Shakedown analysis of shape memory alloy structures

Feng, Xi‐Qiao; Sun, Qingping

doi:10.1016/j.ijplas.2006.04.001

Cited by 57 publications

(26 citation statements)

References 47 publications

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“…They used this solution technique in conjunction with finite element method for dynamic analysis of polycrystalline SMA rods. Feng and Sun [7] presented an algorithm for analyzing shakedown of SMA structures subjected to cyclic or varying loads. They used a plasticity framework and calculated a lower bound of loads for transformational shakedown of SMAs without the necessity of a step-by-step analysis along the loading history.…”

Section: Introductionmentioning

confidence: 99%

A semi-analytic analysis of shape memory alloy thick-walled cylinders under internal pressure

et al. 2010

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In this paper, a new method for analysis of the pseudoelastic response of shape memory alloy thickwalled cylinders subjected to internal pressure is proposed. Two cases of short and long cylinders are considered by assuming the plane stress and plane strain conditions. In each case, a three-dimensional phenomenological SMA constitutive model is simplified to obtain the corresponding two-dimensional constitutive relations. The cylinder is partitioned into a finite number of narrow annular regions, and appropriate assumptions are made in order to find a closed-form solution for the equilibrium equations in each annular region. The global solution is obtained by enforcing the stress continuity condition at the interface of the annular regions and imposing the boundary conditions. Several numerical examples are presented to demonstrate the efficiency of the proposed method, and the results are compared with three-dimensional finite element simulations.

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Section: Introductionmentioning

confidence: 99%

A semi-analytic analysis of shape memory alloy thick-walled cylinders under internal pressure

et al. 2010

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“…The obtained shakedown condition is merely a restriction on the local amplitude of the loading. We note that the obtained condition for shakedown is independent on the function f that appears in the free energy (5). Moreover, it can be observed that the proof detailed above does not require the function f to be convex.…”

Section: Static Shakedown Theoremmentioning

confidence: 70%

“…4 differ from those reported in [5]. Those differences are related to the limits of the approach used in [5], as described in [23].…”

Section: Case E T \ þmentioning

confidence: 80%

“…However, as discussed in detail in [23], some of the extensions proposed in the literature lead to non path-independent results which are therefore of little practical use. This is notably the case for shape memory alloys: shakedown of shape-memory alloys structures has been studied in [5], but the shakedown theorem obtained by those authors has latter been recognized in [23] not to be pathindependent.…”

Section: Introductionmentioning

confidence: 99%

“…4, 5 to study a three-bar truss originally considered in [5]. The results in [5] showed that phase-transformation can either increase of decrease the shakedown limit compared to plasticity. Those results, however, are biased by the fact that they are not path-independent.…”

Section: Introductionmentioning

confidence: 99%

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On shakedown of shape memory alloys structures

Peigney

2014

Ann. Solid Struct. Mech.

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International audienceThis paper is concerned with the large-time be-haviour of shape-memory alloys structures when they are submitted to a given loading history. Extending the approach introduced by Koiter in plasticity, we state sufficient condi-tions for the energy dissipation to remain bounded in time, independently on the initial state. Such a behavior is clas-sically referred to as shakedown and is associated with the idea that the evolution becomes elastic in the large-time limit. The study of a particular example shows that the large-time behaviour of shape-memory alloys structures exhibit some complex features which are not found in standard plasticity

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A time integration algorithm for a 3D constitutive model for SMAs including permanent inelasticity and degradation effects

Peigney

Scalet

Auricchio

2018

Numerical Meth Engineering

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Summary Components based on shape‐memory alloys are often subjected to several loading cycles that result in substantial alteration of material behavior. In such a framework, accurate models, as well as robust and efficient numerical approaches, become essential to allow for the simulation of complex devices. The present paper focuses on the numerical simulation of quasi‐static problems involving shape‐memory alloy structures or components subjected to multiple loading‐unloading cycles. A novel state‐update procedure for a three‐dimensional phenomenological model able to describe the saturation of permanent inelasticity, including degradation effects, is proposed here. The algorithm, being of the predictor‐corrector type and relying on an incremental energy minimization approach, is based on elastic checks, closed‐form solutions of polynomial equations, and nonlinear scalar equations solved through a combination of Newton‐Raphson and bisection methods. This allows for an easy implementation of model equations and to avoid the use of regularization parameters for the treatment of nonsmooth functions. Numerical results assess the good performances of the proposed approach in predicting both pseudoelastic and shape‐memory material behavior under cyclic loading as well as algorithm robustness.

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Shakedown analysis of shape memory alloy structures

Cited by 57 publications

References 47 publications

A semi-analytic analysis of shape memory alloy thick-walled cylinders under internal pressure

A semi-analytic analysis of shape memory alloy thick-walled cylinders under internal pressure

On shakedown of shape memory alloys structures

A time integration algorithm for a 3D constitutive model for SMAs including permanent inelasticity and degradation effects

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