@article{Poya2023b,

title = {Variational schemes and mixed finite elements for large strain isotropic elasticity in principal stretches: Closed‐form tangent eigensystems, convexity conditions, and stabilised elasticity},

author = {Roman Poya and Rogelio Ortigosa and Antonio J. Gil},

doi = {10.1002/nme.7254},

issn = {1097-0207},

year  = {2023},

date = {2023-08-30},

urldate = {2023-08-30},

journal = {Numerical Meth Engineering},

volume = {124},

number = {16},

pages = {3436--3493},

publisher = {Wiley},

abstract = {<jats:title>Abstract</jats:title><jats:p>A new computational framework for large strain elasticity in principal stretches is presented. Distinct from existing literature, the proposed formulation makes direct use of principal stretches rather than their squares that is, eigenvalues of Cauchy‐Green strain tensor. The proposed framework has three key features. First, the eigen‐decomposition of the tangent elasticity and initial (geometric) stiffness operators is obtained in closed‐form from principal information alone. Crucially, these newly found eigenvalues describe the general convexity conditions of isotropic hyperelastic energies. In other words, convexity is postulated concisely through tangent eigenvalues supplementing the original work of Ball (<jats:italic>Arch Ration Mech Anal</jats:italic>. 1976; 63(4): 337–403). Consequently, this novel finding opens the door for designing efficient automated Newton‐style algorithms with stabilised tangents via <jats:italic>closed‐form</jats:italic> semipositive definite projection or spectral shifting that converge irrespective of mesh resolution, quality, loading scenario and without relying on path‐following techniques. A critical study of closed‐form tangent stabilisation in the context of isotropic hyperelasticity is therefore undertaken in this work. Second, in addition to high order displacement‐based formulation, mixed Hu‐Washizu variational principles are formulated in terms of principal stretches by introducing stretch work conjugate Lagrange multipliers that enforce principal stretch‐stress compatibility. This is similar to enhanced strain methods. However, the resulting mixed finite element scheme is cost‐efficient, specially compared to approximating the entire strain tensors since the formulation is in the scalar space of singular values. Third, the proposed framework facilitates simulating rigid and stiff systems and those that are nearly‐inextensible in principal directions, a constituent of elasticity that cannot be easily studied using standard formulations.</jats:p>},

keywords = {Applied Mathematics, DICOPMA, General Engineering, Numerical Analysis},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa-Martínez2023,

title = {Mathematical modeling, analysis and control in soft robotics: a survey},

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

doi = {10.1007/s40324-023-00334-4},

issn = {2281-7875},

year  = {2023},

date = {2023-08-04},

urldate = {2023-08-04},

journal = {SeMA},

publisher = {Springer Science and Business Media LLC},

abstract = {<jats:title>Abstract</jats:title><jats:p>This paper reviews some recent advances in mathematical modeling, analysis and control, both from the theoretical and numerical viewpoints, in the emergent field of soft robotics. The presentation is not focused on specific prototypes of soft robots, but in a more general description of soft smart materials. The goal is to provide a unified and rigorous mathematical approach to open-loop control strategies for soft materials that hopefully might lay the seeds for future research in this field.</jats:p>},

keywords = {Applied Mathematics, Control and Optimization, DICOPMA, Modeling and Simulation, Numerical Analysis},

pubstate = {published},

tppubtype = {article}

}

@article{Franke2023,

title = {A novel mixed and energy‐momentum consistent framework for coupled nonlinear thermo‐electro‐elastodynamics},

author = {M. Franke and Felix Zähringer and Moritz Hille and Rogelio Ortigosa and P. Betsch and Antonio J. Gil},

doi = {10.1002/nme.7209},

issn = {1097-0207},

year  = {2023},

date = {2023-05-30},

urldate = {2023-05-30},

journal = {Numerical Meth Engineering},

volume = {124},

number = {10},

pages = {2135--2170},

publisher = {Wiley},

abstract = {<jats:title>Abstract</jats:title><jats:p>A novel mixed framework and energy‐momentum consistent integration scheme in the field of coupled nonlinear thermo‐electro‐elastodynamics is proposed. The mixed environment is primarily based on a framework for elastodynamics in the case of polyconvex strain energy functions. For this elastodynamic framework, the properties of the so‐called tensor cross product are exploited to derive a mixed formulation via a Hu‐Washizu type extension of the strain energy function. Afterwards, a general path to incorporate nonpotential problems for mixed formulations is demonstrated. To this end, the strong form of the mixed framework is derived and supplemented with the energy balance as well as Maxwell's equations neglecting magnetic and time dependent effects. By additionally choosing an appropriate energy function, this procedure leads to a fully coupled thermo‐electro‐elastodynamic formulation which benefits from the properties of the underlying mixed framework. In addition, the proposed mixed framework facilitates the design of a new energy‐momentum consistent time integration scheme by employing discrete derivatives in the sense of Gonzalez. A one‐step integration scheme of second‐order accuracy is obtained which is shown to be stable even for large time steps. Eventually, the performance of the novel formulation is demonstrated in several numerical examples.</jats:p>},

keywords = {Applied Mathematics, DICOPMA, General Engineering, Numerical Analysis},

pubstate = {published},

tppubtype = {article}

}

@article{García-Cervera2022,

title = {Control of Partial Differential Equations via Physics-Informed Neural Networks},

author = {Carlos J. García-Cervera and Mathieu Kessler and Francisco Periago},

url = {https://link.springer.com/content/pdf/10.1007/s10957-022-02100-4.pdf},

doi = {10.1007/s10957-022-02100-4},

issn = {1573-2878},

year  = {2023},

date = {2023-02-00},

urldate = {2023-02-00},

journal = {J Optim Theory Appl},

volume = {196},

number = {2},

pages = {391--414},

publisher = {Springer Science and Business Media LLC},

abstract = {<jats:title>Abstract</jats:title><jats:p>This paper addresses the numerical resolution of controllability problems for partial differential equations (PDEs) by using physics-informed neural networks. Error estimates for the generalization error for both state and control are derived from classical observability inequalities and energy estimates for the considered PDE. These error bounds, that apply to any exact controllable linear system of PDEs and in any dimension, provide a rigorous justification for the use of neural networks in this field. Preliminary numerical simulation results for three different types of PDEs are carried out to illustrate the performance of the proposed methodology.</jats:p>},

keywords = {Applied Mathematics, Control and Optimization, Management Science and Operations Research},

pubstate = {published},

tppubtype = {article}

}

@article{Martínez-Frutos2021,

title = {Risk-averse approach for topology optimization of fail-safe structures using the level-set method},

author = {Jesús Martínez-Frutos and Rogelio Ortigosa},

doi = {10.1007/s00466-021-02058-6},

issn = {1432-0924},

year  = {2021},

date = {2021-11-00},

urldate = {2021-11-00},

journal = {Comput Mech},

volume = {68},

number = {5},

pages = {1039--1061},

publisher = {Springer Science and Business Media LLC},

keywords = {Applied Mathematics, Computational Mathematics, Computational Mechanics, Computational Theory and Mathematics, DICOPMA, Mechanical Engineering, Ocean Engineering},

pubstate = {published},

tppubtype = {article}

}

@article{Ortigosa2021b,

title = {Multi-resolution methods for the topology optimization of nonlinear electro-active polymers at large strains},

author = {Rogelio Ortigosa and Jesús Martínez-Frutos},

doi = {10.1007/s00466-021-02030-4},

issn = {1432-0924},

year  = {2021},

date = {2021-08-00},

urldate = {2021-08-00},

journal = {Comput Mech},

volume = {68},

number = {2},

pages = {271--293},

publisher = {Springer Science and Business Media LLC},

keywords = {Applied Mathematics, Computational Mathematics, Computational Mechanics, Computational Theory and Mathematics, DICOPMA, Mechanical Engineering, Ocean Engineering},

pubstate = {published},

tppubtype = {article}

}

@article{Periago2013,

title = {Optimal Design of the Time-Dependent Support of Bang–Bang Type Controls for the Approximate Controllability of the Heat Equation},

author = {Francisco Periago},

doi = {10.1007/s10957-013-0447-9},

issn = {1573-2878},

year  = {2014},

date = {2014-06-00},

urldate = {2014-06-00},

journal = {J Optim Theory Appl},

volume = {161},

number = {3},

pages = {951--968},

publisher = {Springer Science and Business Media LLC},

keywords = {Applied Mathematics, Control and Optimization, Management Science and Operations Research},

pubstate = {published},

tppubtype = {article}

}

@article{Font2012,

title = {A numerical method for computing optimal controls in feedback and digital forms and its application to the blowing‐venting control system of manned submarines},

author = {Roberto Font and Pablo Pedregal and Francisco Periago},

doi = {10.1002/oca.2024},

issn = {1099-1514},

year  = {2013},

date = {2013-03-00},

urldate = {2013-03-00},

journal = {Optim Control Appl Methods},

volume = {34},

number = {2},

pages = {236--252},

publisher = {Wiley},

abstract = {<jats:title>SUMMARY</jats:title><jats:p>On the basis of the classical variational reformulation of optimal control problems, we introduce a numerical scheme for solving those problems where the goal is the computation of optimal controls in feedback and digital forms defined on a discrete time mesh. The algorithm reduces the computation of such controls to solving a suitable nonlinear mathematical programming problem where the unknowns are the controls and slope of the state variable of the original problem. The motivation for this study comes from the real‐world engineering problem which consists of maneuvering a manned submarine by using the blowing‐venting control system of the ballast tanks of the vehicle. After checking the proposed algorithm in an academic example, we apply it to the maneuvering problem of submarines whose mathematical model includes a state law which is composed of a system of twenty‐four nonlinear ordinary differential equations. Numerical results illustrate the performance of the numerical scheme. Copyright © 2012 John Wiley & Sons, Ltd.</jats:p>},

keywords = {Applied Mathematics, Control and Optimization, Control and Systems Engineering, Software},

pubstate = {published},

tppubtype = {article}

}

@article{Ovalle2011,

title = {Analysis and numerical simulation of a nonlinear mathematical model for testing the manoeuvrability capabilities of a submarine},

author = {Diana M. Ovalle and Javier García and Francisco Periago},

doi = {10.1016/j.nonrwa.2010.11.001},

issn = {1468-1218},

year  = {2011},

date = {2011-06-00},

urldate = {2011-06-00},

journal = {Nonlinear Analysis: Real World Applications},

volume = {12},

number = {3},

pages = {1654--1669},

publisher = {Elsevier BV},

keywords = {Analysis, Applied Mathematics, Computational Mathematics, Econometrics and Finance, General Economics, General Engineering, General Medicine},

pubstate = {published},

tppubtype = {article}

}

@article{Münch2011,

title = {Optimal distribution of the internal null control for the one-dimensional heat equation},

author = {Arnaud Münch and Francisco Periago},

doi = {10.1016/j.jde.2010.10.020},

issn = {0022-0396},

year  = {2011},

date = {2011-01-00},

urldate = {2011-01-00},

journal = {Journal of Differential Equations},

volume = {250},

number = {1},

pages = {95--111},

publisher = {Elsevier BV},

keywords = {Analysis, Applied Mathematics},

pubstate = {published},

tppubtype = {article}

}

@article{Font2010,

title = {Numerical simulation of the boundary exact control for the system of linear elasticity},

author = {Roberto Font and Francisco Periago},

doi = {10.1016/j.aml.2010.04.030},

issn = {0893-9659},

year  = {2010},

date = {2010-09-00},

urldate = {2010-09-00},

journal = {Applied Mathematics Letters},

volume = {23},

number = {9},

pages = {1021--1026},

publisher = {Elsevier BV},

keywords = {Applied Mathematics},

pubstate = {published},

tppubtype = {article}

}

@article{Periago2010,

title = {A local existence result for an optimal control problem modeling the manoeuvring of an underwater vehicle},

author = {Francisco Periago and Jorge Tiago},

doi = {10.1016/j.nonrwa.2009.09.002},

issn = {1468-1218},

year  = {2010},

date = {2010-08-00},

urldate = {2010-08-00},

journal = {Nonlinear Analysis: Real World Applications},

volume = {11},

number = {4},

pages = {2573--2583},

publisher = {Elsevier BV},

keywords = {Analysis, Applied Mathematics, Computational Mathematics, Econometrics and Finance, General Economics, General Engineering, General Medicine},

pubstate = {published},

tppubtype = {article}

}

@article{Allaire2010,

title = {Long Time Behavior of a Two-Phase Optimal Design for the Heat Equation},

author = {Grégoire Allaire and Arnaud Münch and Francisco Periago},

doi = {10.1137/090780481},

issn = {1095-7138},

year  = {2010},

date = {2010-01-00},

urldate = {2010-01-00},

journal = {SIAM J. Control Optim.},

volume = {48},

number = {8},

pages = {5333--5356},

publisher = {Society for Industrial & Applied Mathematics (SIAM)},

keywords = {Applied Mathematics, Control and Optimization},

pubstate = {published},

tppubtype = {article}

}

@article{Pedregal2008,

title = {A Numerical Method of Local Energy Decay for the Boundary Controllability of Time‐Reversible Distributed Parameter Systems},

author = {Pablo Pedregal and Francisco Periago and Jorge Villena},

doi = {10.1111/j.1467-9590.2008.00406.x},

issn = {1467-9590},

year  = {2008},

date = {2008-07-00},

urldate = {2008-07-00},

journal = {Stud Appl Math},

volume = {121},

number = {1},

pages = {27--47},

publisher = {Wiley},

abstract = {<jats:p>This paper deals with the numerical computation of the boundary controls of linear, time‐reversible, second‐order evolution systems. Based on a method introduced by Russell (<jats:italic>Stud. Appl. Math.</jats:italic> LII(3) (1973)) for the wave equation, a numerical algorithm is proposed for solving this type of problems. The convergence of the method is based on the local energy decay of the solution of a suitable Cauchy problem associated with the original control system. The method is illustrated with several numerical simulations for the Klein–Gordon and the Euler–Bernoulli equations in 1D, the wave equation on a rectangle, and the plate equation on a disk.</jats:p>},

keywords = {Applied Mathematics},

pubstate = {published},

tppubtype = {article}

}

@article{Münch2008b,

title = {Relaxation of an optimal design problem for the heat equation},

author = {Arnaud Münch and Pablo Pedregal and Francisco Periago},

doi = {10.1016/j.matpur.2007.12.009},

issn = {0021-7824},

year  = {2008},

date = {2008-03-00},

urldate = {2008-03-00},

journal = {Journal de Mathématiques Pures et Appliquées},

volume = {89},

number = {3},

pages = {225--247},

publisher = {Elsevier BV},

keywords = {Applied Mathematics, General Mathematics},

pubstate = {published},

tppubtype = {article}

}

@article{Münch2006b,

title = {Optimal design of the damping set for the stabilization of the wave equation},

author = {Arnaud Münch and Pablo Pedregal and Francisco Periago},

doi = {10.1016/j.jde.2006.06.009},

issn = {0022-0396},

year  = {2006},

date = {2006-12-00},

urldate = {2006-12-00},

journal = {Journal of Differential Equations},

volume = {231},

number = {1},

pages = {331--358},

publisher = {Elsevier BV},

keywords = {Analysis, Applied Mathematics},

pubstate = {published},

tppubtype = {article}

}

@article{Pedregal2006,

title = {Some remarks on homogenization and exact boundary controllability for the one-dimensional wave equation},

author = {Pablo Pedregal and Francisco Periago},

doi = {10.1090/s0033-569x-06-01022-4},

issn = {1552-4485},

year  = {2006},

date = {2006-09-00},

urldate = {2006-09-00},

journal = {Quart. Appl. Math.},

volume = {64},

number = {3},

pages = {529--546},

publisher = {American Mathematical Society (AMS)},

abstract = {<p>This paper contains three results concerning the homogenization and exact controllability for the one-dimensional wave equation. First, we give sufficient conditions on the initial data to ensure the convergence of the conormal derivatives associated with the wave equation with a rapidly oscillating coefficient and zero Dirichlet boundary conditions. Secondly, we apply this result to prove the existence of a class of initial data whose associated boundary controls are uniformly bounded and obtain some information (in particular, its limit behavior) on this class of data. Finally, we prove that all initial data in <inline-formula content-type="math/mathml">

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L squared times upper H Superscript negative 1">

  <mml:semantics>

    <mml:mrow>

      <mml:msup>

        <mml:mi>L</mml:mi>

        <mml:mn>2</mml:mn>

      </mml:msup>

      <mml:mo>×<!-- × --></mml:mo>

      <mml:msup>

        <mml:mi>H</mml:mi>

        <mml:mrow class="MJX-TeXAtom-ORD">

          <mml:mo>−<!-- − --></mml:mo>

          <mml:mn>1</mml:mn>

        </mml:mrow>

      </mml:msup>

    </mml:mrow>

    <mml:annotation encoding="application/x-tex">L^2times H^{-1}</mml:annotation>

  </mml:semantics>

</mml:math>

</inline-formula> may be uniformly controlled but at the price of adding an internal feedback control in our system. The main advantage of this last procedure is that we have explicit formulae for both states and controls.</p>},

keywords = {Applied Mathematics},

pubstate = {published},

tppubtype = {article}

}

@article{Periago2003,

title = {Global existence, uniqueness, and continuous dependence for a semilinear initial value problem},

author = {Francisco Periago},

doi = {10.1016/s0022-247x(03)00126-4},

issn = {0022-247X},

year  = {2003},

date = {2003-04-00},

urldate = {2003-04-00},

journal = {Journal of Mathematical Analysis and Applications},

volume = {280},

number = {2},

pages = {413--423},

publisher = {Elsevier BV},

keywords = {Analysis, Applied Mathematics},

pubstate = {published},

tppubtype = {article}

}

@article{Periago2003c,

title = {Global existence, uniqueness, and continuous dependence for a semilinear initial value problem},

author = {Francisco Periago},

doi = {10.1016/s0022-247x(03)00126-4},

issn = {0022-247X},

year  = {2003},

date = {2003-04-00},

journal = {Journal of Mathematical Analysis and Applications},

volume = {280},

number = {2},

pages = {413--423},

publisher = {Elsevier BV},

keywords = {Analysis, Applied Mathematics},

pubstate = {published},

tppubtype = {article}

}