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2022
 Ortigosa, Rogelio;  Martínez-Frutos, Jesús;  Mora-Corral, Carlos;  Pedregal, Pablo;  Periago, Francisco
Optimal control and design of magnetic field-responsive smart polymer composites Journal Article 
In: Applied Mathematical Modelling, vol. 103, pp. 141-161, 2022, ISSN: 0307-904X.
Abstract | BibTeX | Tags: DICOPMA, Hard-magnetic soft materials, Magneto-elasticity, Optimal control, Optimal design, Polyconvexity, Shape-morphing | Links: 
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@article{ORTIGOSA2022141,

title = {Optimal control and design of magnetic field-responsive smart polymer composites},

author = {Rogelio Ortigosa and Jesús Martínez-Frutos and Carlos Mora-Corral and Pablo Pedregal and Francisco Periago},

url = {https://www.sciencedirect.com/science/article/pii/S0307904X21005096},

doi = {https://doi.org/10.1016/j.apm.2021.10.033},

issn = {0307-904X},

year  = {2022},

date = {2022-01-01},

urldate = {2022-01-01},

journal = {Applied Mathematical Modelling},

volume = {103},

pages = {141-161},

abstract = {This paper presents a novel in-silico framework for the simultaneous optimal control and design of complex magnetic responsive polymer composite materials. State-of-the-art optimisation techniques are used in conjunction with the latest developments in the numerical solution of hard-magnetic soft materials undergoing large (potentially extreme) deformations, in order to address the challenging task of designing shape-morphing two-dimensional composite magnetic sheets. This paper introduces the following key novelties: (i) an optimisation-driven method for the simultaneous optimal control and design of the externally applied magnetic flux density as well as the remnant magnetisation of hard particles within the elastomer matrix, (ii) the well-posedness character of the optimisation problem is established by proving existence of solutions for both the underlying state equation and the control problem itself, (iii) a gradient-based optimisation algorithm is proposed for the numerical approximation of the problem, where explicit expressions of the continuous gradients are obtained by using the formal Lagrangian method. Furthermore, a series of numerical examples are presented in order to demonstrate the capability of the proposal as an alternative to intuition or experimentally-based approaches, representing an optimisation-driven method that facilitates the design of smart materials yielding complex magnetically induced shape morphing configurations.},

keywords = {DICOPMA, Hard-magnetic soft materials, Magneto-elasticity, Optimal control, Optimal design, Polyconvexity, Shape-morphing},

pubstate = {published},

tppubtype = {article}

}

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This paper presents a novel in-silico framework for the simultaneous optimal control and design of complex magnetic responsive polymer composite materials. State-of-the-art optimisation techniques are used in conjunction with the latest developments in the numerical solution of hard-magnetic soft materials undergoing large (potentially extreme) deformations, in order to address the challenging task of designing shape-morphing two-dimensional composite magnetic sheets. This paper introduces the following key novelties: (i) an optimisation-driven method for the simultaneous optimal control and design of the externally applied magnetic flux density as well as the remnant magnetisation of hard particles within the elastomer matrix, (ii) the well-posedness character of the optimisation problem is established by proving existence of solutions for both the underlying state equation and the control problem itself, (iii) a gradient-based optimisation algorithm is proposed for the numerical approximation of the problem, where explicit expressions of the continuous gradients are obtained by using the formal Lagrangian method. Furthermore, a series of numerical examples are presented in order to demonstrate the capability of the proposal as an alternative to intuition or experimentally-based approaches, representing an optimisation-driven method that facilitates the design of smart materials yielding complex magnetically induced shape morphing configurations.
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