Mathematical methods applied in the study of mechanical systems

Contract No. 127 from 01/10/2015

Duration: October 2015- October 2017

Financially supported by Romanian National Authority for Scientific Research and Innovation, CNCS-UEFISCDI

Host Institution: "Alexandru Ioan Cuza" University of Iasi


Principal Investigator: Dr. Ionel-Dumitrel Ghiba

Research Team:

• Conf.dr. Catalin Gales


• Conf.dr. Ionel Roventa


• Phd Student Cosmin Burtea


• Phd Student Andreea Valentina Bucur

Project Summary:

This project is devoted to the study of some mathematical problems concerning nonlinear mechanics, generalized continuous mechanics, hybrid systems, systems of particles as well as the conception of new models and mathematical tools in order to correct some discrepancies of some existing models and to improve the generality of the mathematical results. For each specific model, analytical and/or numerical mathematical methods and techniques are developed and some topics such as the following ones are addressed: rank-one convexity, polyconvexity, constitutive requirements, analytical solutions vs. experimental data, asymptotic behavior, uniqueness, existence, controllability, stabilizability, resonances, bifurcation phenomena, stable and unstable equilibrium points, determination of regular and chaotic motions.


Objectives:

• Nonlinear problems in mechanics;


• Relaxed theories in elasticity;


• The study of Euler equations and of hybrid interaction systems;


• Hamiltonian methods applied in the study of dynamics of mechanical systems.

Expected results:

• We shall promote international scientific cooperation and we shall increase the visibility of Romanian research by publishing highly original research papers (minimum 8 articles in international ISI journals).

Publications:

• P. Neff, I.D. Ghiba, The exponentiated Hencky-logarithmic strain energy: Part III-coupling with idealized multiplicative isotropic finite strain plasticity, Continuum Mechanics and Thermodynamics 28: 477-487, 2016. IF: 1.849 AIS: 1.808


• A. Celletti, C. Gales, Dynamical investigation of minor resonances for space debris, Celestial Mechanics and Dynamical Astronomy 123: 203-222, 2015. IF: 1.594 AIS: 1.110


• I.D. Ghiba, P. Neff, R.J. Martin, An ellipticity domain for the distortional Hencky-logarithmic strain energy, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences 471, doi:10.1098/rspa.2015.0510, 2015. IF: 1.935 AIS: 2.223


• R.J. Martin, I.D. Ghiba, P. Neff. Rank-one convexity implies polyconvexity for isotropic, objective and isochoric elastic energies in the two-dimensional case, Proceedings of the Royal Society of Edinburgh, Section: A Mathematics 147 (3): 571-597, 2017. IF: 1.158 AIS: 1.166. IF: 0.983 AIS: 1.616


• A. Bucur, Rayleigh surface waves problem in linear thermoviscoelasticity with voids, Acta mechanica 227: 1199-1212, 2016. IF: 1.694 AIS: 1.024


• I. Roventa, A note on majorization via perturbed minimizers, Journal of Mathematical Inequalities, in print, 2017. IF: 0.777 AIS 0.282.


• C. Burtea, New long time existence results for a class of Boussinesq-type systems, Journal de Mathematiques Pures et Appliquees 106: 203-236. IF: 1.818 AIS: 3.117


• C. Burtea, Long time existence results for bore-type initial data for BBM-Boussinesq systems, Journal of Differential Equation 261: 4729-5288. IF: 1.821 AIS: 2.386


• P. Lissy, I. Roventa, Optimal filtration for the approximation of boundary controls for the one-dimensional wave equation, acceptata, Mathematics of Computation. IF: 1.569 AIS: 1.279.


• A. Celletti, C. Gales, G. Pucacco, Bifurcation of lunisolar secular resonances for space debris orbits, SIAM Journal on Applied Dynamical Systems 15: 1352-1383, 2016. IF: 1.819 AIS: 1.730


• C. Lhotka, A. Celletti, C. Gales, Poynting-Robertson drag and solar wind in the space debris problem, Monthly Notices of the Royal Astronomical Society 460: 802-815, 2016. IF: 4.952 AIS 1.855


• A. Celletti, C. Gales, A study of the lunisolar secular resonance $2\dot{\omega}+\dot{\Omega}=0$, Frontiers in Astronomy and Space Sciences - Fundamental Astronomy, 31 March 2016, (on-line paper) http://dx.doi.org/10.3389/fspas.2016.00011.


• G. Barbagallo, M.V. D'Agostino, R. Abreu, I.D. Ghiba, A. Madeo, P. Neff, Transparent anisotropy for the relaxed micromorphic model: macroscopic consistency conditions and long wave length asymptotics, International Journal of Solids and Structures, 120: 7-30, 2017. IF: 2.760 AIS 1.016.


• A. Madeo, P. Neff, G. Barbagallo, M.V. D'Agostino, I.D. Ghiba. A review on wave propagation modeling in band-gap metamaterials via enriched continuum models, In F. dell'Isola, M. Sofonea and D. Steigmann (eds), Mathematical Modelling in Solid Mechanics, Volume 69 of the series Advanced Structured Materials, pp. 89-105, Springer, 2017.
  
  
• C. Burtea, Optimal well-posedness for the inhomogeneous incompressible Navier-Stokes system with general viscosity. Analysis and PDE Vol. 10, 2: 439-479, 2017. IF: 1.532 AIS 2.780


• C. Burtea, F. Charve, Lagrangian methods for a general inhomogeneous incompressible Navier-Stokes-Korteweg system with variable capillarity and viscosity coefficients, sub tipar, SIAM J. on Math. Anal., 2017. IF: 1.648 AIS 1.657


• A. Celletti, C. Gales, G. Pucacco, A. Rosengren, Analytical development of the lunisolar disturbing function and the critical inclination secular resonance, Celestial Mechanics and Dynamical Astronomy, 127: 259-283, 2017. IF: 1.584 AIS 0.746


• A. Bucur, Existence and Uniqueness in the Linear Theory of Thermoviscoelastic Materials with Voids, in print Annals of the University of Bucharest (mathematical series), 2017.


• A. Bucur, Spatial Behavior in Linear Theory of Thermoelastic Materials with a Double Porosity Structure, submitted, 2017.

Total IF: 28.51;         Total AIS: 24.179


Conferences:

• I.D. Ghiba, Loss of ellipticity for non-coaxial plastic deformations in additive logarithmic finite strain plasticity and other related results on Hencky-type energies, 86th Annual Meeting of the GAMM, Braunschweig, Germany, March 7-11, 2016.


• I.D. Ghiba, On some Hencky-type energies, XIII-eme Colloque Franco-Roumain de Mathematiques Applieques, Iasi, August 25-29, 2016.


• C. Gales, A study of the lunisolar secular resonances for space debris by using the Hamiltonian formalism, Computational perturbative methods for Hamiltonian systems - Applications in physics and astronomy, Athens, June 11-July 13, 2016.


• C. Gales, Resonance effects in the dynamics of space debris, XIII-eme Colloque Franco-Roumain de Mathematiques Applieques, Iasi, August 25-29, 2016.


• C. Gales, Dynamics of resonances in the space debris problem, Final Stardust Conference, ESA ESTEC, Leiden (The Netherlands), October 31- November 4, 2016.


• C. Burtea, New long time existence results for a class of Boussinesq-type systems, XIII-eme Colloque Franco-Roumain de Mathematiques Applieques, Iasi, August 25-29, 2016.


• A. Bucur, Rayleigh surface waves problem in thermoviscoelastic medium with voids, 11th International Congress on Thermal Stresses 2016 (TS 2016), Salerno, Italy, June 5-9, 2016.


• A. Bucur, Spatial behavior in linear theory of thermoviscoelasticity backward in time for porous media, XIII-eme Colloque Franco-Roumain de Mathematiques Applieques, Iasi, August 25-29, 2016.


• C. Gales, Dissipative effects in the space debris problem, 9th Humboldt Colloquium on Celestial Mechanics, March 19-25, 2017, Bad Hofgastein (Austria).

https://avhc9.wordpress.com/

• C. Gales, Resonance effects within LEO, MEO and GEO regions, The Seventh International Meeting on Celestial Mechanics (CELMEC VII), September 3-9, 2017, San Martino al Cimino (VT), Italy. http://adams.dm.unipi.it/ simca/celmecVII/index.html


• I.D. Ghiba, P. Neff, R. Martin, A non-rank-one convexity result involving geodesically motivated logarithmic strain measures, ISDMM, 26-29 June, Lyon, Franta, 2017.

Academic visits:

• I.D. Ghiba was guest of Prof. dr. Patrizio Neff, Duisburg-Essen University, Germany, January 11 ianuarie- March 18, 2016.


• C. Gales was guest of Prof. dr. Alessandra Celletti, Department of Mathematics, University Tor Vergata, Rome, Italy, June 5-12, 2016.


• I.D. Ghiba was guest of Prof. dr. Mircea Birsan, Duisburg-Essen University, Germany, May 16-August 12, 2016.


• C. Gales was guest of Prof. dr. Alessandra Celletti, Department of Mathematics, University Tor Vergata, Rome, Italy, June 25-July 9, 2016.


• I.D. Ghiba was guest of Prof. dr. Patrizio Neff, Duisburg-Essen University, Germany, November 28-December 5, 2016.


• C. Gales, member of the organizing committee of the summer school entitled Satellite Dynamics and Space Missions: Theory and Applications of Celestial Mechanics, 28 August- 2 Septembrie, 2017, San Martino al Cimino (VT), Italy. http://adams.dm.unipi.it/ simca/sdsm2017/


• I.D. Ghiba was guest of Prof. dr. Patrizio Neff, Duisburg-Essen University, Germany 21 April- Mai 9, 2017.

Others:

• I.D. Ghiba has received in October 2016 the Award Iuventas Scientiae from Alexandru Ioan Cuza University of Iasi for the scientific results obtained during the academic year 2015-2016.


• A paper by C. Gales appears as FEATURED ARTICLE on the web page of SIAM Journal on Applied Dynamical Systems: http://epubs.siam.org/journal/sjaday.

Scientific reports:

• Scientific report 2015


• Scientific report 2016


• Scientific report 2017-Final report