Nicolas Van Goethem UNIVERSIDADE DE LISBOA FACULDADE DE CIÊNCIAS DEPARTAMENTO DE MATEMÁTICA Centro de Matemática e Aplicações Fundamentais (CMAFcIO research center) Campo Grande, Edifício C6, Piso 2, 1749-016 - Lisboa Sala 6.2.20 Phone [+351] 217500486 (office) [+351] 930416751 (mobile) Email vangoeth@fc.ul.pt

Professor of mathematics at FCUL and researcher at CMFcIO

• PROJECT & GROUP: MATH2DISLOC (FCT Grant, PI, 2014-2019)
  • Former members: Pedro Campos (9/2017-6/2019), Riccardo Scala (1/2017-6/2018), Marco Caroccia (9/2017-8/2018)
• Associate professor qualification (Italy, 2013)
• H-index = 11
• Curriculum: May 2021

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Research

• Field: Mathematical modelling in material science: theory, numerics & applications.
Current project: Inelastic solids with defect singularities: mathematical analysis for models of fracture and dislocations.
• Topics: Continuum mechanics & thermodynamics of defects in solids (damage, fracture & dislocations); Finite elasticity & linearized elasto-plasticity; Axiomatic approach to thermodynamics; Variational methods in material science: Gamma-convergence & shape and topological optimization methods (theory and numerics); Partial differential equations (elliptic & parabolic) and functional analysis; Geometric measure theory (theory of currents for dislocation modelling); Differential geometry (non-Riemannian geometry of crystals with defects).

• Short description:

  My research interests are connected to defect modelling in solid materials by mathematical analysis. This encompasses damage-based fracture in elastic and elasto/plastic materials, and dislocation and disclinations modelling in single crystals. The mathematical tools used and developed for this purposes are variational methods, differential geometry and topological sensitivity analysis. Continuum mechanics and thermodynamics are also required to comprehend the involved phenomena and further develop these models. Theoretical and numerical results are sought.

Data: Thomson Reuters Researcher ID - Scopus ID - Google Scholar Profile - Researchgate Profile

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Selected Publications

• with S. Amstutz: A second-order model of small-strain incompatible elasticity, Mathematics and Mechanics of Solids (2023). Link to file: published version

• with L. De Luca and R. Scala: A new approach to topological singularities via a weak notion of Jacobian for functions of bounded variation, Indiana Univ. Math. J. (2022). Link to file: published version

• with M. Caroccia and M. Focardi: On integral representation of local energy functionals on BD, Siam J. Math. Analysis (2020). Link to file: published version

• with S. Amstutz: Existence and asymptotic results for an intrinsic model of incompatible elasticity, DCDS-B (2020). Link to file: published version

• with M. Xavier and A. Novotny: Hydro-mechanical fracture modelling governed by topological derivatives, CMAME (2020). Link to file: published version

• with S. Amstutz: The incompatibility operator: from Riemann’s intrinsic view of geometry to a new model of elasto-plasticity, survey paper appeared in TOPICS IN APPLIED ANALYSIS AND OPTIMIZATION, CIM Series in Mathematical Sci. (2019). Link to file: published version

• with R. Scala: A variational approach to single crystals with dislocations, Siam J. Math. Analysis (2019). Link to file: published version

• with R. Scala: Analytic and geometric properties of dislocation singularities, RSE Proc. A Math. (2019). Link to file: published version

• with S. Amstutz: Incompatibility-governed elasto-plasticity for continua with dislocations, Proc. R. Soc. Lond., Ser. A. (2017). Link to file: published version

• with S. Amstutz: Analysis of the incompatibility operator and application in intrinsic elasticity with dislocations, Siam J. Math. Analysis. (2016). Link to file: published version

• with G. Maggiani and R. Scala: A compatible-incompatible decomposition of symmetric tensors in L^p with application to elasticity, M2AS (2015). Link to file: published version

• with S. Amstutz and A. Novotny: Topological sensitivity analysis for elliptic differential operators of order 2m, J. Diff. Eqs. (2014). Link to file: published version

• with F. Dupret: A distributional approach to 2D Volterra dislocations at the continuum scale, Europ. Jnl. Applied Math. (2012). Link to file: published version

• with G. Allaire, F. Jouve: Damage and crack evolution by shape optimization methods, J. Comput. Phys. (2011). Link to file: published version

• with A. Novotny: Crack nucleation sensitivity analysis, M2AS (2010). Link to file: published version

Recent preprints go to CMAF preprint server - Download publications try Researchgate

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Teaching (current)

• Cálculo Infinitesimal II (2022-)

  • Lecture Notes: lecture notes on Infinitesimal Calculus II (Portuguese version), 06/2023

  • Differential geometry (2021-)

    • Lecture Notes: lecture notes on Differential geometry (Portuguese version), 06/2023
    • Exercices (Teorica-Prática): exercices on Differential geometry (Portuguese version), 05/2021

  • Rational Mechanics (2015-2018)

    • Lecture Notes: lecture notes Rational Mechanics (Portuguese version), 07/2017

  • Mathematical Methods in Physics (2020-2022)

    • Lecture Notes: lecture notes on "Invariance in Physics: tensors, differential forms & exterior calculus with applications to electro-magnetism and special relativity" (Portuguese version), 12/2022

  • Mathematical Methods in Physics (2016-2018)

    • Lecture Notes: lecture notes on "Continuum Mechanics" (Portuguese version), 07/2017
    • Lecture Notes: lecture notes on "Heat Equation" (Portuguese version), 10/2016

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    Short bio

    After undergraduate studies at the European school of Varese, Italy (1976-1992) and Brussels, Belgium (1992-1994), I graduated in Applied Mathematics at UCL, Louvain-la-Neuve, Belgium (currently Ecole Polytechnique de Louvain) in 1999. In 1999-2000, before starting a PhD thesis, I took the opportunity to work with G. Buttazzo in Pisa (Italy) on some Shape Optimization Problems. In 2000-2006 I was PhD student of F. Dupret and teaching assistant at Ecole Polytechnique de Louvain (Louvain-la-Neuve, Belgium). In Fall 2003 I was invited by D. Preiss to work during a trimester on some problems of Real Analysis at University College of London (Marie Curie ESR fellowship). In 2007-2008, I was Marie-Currie post-doc fellow (ER fellowship) at Ecole Polytechnique of Palaiseau, France, in the group and under the supervision of G. Allaire, where I worked on fracture evolution by shape optimization methods. In 2008, I won a faculty researcher position at CMAF, University of Lisbon, Portugal, under the programme Ciência 2007. This position was interrupted in 2012-2014 to take the opportunity of joining G. Dal Maso group at SISSA, Trieste, Italy, and participate to the research programme of his ERC grant "Quasistatic and Dynamic Evolution Problems in Plasticity and Fracture``. In 2013, I was selected for the FCT research fellow call and hence went back to Lisbon in July 2014. Besides this 5-year position, I also was awarded an "exploratory research project" grant with title "Mathematical theory of dislocations : geometry, analysis, and modelling". In 2013, I received the Italian Science Foundation qualification for Associate professor (''abilitazione alle funzioni di professore di seconda fascia in analisi matematica, probabilita e statistica matematica``). I am currently lecturing Differential geometry, Rational Mechanics and Mathematical Methods in Physics courses.