Strongly Nonlinear Problems in Contact Mechanics
PN-II-RU-TE-2011-3-0223
GRANT of the Romanian National Autority for Scientific Research, CNCS-UEFISCDI [05.10.2011-04.10.2014]
The overall goal of the project is to improve the understanding of real-world problems governed by Partial Differential Equations in Contact Mechanics. We focus on the existence, uniqueness and stability of the weak solutions; also, the efficient approximation of the weak solutions and optimal control on the boundary for some contact models, are of interest for us. To achieve these targets, new trends in Advanced Applied Mathematics are required, combining Mechanics of Continua, Contact Mechanics and Mechanics of Materials with mathematical areas as PDEs, Nonlinear Analysis, Convex Analysis and Numerical Analysis.
Main objectives
The first objective concerns alternative variational approaches in the mathematical treatment of contact problems, including the approach with dual Lagrange multipliers and the approach via bipotentials.
The second objective focuses on qualitative properties in the variational study of new contact models for non-standard materials such as materials whose constitutive laws involve terms with variable exponent, materials with coupled properties, viscoelastic materials.
Team
Andaluzia-Cristina Matei (Director) Curriculum Vitae
Maria Magdalena Boureanu Curriculum Vitae
Ionel Roventa Curriculum Vitae
Published articles
M. Barboteu, A. Matei and M. Sofonea, On the behavior of the solution of a viscoplastic contact problem, Quarterly of Applied Mathematics ISI , published electronically: September 25, 2014, DOI: http://dx.doi.org/10.1090/S0033-569X-2014-01345-4.
A. Matei, Weak Solutions via Lagrange Multipliers for a Slip-dependent Frictional Contact Model, IAENG International Journal of Applied Mathematics, 44 (3), 2014, 151-156. Special issue WCE 2014-ICAEM; http://www.iaeng.org/IJAM/issues_v44/issue_3/index.html.
A. Matei, Weak solvability via Lagrange multipliers for contact problems involving multi-contact zones, Mathematics and Mechanics of Solids ISI , DOI: 10.1177/1081286514541577.
A. Matei, A mixed variational formulation for a slip-dependent frictional contact model, Lecture Notes in Engineering and Computer Science:
Proceedings of The World Congress on Engineering 2014,
2-4 July, 2014, London, U.K., vol II, pp 750-754 (ISBN: 978-988-19253-5-0).
A. Matei, An existence result for a mixed variational problem arising from Contact Mechanics, Nonlinear Analysis: Real World Applications ISI , online 20 May 2014, DOI: 10.1016/j.nonrwa.2014.01.010, vol. 20, December 2014, 74-81.
A. Matei, A variational approach via bipotentials for a class of frictional contact problems, Acta Applicandae Mathematicae ISI , DOI: 10.1007/s10440-014-9868-1.
M. Boureanu, A. Matei and M. Sofonea, Nonlinear problems with p(.)-growth conditions and applications to antiplane contact models, Advanced Nonlinear Studies ISI , ISSN 1536-1365, 14 (2014), 295-313.
I. Roventa, Generalized equilibrium problems related to Ky Fan inequalities, Abstract and Applied Analysis
Volume 2014 (2014), Article ID 301901, 6 pages
http://dx.doi.org/10.1155/2014/301901.
A. Matei, On the solvability of mixed variational problems with solution-dependent sets of Lagrange multipliers, Proceedings of The Royal Society of Edinburgh,Section: A Mathematics, ISI , published online 25 September 2013; 143(05), October 2013, 1047-1059, http://dx.doi.org/10.1017/S0308210512000637 ; ISSN: 0308-2105.
S. Hueeber, A. Matei, B. Wohlmuth, A contact problem for electro-elastic materials, Journal of Applied Mathematics and Mechanics (ZAMM) ISI , DOI: 10.1002/zamm.201200235, 93 (10-11), 789-800, October 2013. Special Issue: Mathematical Modeling: Contact Mechanics, Phase Transition, Multiscale Problems. In Memory of Christof Eck.(Online ISSN: 1521-4001 Print ISSN 0044-2267)
A. Matei, Weak solvability via Lagrange multipliers for two
frictional contact models, Proceedings of 11-th French-Romanian Conference on Applied Mathematics (Colloque Franco- Roumain), 2012, Bucharest, Annals of the University of Bucharest (mathematical series), 4(LXII), 179-191, 2013.
A. Matei, A variational approach via bipotentials for unilateral contact problems, Journal of Mathematical Analysis and Applications ISI , ISSN 0022-247X, Volume 397, Issue 1, 1 January 2013, Pages 371-380.
http://dx.doi.org/10.1016/j.jmaa.2012.07.065.
I. Andrei, N. Costea and A. Matei, Antiplane shear
deformation of piezoelectric bodies in contact with a conductive
support, Journal of Global Optimization ISI ; ISSN: 0925-5001
DOI: 10.1007/s10898-011-9815-x; Volume 56, Issue 1, pp 103-119, May 2013.
M. Barboteu, A. Matei and M. Sofonea, Analysis of
Quasistatic Viscoplastic Contact Problems with Normal Compliance, The Quarterly Journal of Mechanics and Applied Mathematics ISI , DOI: 10.1093/qjmam/hbs016, 65(4), 555-579, 2012, ISSN 0033-5614.
I. Roventa, A note on Schur-concave functions,
Journal of Inequalities and Applications ISI ,
DOI: 10.1186/1029-242X-2012-159, 2012:159, 9 pages.
M.M. Boureanu, Remarks on Neumann boundary value problems with variable exponents, Bulletin of the Transilvania University of Brasov, Series III: Mathematics,
Informatics, Physics, 5(54), 55-66, 2012.
Published research monograph
M. Sofonea and A. Matei, Mathematical Models in Contact Mechanics, London Mathematical Society, Lecture Note Series 398, Cambridge University Press, 2012 (research monograph).
Accepted article
A. Matei, Two abstract mixed variational problems and applications in Contact Mechanics, Nonlinear Analysis: Real World Applications ISI , http://dx.doi.org/10.1016/j.nonrwa.2014.09.014, DOI: 10.1016/j.nonrwa.2014.09.014.
Submitted articles
I. Roventa, Strongly majorization properties and applications related to Schur-convexity, submitted.
A. Matei, Weak solutions via Lagrange multipliers for contact models with normal compliance, Proceedings of 3rd International Eurasian Conference on Mathematical Sciences and Applications IECMSA 2014, special issue, submitted.
Conferences
The 3rd International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2014), Vienna University of Technology (TU Vienna), 25-28 August 2014 (A. Matei).
The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 07- July 11, 2014, Madrid, Spain (M. Boureanu).
The 2014 International Conference of Applied and Engineering Mathematics, Imperial College London, U.K., 2-4 July 2014 (ICAEM'14), into the frame of The World Congress on Engineering 2014 (WCE 2014) London. (A. Matei).
The 21-st Conference of Applied and Industrial Mathematics-CAIM 2013, 19-22 September, Bucharest, Romania (A. Matei)
Workshop for Young Researchers in Mathematics, May 09-10, 2013 Ovidius University, Constanta, Romania (A. Matei).
XI-eme Colloque Franco-Roumain de Mathematiques Appliquees, Universite de Bucarest, 24-30 Aout 2012, Bucarest, Roumanie (joint work A. Matei and Mircea Sofonea)
41-eme Congres National d'Analyse Numerique, SuperBesse- Puy-de-Dome, 21-25 mai 2012, Universite Blaise Pascal, Clermont-Ferrand, France (joint work A. Matei and I. Roventa).
Workshop for Young Researchers in Mathematics, May 10-11, 2012, Ovidius University, Constanta, Romania (A. Matei).
Research visits
Technische Universitat Munchen (TUM), Mathematik und Informatik Zentrum: August 10- August 18, 2014 (A. Matei)
Technische Universitat Munchen (TUM), Mathematik und Informatik Zentrum: August 26- September 12, 2013 (A. Matei)
Technische Universitat Munchen (TUM), Mathematik und Informatik Zentrum: July 22- August 02, 2013 (A. Matei)
University of Perpignan (LAMPS): June 10-23, 2012 (A. Matei)
Technische Universitat Munchen (TUM), Mathematik und Informatik Zentrum: April 19-30, 2012 (A. Matei)
Milano Bicocca University: May 2-11, 2012 (M.M. Boureanu)
Invited talk
History-dependent operators in Contact Mechanics
Professor Mircea Sofonea, University of Perpignan, France
October 12, 2012, University of Craiova, Department of Mathematics, Scientific Seminar of the project PN-II-RU-TE-2011-3-0223.
Reports (EN) / Rapoarte (RO)
October 20, 2014
The overall goal of the project is to improve the understanding of real-world problems governed by Partial Differential Equations in Contact Mechanics. We focus on the existence, uniqueness and stability of the weak solutions; also, the efficient approximation of the weak solutions and optimal control on the boundary for some contact models, are of interest for us. To achieve these targets, new trends in Advanced Applied Mathematics are required, combining Mechanics of Continua, Contact Mechanics and Mechanics of Materials with mathematical areas as PDEs, Nonlinear Analysis, Convex Analysis and Numerical Analysis.
Main objectives
The first objective concerns alternative variational approaches in the mathematical treatment of contact problems, including the approach with dual Lagrange multipliers and the approach via bipotentials.
The second objective focuses on qualitative properties in the variational study of new contact models for non-standard materials such as materials whose constitutive laws involve terms with variable exponent, materials with coupled properties, viscoelastic materials.
Team
Andaluzia-Cristina Matei (Director) Curriculum Vitae
Maria Magdalena Boureanu Curriculum Vitae
Ionel Roventa Curriculum Vitae
Published articles
M. Barboteu, A. Matei and M. Sofonea, On the behavior of the solution of a viscoplastic contact problem, Quarterly of Applied Mathematics ISI , published electronically: September 25, 2014, DOI: http://dx.doi.org/10.1090/S0033-569X-2014-01345-4.
A. Matei, Weak Solutions via Lagrange Multipliers for a Slip-dependent Frictional Contact Model, IAENG International Journal of Applied Mathematics, 44 (3), 2014, 151-156. Special issue WCE 2014-ICAEM; http://www.iaeng.org/IJAM/issues_v44/issue_3/index.html.
A. Matei, Weak solvability via Lagrange multipliers for contact problems involving multi-contact zones, Mathematics and Mechanics of Solids ISI , DOI: 10.1177/1081286514541577.
A. Matei, A mixed variational formulation for a slip-dependent frictional contact model, Lecture Notes in Engineering and Computer Science:
Proceedings of The World Congress on Engineering 2014,
2-4 July, 2014, London, U.K., vol II, pp 750-754 (ISBN: 978-988-19253-5-0).
A. Matei, An existence result for a mixed variational problem arising from Contact Mechanics, Nonlinear Analysis: Real World Applications ISI , online 20 May 2014, DOI: 10.1016/j.nonrwa.2014.01.010, vol. 20, December 2014, 74-81.
A. Matei, A variational approach via bipotentials for a class of frictional contact problems, Acta Applicandae Mathematicae ISI , DOI: 10.1007/s10440-014-9868-1.
M. Boureanu, A. Matei and M. Sofonea, Nonlinear problems with p(.)-growth conditions and applications to antiplane contact models, Advanced Nonlinear Studies ISI , ISSN 1536-1365, 14 (2014), 295-313.
I. Roventa, Generalized equilibrium problems related to Ky Fan inequalities, Abstract and Applied Analysis
Volume 2014 (2014), Article ID 301901, 6 pages
http://dx.doi.org/10.1155/2014/301901.
A. Matei, On the solvability of mixed variational problems with solution-dependent sets of Lagrange multipliers, Proceedings of The Royal Society of Edinburgh,Section: A Mathematics, ISI , published online 25 September 2013; 143(05), October 2013, 1047-1059, http://dx.doi.org/10.1017/S0308210512000637 ; ISSN: 0308-2105.
S. Hueeber, A. Matei, B. Wohlmuth, A contact problem for electro-elastic materials, Journal of Applied Mathematics and Mechanics (ZAMM) ISI , DOI: 10.1002/zamm.201200235, 93 (10-11), 789-800, October 2013. Special Issue: Mathematical Modeling: Contact Mechanics, Phase Transition, Multiscale Problems. In Memory of Christof Eck.(Online ISSN: 1521-4001 Print ISSN 0044-2267)
A. Matei, Weak solvability via Lagrange multipliers for two
frictional contact models, Proceedings of 11-th French-Romanian Conference on Applied Mathematics (Colloque Franco- Roumain), 2012, Bucharest, Annals of the University of Bucharest (mathematical series), 4(LXII), 179-191, 2013.
A. Matei, A variational approach via bipotentials for unilateral contact problems, Journal of Mathematical Analysis and Applications ISI , ISSN 0022-247X, Volume 397, Issue 1, 1 January 2013, Pages 371-380.
http://dx.doi.org/10.1016/j.jmaa.2012.07.065.
I. Andrei, N. Costea and A. Matei, Antiplane shear
deformation of piezoelectric bodies in contact with a conductive
support, Journal of Global Optimization ISI ; ISSN: 0925-5001
DOI: 10.1007/s10898-011-9815-x; Volume 56, Issue 1, pp 103-119, May 2013.
M. Barboteu, A. Matei and M. Sofonea, Analysis of
Quasistatic Viscoplastic Contact Problems with Normal Compliance, The Quarterly Journal of Mechanics and Applied Mathematics ISI , DOI: 10.1093/qjmam/hbs016, 65(4), 555-579, 2012, ISSN 0033-5614.
I. Roventa, A note on Schur-concave functions,
Journal of Inequalities and Applications ISI ,
DOI: 10.1186/1029-242X-2012-159, 2012:159, 9 pages.
M.M. Boureanu, Remarks on Neumann boundary value problems with variable exponents, Bulletin of the Transilvania University of Brasov, Series III: Mathematics,
Informatics, Physics, 5(54), 55-66, 2012.
Published research monograph
M. Sofonea and A. Matei, Mathematical Models in Contact Mechanics, London Mathematical Society, Lecture Note Series 398, Cambridge University Press, 2012 (research monograph).
Accepted article
A. Matei, Two abstract mixed variational problems and applications in Contact Mechanics, Nonlinear Analysis: Real World Applications ISI , http://dx.doi.org/10.1016/j.nonrwa.2014.09.014, DOI: 10.1016/j.nonrwa.2014.09.014.
Submitted articles
I. Roventa, Strongly majorization properties and applications related to Schur-convexity, submitted.
A. Matei, Weak solutions via Lagrange multipliers for contact models with normal compliance, Proceedings of 3rd International Eurasian Conference on Mathematical Sciences and Applications IECMSA 2014, special issue, submitted.
Conferences
The 3rd International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2014), Vienna University of Technology (TU Vienna), 25-28 August 2014 (A. Matei).
The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 07- July 11, 2014, Madrid, Spain (M. Boureanu).
The 2014 International Conference of Applied and Engineering Mathematics, Imperial College London, U.K., 2-4 July 2014 (ICAEM'14), into the frame of The World Congress on Engineering 2014 (WCE 2014) London. (A. Matei).
The 21-st Conference of Applied and Industrial Mathematics-CAIM 2013, 19-22 September, Bucharest, Romania (A. Matei)
Workshop for Young Researchers in Mathematics, May 09-10, 2013 Ovidius University, Constanta, Romania (A. Matei).
XI-eme Colloque Franco-Roumain de Mathematiques Appliquees, Universite de Bucarest, 24-30 Aout 2012, Bucarest, Roumanie (joint work A. Matei and Mircea Sofonea)
41-eme Congres National d'Analyse Numerique, SuperBesse- Puy-de-Dome, 21-25 mai 2012, Universite Blaise Pascal, Clermont-Ferrand, France (joint work A. Matei and I. Roventa).
Workshop for Young Researchers in Mathematics, May 10-11, 2012, Ovidius University, Constanta, Romania (A. Matei).
Research visits
Technische Universitat Munchen (TUM), Mathematik und Informatik Zentrum: August 10- August 18, 2014 (A. Matei)
Technische Universitat Munchen (TUM), Mathematik und Informatik Zentrum: August 26- September 12, 2013 (A. Matei)
Technische Universitat Munchen (TUM), Mathematik und Informatik Zentrum: July 22- August 02, 2013 (A. Matei)
University of Perpignan (LAMPS): June 10-23, 2012 (A. Matei)
Technische Universitat Munchen (TUM), Mathematik und Informatik Zentrum: April 19-30, 2012 (A. Matei)
Milano Bicocca University: May 2-11, 2012 (M.M. Boureanu)
Invited talk
History-dependent operators in Contact Mechanics
Professor Mircea Sofonea, University of Perpignan, France
October 12, 2012, University of Craiova, Department of Mathematics, Scientific Seminar of the project PN-II-RU-TE-2011-3-0223.
Reports (EN) / Rapoarte (RO)