Nicolas Van Goethem

Professor Associado com Agregação
Department of Mathematical Sciences
Faculty of Sciences, University of Lisbon
Portugal

Mathematical Modelling in Mechanics • Fracture • Dislocations • Calculus of Variations • PDEs

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About

Nicolas Van Goethem

I am Associate Professor at the Department of Mathematical Sciencers of the Faculty of Sciences, University of Lisbon, and researcher at CEMSUL.

My research focuses on the mathematical modelling, analysis, and numerical simulation of defects in materials and structures. I work at the intersection of continuum mechanics, applied analysis, and materials science, with interests spanning elasticity, elasto-plasticity, fracture, damage, and dislocation theory.

My approach combines variational methods, partial differential equations, geometric measure theory, differential geometry, and topological sensitivity analysis to develop rigorous mathematical frameworks for solids with defects and evolving microstructures.

Research Interests

Continuum Mechanics

Elasticity, elasto-plasticity, constitutive modeling, thermodynamics, and incompatibility-governed models for defects in solids. Includes geometric measure theory and non-Riemannian geometry of crystals.

Defects & Dislocation Theory

Geometric and analytical descriptions of defects in crystalline solids. Variational evolution of dislocations, Cartesian currents, and topological singularities.

Fracture & Damage Mechanics

Variational and computational approaches to crack initiation and propagation. Topological derivatives, shape optimization, and hydro-mechanical fracture modeling. Collaboration with engineers for computational applications.

Calculus of Variations & PDEs

111

Γ-convergence, relaxation, homogenization, and free-discontinuity problems. Applications to image processing and PDEs with Amstutz and Novotny. Includes bounded deformation and incompatibility operators.

Selected Publications

Rigidity and Functional Properties of BDdev(Ω)
M. Caroccia, N. Van Goethem
Arch. Rational Mech. Anal., 2026
Iterative blow-ups for maps with bounded 𝒜-variation: A refinement, with application to BD and BV
M. Caroccia, N. Van Goethem
Adv. Calc. Var., 2025
A new approach to topological singularities via a weak notion of Jacobian for functions of bounded variation
L. De Luca, R. Scala, N. Van Goethem
Indiana Univ. Math. J., 2024
A second-order model of small-strain incompatible elasticity
S. Amstutz, N. Van Goethem
Math. Mech. Solids, 2024
On integral representation of local energy functionals on BD
M. Caroccia, M. Focardi, N. Van Goethem
SIAM J. Math. Analysis (SIMA), 2020
Hydro-Mechanical Fracture Modelling Governed by Topological Derivatives
M. Xavier, N. Van Goethem, A. Novotny
Comp. Meth. Appl. Mech. Eng. (CMAME), 2019
Variational Evolution of Dislocations in Single Crystals
R. Scala, N. Van Goethem
J. Nonlinear Sci., 2019
A Variational Approach to Single Crystals with Dislocations
R. Scala, N. Van Goethem
SIAM J. Math. Analysis (SIMA), 2019
Incompatibility-governed elasto-plasticity for continua with dislocations
S. Amstutz, N. Van Goethem
Proc. R. Soc. Lond. A, 2017
S. Amstutz and N. Van Goethem, Analysis of the incompatibility operator and application in intrinsic elasticity with dislocations
S. Amstutz, N. Van Goethem
SIAM J. Math. Analysis (SIMA), 2016
A compatible-incompatible decomposition of symmetric tensors in L^p with application to elasticity
G. Maggiani, R. Scala, N. Van Goethem Math. Meth. Appl. Sc., 2011
Damage and crack evolution by shape optimization methods
G. Allaire, F. Jouve, N. Van Goethem
J. Comput. Phys. , 2011

For a complete publication list, see my CV and research profiles.

Teaching

  • Calculus II
  • Calculus III
  • Differential Geometry
  • Integral and Measure Theory
  • Mathematical Methods in Physics
  • Rational Mechanics
  • Computational Methods in Geology

Academic Service

  • Member of the Scientific Council of the Faculty of Sciences, University of Lisbon.
  • Member of the Strtegic Board of CEMSUL.
  • Former Vice-President of the Department of Mathematics (2022–2023).
  • Organizer of mathematical colloquia ("Colóquios do DCM") and scientific seminar activities (

    WADE – Webinar in Analysis and Differential Equations)

    .
  • Reviewer for numerous international journals including SIAM Journal on Mathematical Analysis, Journal of Computational Physics, ESAIM, CMAME, Calculus of Variations and Partial Differential Equations, Advances in Calculus of Variations, and Archive for Rational Mechanics and Analysis.

Contact

Department of Mathematical Sciences
Faculty of Sciences, University of Lisbon
Campo Grande, Edifício C6
1749-016 Lisboa, Portugal

Email: nvgoethem@ciencias.ulisboa.pt

ORCID: 0000-0002-5356-8383

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