Profile
Profile

Prof. Dr. Sergio Conti

E-Mail: sergio.conti(at)uni-bonn.de
Telefon: +49 228 73 62211
Fax: +49 228 73 62248
Homepage: https://www.iam.uni-bonn.de/aaa2/people/sergio-conti/
Raum: 2.027
Standort: Mathematics Center
Institute: Institute for Applied Mathematics
Forschungsbereich: Research Area B
Geburtsdatum: 03.Dec 1971
Mathscinet-Number: 666185

Academic Career

1997

PhD, Scuola Normale Superiore di Pisa, Italy

1997 - 2004

Postdoctoral Associate, Max Planck Institute for Mathematics in the Sciences, Leipzig

2004

Habilitation in Mathematics, University of Leipzig

2004 - 2008

Professor (C4), University of Duisburg-Essen

Since 2008

Professor (W3), Institute for Applied Mathematics, University of Bonn

Research Profile

My research activity focuses on variational problems with applications to materials science, in particular in elasticity and plasticity. One key theme is the elastic behavior of thin sheets. The starting point was a variational analysis of blistering in thin films [1], which contributed to a new understanding of the origin of microstructure in these systems. I then turned to the situation where compressive Dirichlet boundary conditions by confinement, as in an obstacle problem. The optimal scaling turned out to be different, being proportional to the thickness to the power 5/3 [3]. A second line of thought focused on variational models in crystal plasticity and their relaxation. An explicit relaxation of a geometrically linear model in which finitely many slip systems are active was obtained in [4], and applied to simulate numerically an indentation test in [5]. At a finer scale, a line-tension model for dislocations was derived in [10,9].

Future work will address interaction between different defects, such as damage and fracture, or density of interstitials and motion of dislocations. At the same time I intend to address microstructure formation in situations which cannot be addressed purely by energy minimization, such as plastic deformation under non-monotonous loadings, or fracture propagation, or cycling in phase transformation in shape-memory alloys. This will involve both the study of path-dependence in inelastic deformation and the study of hysteresis, and can be attacked by macroscopic rate-independent models or at a more microscopic level using transition-state theory.

Research Projects and Activities

HIM Trimester on “Mathematical challenges of materials science and condensed matter physics",
organizer, 2012

Project “From pair potentials to macroscopic plasticity”
within DFG Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”,
jointly with Stefan Müller and Michael Ortiz

Project “Hysteresis and microstructure in shape memory alloys”
within DFG Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”,
jointly with Barbara Zwicknagl

Project “Numerical optimization of shape microstructures”
within DFG Collaborative Research Center SFB 1060 “The Mathematics of Emergent Effects”,
jointly with Martin Rumpf

Contribution to Research Areas

Research Area B
My research activity focuses on variational problems with applications to materials science, in particular in elasticity and plasticity. One key theme is the elastic behavior of thin sheets. The starting point was a variational analysis of blistering in thin films [1], which contributed to a new understanding of the origin of microstructure in these systems. A simplification of the blistering model leads to the scalar Aviles-Giga functional, which was studied in [2]. I then turned to the situation where compressive Dirichlet boundary conditions by confinement, as in an obstacle problem. The optimal scaling turned out to be different, being proportional to the thickness to the power 5/3 [3].

A second line of thought focused on variational models in crystal plasticity and their relaxation. An explicit relaxation of a geometrically linear model in which finitely many slip systems are active was obtained in [4], and applied to simulate numerically an indentation test in [5]. The situation in a geometrically nonlinear setting is considerably more subtle. The relaxation for an elastically rigid problem with one-slip-system was obtained in [6], the case of two slip systems was then addressed in [7]. The inclusion of a realistic elastic energy strongly reduces the coercivity of the functional, due to the multiplicative decomposition of the deformation gradient which is used in finite plasticity, leading to a soft behavior if hardening is not included [8]. At a finer scale, self-similar dislocation microstructures have been related to Hall-Petch effect [4] and a line-tension model for dislocations was derived in [9].

Selected Publications

[1] Hafedh Ben Belgacem, Sergio Conti, Antonio DeSimone, Stefan Müller
Energy scaling of compressed elastic films---three-dimensional elasticity and reduced theories
Arch. Ration. Mech. Anal. , 164: (1): 1--37
2002
DOI: 10.1007/s002050200206
[2] Sergio Conti, Camillo De Lellis
Sharp upper bounds for a variational problem with singular perturbation
Math. Ann. , 338: (1): 119--146
2007
DOI: 10.1007/s00208-006-0070-2
[3] Sergio Conti, Francesco Maggi
Confining thin elastic sheets and folding paper
Arch. Ration. Mech. Anal. , 187: (1): 1--48
2008
DOI: 10.1007/s00205-007-0076-2
[4] Sergio Conti, Michael Ortiz
Dislocation microstructures and the effective behavior of single crystals
Arch. Ration. Mech. Anal. , 176: (1): 103--147
2005
DOI: 10.1007/s00205-004-0353-2
[5] Sergio Conti, Patrice Hauret, Michael Ortiz
Concurrent multiscale computing of deformation microstructure by relaxation and local enrichment with application to single-crystal plasticity
Multiscale Model. Simul. , 6: (1): 135--157
2007
DOI: 10.1137/060662332
[6] Sergio Conti, Florian Theil
Single-slip elastoplastic microstructures
Arch. Ration. Mech. Anal. , 178: (1): 125--148
2005
DOI: 10.1007/s00205-005-0371-8
[7] Nathan Albin, Sergio Conti, Georg Dolzmann
Infinite-order laminates in a model in crystal plasticity
Proc. Roy. Soc. Edinburgh Sect. A , 139: (4): 685--708
2009
DOI: 10.1017/S0308210508000127
[8] Sergio Conti, Georg Dolzmann, Carolin Klust
Relaxation of a class of variational models in crystal plasticity
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. , 465: (2106): 1735--1742
2009
DOI: 10.1098/rspa.2008.0390
[9] Sergio Conti, Adriana Garroni, Stefan Müller
Singular kernels, multiscale decomposition of microstructure, and dislocation models
Arch. Ration. Mech. Anal. , 199: (3): 779--819
2011
DOI: 10.1007/s00205-010-0333-7
[10] Sergio Conti, Adriana Garroni, Michael Ortiz
The line-tension approximation as the dilute limit of linear-elastic dislocations
Arch. Ration. Mech. Anal. , 218: (2): 699--755
2015
DOI: 10.1007/s00205-015-0869-7
[11] Sergio Conti, Adriana Garroni, Stefan Müller
Dislocation microstructures and strain-gradient plasticity with one active slip plane
J. Mech. Phys. Solids , 93: : 240--251
2016
DOI: 10.1016/j.jmps.2015.12.008
[12] C. Reina, S. Conti
Kinematic description of crystal plasticity in the finite kinematic framework: a micromechanical understanding of F=FeFp
J. Mech. Phys. Solids , 67: : 40--61
2014
DOI: 10.1016/j.jmps.2014.01.014
[13] Sergio Conti, Georg Dolzmann
On the theory of relaxation in nonlinear elasticity with constraints on the determinant
Arch. Ration. Mech. Anal. , 217: (2): 413--437
2015
DOI: 10.1007/s00205-014-0835-9

Publication List

Selected Invited Lectures

2008

79th Annual Meeting of GAMM, Bremen

2008

SIAM, Mathematical Aspects of Materials Science, Philadelphia, PA, USA

2011

ICIAM, Vancouver, BC, Canada

2016

European Congress of Mathematics, Berlin

Selected PhD students

Peter Gladbach (2016): “A phase-field model of dislocations on parallel slip planes”

Johannes Diermeier (2016): “Analysis of Martensitic Microstructures in Shape-Memory Alloys: A Low Volume-Fraction Limit”,
now Researcher, Institute for Applied Mathematics, University of Bonn

Supervised Theses

  • Master theses: 9
  • Diplom theses: 3
  • PhD theses: 3
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