&lt;title&gt;Coupled thermomechanical simulation of shape memory alloys&lt;/title&gt;

Panahandeh, M.; Kasper, Eric P.

doi:10.1117/12.276565

Cited by 4 publications

(2 citation statements)

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“…The second trial stress is used to distinguish the elastic state at the end of the phase transformation. This will be explained further in the section on the implementation of the algorithms in Appendix I. Panahandeh and Kasper [27] presented a general formulation for coupled thermomechanical simulation of shape memory alloys in the context of ÿnite element method. They proposed a SMA constitutive model composed of a set of non-linear algebraic equations that did not require integration of a rate type evolution equation.…”

Section: Introductionmentioning

confidence: 99%

Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms

Qidwai¹,

Lagoudas²

2000

Int. J. Numer. Meth. Engng.

276

247

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SUMMARYPrevious studies by the authors and their co-workers show that the structure of equations representing shape Memory Alloy (SMA) constitutive behaviour can be very similar to those of rate-independent plasticity models. For example, the Boyd-Lagoudas polynomial hardening model has a stress-elastic strain constitutive relation that includes the transformation strain as an internal state variable, a transformation function determining the onset of phase transformation, and an evolution equation for the transformation strain. Such a structure allows techniques used in rate-independent elastoplastic behaviour to be directly applicable to SMAs. In this paper, a comprehensive study on the numerical implementation of SMA thermomechanical constitutive response using return mapping (elastic predictor-transformation corrector) algorithms is presented. The closest point projection return mapping algorithm which is an implicit scheme is given special attention together with the convex cutting plane return mapping algorithm, an explicit scheme already presented in an earlier work. The closest point algorithm involves relatively large number of tensorial operations than the cutting plane algorithm besides the evaluation of the gradient of the transformation tensor in the ow rule and the inversion of the algorithmic tangent tensor. A uniÿed thermomechanical constitutive model, which does not take into account reorientation of martensitic variants but uniÿes several of the existing SMA constitutive models, is used for implementation. Remarks on numerical accuracy of both algorithms are given, and it is concluded that both algorithms are applicable for this class of SMA constitutive models and preference can only be given based on the computational cost.

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Section: Introductionmentioning

confidence: 99%

Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms

Qidwai¹,

Lagoudas²

2000

Int. J. Numer. Meth. Engng.

276

247

View full text Add to dashboard Cite

show abstract

“…Many simulations of SMA structures and devices reported in the literature (see e.g. Liang and Rogers, 1990;Baz et al, 1990;Lagoudas and Tadjbakhsh, 1993;Birman, 1997;Panahandeh and Kasper, 1997;Gillet et al, 1998) involve strength of materials analysis of different structural SMA members (e.g. wires, rods, beams, springs), Finite Element Method (FEM) simulations of truss elements, specialized FEM beam elements, etc.…”

Section: Some Applications Of Sma Constitutive Models Using Numericalmentioning

confidence: 99%