelastic effect as well as the one‐way and two‐way shape memory effects are utilized. These material properties are caused by martensitic phase transitions between austenite and martensite. In the present contribution, a recently proposed constitutive theory is numerically treated in the context of the finite element method. This constitutive theory is formulated in the framework of continuum thermomechanics for geometrically linear problems and is able to represent the occurring martensitic phase transitions in shape memory alloys. For the numerical integration of the evolution equations, the backward Euler method is applied. In spite of the complexity of the constitutive theory, it is shown that an improved integration procedure can be formulated, which merely involves the solution of three non‐linear equations for three scalar‐valued unknown variables. Numerical examples show the capability of the proposed model and the improved integration algorithm. Copyright © 2006 John Wiley & Sons, Ltd.