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Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik × Subject: shape memory alloys ×

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Now showing 1 - 3 of 3
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    A molecular dynamics view of hysteresis and functional fatigue in martensitic transformations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Kastner, Oliver; Ackland, Graeme J.; Eggeler, Gunther; Weiss, Wolf
    Shape memory alloys (SMA) exhibit a number of features which are not easily explained by equilibrium thermodynamics, including hysteresis in the phase transformation and ?reverse? shape memory in the high symmetry phase. Processing can change these features: repeated cycling can ?train? the reverse shape memory effect, while changing the amount of hysteresis and other functional properties. These effects are likely to be due to creation of persistent localised defects, which are impossible to study using non-atomistic methods. Here we present a molecular dynamics simulation study of this behaviour. To ensure the largest possible system size, we use a two dimensional binary Lennard-Jones model, which represents a reliable qualitative model system for martensite/austenite transformations. The evolution of the defect structure and its excess energy is investigated in simulations of cyclic transformation/ reverse transformation processes with 160,000 atoms. The simulations show that the transformation proceeds by non-diffusive nucleation and growth processes and produces distinct microstructure. Upon transformation, lattice defects are generated which affect subsequent transformations and vary the potential energy landscape of the sample. Some of the defects persist through the transformation, providing nucleation centres for subsequent cycles. Such defects may provide a memory of previous structures, and thereby may be the basis of a reversible shape memory effect.
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    Optimal control for shape memory alloys of the one-dimensional Frémond model
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Colli, Pierluigi; Farshbaf Shaker, Mohammad Hassan; Shirakawa, Ken; Yamazaki, Noriaki
    In this paper, we consider optimal control problems for the one-dimensional Frémond model for shape memory alloys. This model is constructed in terms of basic functionals like free energy and pseudo-potential of dissipation. The state problem is expressed by a system of partial differential equations involving the balance equations for energy and momentum. We prove the existence of an optimal control that minimizes the cost functional for a nonlinear and nonsmooth state problem. Moreover, we show the necessary condition of the optimal pair by using optimal control problems for approximating systems.
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    Gradient polyconvexity and modeling of shape memory alloys
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Horák, Martin; Kružík, Martin; Pelech, Petr; Schlömerkemper, Anja
    We show existence of an energetic solution to a model of shape memory alloys in which the elastic energy is described by means of a gradient-polyconvex functional. This allows us to show existence of a solution based on weak continuity of nonlinear minors of deformation gradients in Sobolev spaces. Admissible deformations do not necessarily have integrable second derivatives. Under suitable assumptions, our model allows for solutions which are orientation-preserving and globally injective everywhere in the domain representing the specimen. Theoretical results are supported by three-dimensional computational examples. This work is an extended version of [36].