Modeling, Characterization and Design of Dense and Architectured Iron-based Shape Memory Alloys

  • Cheikh Cisse

Student thesis: Doctoral Thesis


Shape memory alloys (SMAs) stand out from common metals due to their capability to sustain and recover large inelastic strain by undergoing a reversible transformation between a parent phase called autenite and a product phase called martensite. The martensitic transformation can proceed by various mechanisms including shape memory effect (SME) and pseudoelasticity (PE). Recent work on iron-based shape memory alloys (Fe-SMAs) point out a SME strain of up to 7.6% [1] and a PE strain of up to 13% [2]. These low-cost Fe-SMAs are very attractive due to their capability to dissipate large amount of energy per unit weight thorough phase transformation, transformation-induced plasticity and plastic slip. This intrinsic ability of the material can be exploited better at the structural level by designing architectured periodic lattice structures with controllable properties in order to achieve maximum specific dissipation. The design of these materials by means of numerical simulation requires the development of accurate constitutive models for both monolithic and architectured cellular Fe-SMAs, which can be utilized for finite element analysis of structures. This thesis proposes 3D nonlinear constitutive models for dense and architectured cellular Fe-SMAs. The models are developed within the framework of generalized standard materials, considering different thermomechanical properties between austenite and martensite. The coupling effects between transformation and plasticity are accounted for through new interaction energy potential and evolution equations. The models are implemented in ABAQUS via a user-defined subroutine using an implicit time-discrete integration scheme based on a 'multisurface plasticity'-like return mapping algorithm. The validated dense model shows much higher accuracy than the rarely existing ones. Finite element analyses of complex boundary value problems involving material nonlinearity, geometric nonlinearity and interaction nonlinearity, with heterogeneous stress distribution and strain singularity. For computationally efficient simulations of architectured cellular Fe-SMAs, a pressure-dependent effective model (PDEM) is derived. The parameters and input data of the PDEM are obtained by running a Python script to have the volume-averaged output data of various unit cells simulated with the dense model. The numerical simulations using the PDEM provide pioneering results for architectured cellular Fe-SMAs with a high level of accuracy as using the dense model along with actual hollow material. The two constitutive models and their implementation constitute a powerful computer assisted design environment that will help reduce the design cycles and production costs of Fe-SMA devices. These design tools will enable rapid exploration of various configurations, which will allow to test suitable combinations that can be subsequently refined conveniently.
Date of AwardDec 2017
Original languageAmerican English
SupervisorWael Zaki (Supervisor)


  • iron-based shape memory alloys
  • architectured cellular materials
  • plasticity
  • constitutive modeling
  • finite element method.

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