Advanced Design of SMA Devices Through Finite Element Structural Analysis

Shape Memory Alloys (SMAs) and in particular NiTi are widely considered for large range of applications in various domains as biomechanics, aeronautics, automotive, civil engineering, etc… Design of such smart (adaptive) applications is mainly based on experimental analysis. In fact, most of commercial finite element codes did not offer a specific constitutive model for SMAs in their material standard databases despite the large progress made by research in this area. In fact, many interesting thermo-mechanical constitutive laws, well adapted to SMA behavior, were proposed by research groups in the world (among them Lexcellent’s group, Auricchio’s group, Patoor’s group, Lagoudas’s group, Moumni’s group …). These models are based either on micromechanical or on phenomenological approaches and well describe all the specificities of SMAs thermo-mechanical behavior (transformation and reorientation strains, hysteretic behavior, transformation saturation, internal loop, difference between tension and compression, coupling transformation – plasticity, …). These constitutive laws were successfully implemented in various commercial codes as Abaqus, Marc, Castem 2000, FemLab …, generally via user subroutines as UMAT for Abaqus. This allowed analyzing by finite element method the response of applications in SMAs (stents, endodontic file, micro-actuators, springs, connection systems, damping systems, …).

In this presentation, a global review of an example of a research activity illustrating these progresses in finite element based SMA application design will be developed. A family of macroscopic constitutive models based on micromechanical approach and considering macroscopic material parameters and internal variables will be detailed. Their implementation in the Abaqus finite element code via the subroutine UMAT will be then presented. Examples of patch-tests on SMA behavior and structure response will be showed with comparison to experimental results in order to prove the validity of the developed approach. The last part of the presentation will concern the application of the developed approach for the design of SMA based applications in various domains. Biomedical (endodontic file, stents, …), connection (tightening rings, fish plates for rails, …) and  micro-actuator examples will be developed by showing how finite element analysis contributes in the design of such applications.