Incompatibility-governed elasto-plasticity
A small-strain formulation based on incompatibility as the primary kinematic descriptor of plastic deformation.
Nicolas
Van Goethem
Associate Professor (with Habilitation)
Department of Mathematical Sciences
Faculty of Sciences, University of Lisbon, Portugal
01
About
I am Associate Professor at the Department of Mathematical Sciences of the Faculty of Sciences, University of Lisbon, and a researcher at CEMSUL.
My research concerns the mathematical analysis and numerical approximation of models for solids with defects, with particular emphasis on elasticity, elasto-plasticity, fracture, damage and dislocation theory.
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Research
Mathematical Analysis and Modelling in Continuum Mechanics
Continuum Mechanics
Elasticity, elasto-plasticity, constitutive modelling, thermodynamics and incompatibility-governed models for defects in solids.
Defects & Dislocation Theory
Geometric and analytical descriptions of crystalline defects, variational evolution, Cartesian currents and topological singularities.
Fracture & Damage Mechanics
Variational and computational approaches to crack initiation and propagation, using topological derivatives and level-set methods.
Calculus of Variations & PDEs
Γ-convergence, relaxation, homogenization, BD and BV, differential constraints and free-discontinuity problems.
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Current Work
Higher-order models and numerical approximation
Analysis, finite-element approximation, and numerical simulation of second-gradient incompatible elasticity and elasto-plasticity, with discretizations tailored to the incompatibility operator and benchmarking against classical formulations.
BD, rigidity and homogenization
Rigidity, blow-up methods, integral representation and homogenization in spaces of bounded deformation and under differential constraints.
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Selected Publications
Rigidity and Functional Properties of BDdev(Ω)
Iterative blow-ups for maps with bounded 𝒜-variation: a refinement, with application to BD and BV
A new approach to topological singularities via a weak notion of Jacobian for functions of bounded variation
A second-order model of small-strain incompatible elasticity
On integral representation of local energy functionals on BD
Hydro-Mechanical Fracture Modelling Governed by Topological Derivatives
Variational Evolution of Dislocations in Single Crystals
Analysis of the incompatibility operator and application in intrinsic elasticity with dislocations
For the complete publication list, see my CV.
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Selected Presentations
Incompatible Deformations in Solids with Dislocation Microstructure: A Strain-Gradient Approach with Finite Elements
COMPLAS 2025, XVIII International Conference on Computational Plasticity, Barcelona, Spain — 4 September 2025
C3M 2025, Computational Methods for Multi-scale, Multi-uncertainty and Multi-physics Problems, Porto, Portugal — 2 July 2025
Integral Representation of Local Energies on BD: Towards 𝒜-Free Operators
Department of Mathematics, University of Salento, Lecce, Italy — 25 June 2024
Some Fracture Evolution Problems by Topological Sensitivity Analysis
Keynote Lecture, ESI Workshop New Perspectives on Shape and Topology Optimization, Vienna, Austria — 15 December 2023
Incompatibility-Governed Deformations: A New Approach to Elastoplasticity
ICIAM 2023, Tokyo, Japan — 25 August 2023
A New Approach to Topological Singularities
8th Iberian Mathematical Meeting, Seville, Spain — 6 October 2022
Seminar, University of Palermo, Italy — 20 July 2022
The Incompatibility Operator: Old and New
Keynote Lecture, International Conference Dynamics, Equations and Applications (DEA 2019), Kraków, Poland — 19 September 2019
Invited Talk, ESI Workshop New Trends in the Variational Modeling of Failure Phenomena, Vienna, Austria — 22 August 2018
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Teaching
- Calculus II
- Calculus III
- Differential Geometry
- Integral and Measure TheoryLecture Notes (PDF)
- Mathematical Methods in Physics
- Rational Mechanics
- Computational Methods in Geology
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Academic Service
- Member of the Scientific Council of the Faculty of Sciences, University of Lisbon
- Member of the Executive Board of CEMS.UL since 2023
- Member of the Executive Board of Department of Mathematical Sciences (2022–2023)
- Organizer of the DCM Mathematical Colloquia and member of the organizing team of WADE – Webinar in Analysis and Differential Equations
- Referee for journals in analysis, mechanics and scientific computation