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Doctoral Workshop on Model Reduction in nonlinear mechanics,  February 13-17 2017 at Mines ParisTech.

MINES ParisTech, 60 bvd St Michel, 75272 Paris, Train station RER B Luxembourg.

Supported by the scientific network COSIMOR (DFG-FR2702/4, 7).


Deadline for registration: December 1st 2016.

R. Chackir (IFSTTAR), F. Daim (ESI group), A. Hamdouni (Université de La Rochelle), F. Fritzen (Stuttgart University), B. Haasdonk (Stuttgart University), D. Néron (ENS Cachan), O. Thomas (ENSAM), D. Ryckelynck (MINES ParisTech), J. Salomon (Université de Paris Dauphine).

Reduced-Order models aim at reducing the computational time required to obtain solutions of Partial Differential Equations which are physically-based and parameter dependent. They reduce the computational complexity of optimization procedures, parametric analyses, or metamodel generation. 

Reduced-Order Models are very useful to model complex mechanical phenomena, when parametric studies are mandatory to setup convenient nonlinear constitutive equations, boundary conditions, or numerical parameters. In such situations, many open questions about physical assumptions arise and the scientist's intuition alone cannot guarantee that convenient simplified numerical approximations are chosen. Nowadays several algorithmic approaches are available to reduce models. This course aim to present recent advances in model reduction in the fields of structural dynamics, mechanics of materials and fluid dynamics.







February 13th



POD for parametric partial differential equations

D. Ryckelynck

Hyper-reduction in mechanics of materials

(D. Ryckelynck)


February 14th

Proper Generalized Decomposition

D. Néron

Error estimation and adaptivity

D. Ryckelynck

Reduced Basis Methods – 1

B. Haasdonk

Reduced Basis Methods – 2

B. Haasdonk


February 15th

Hyper-reduction for crash simulations

F. Daim

Two grids non-intrusive reduced basis methods

R. Chakir

Numerical exercices using Zset

D. Ryckelynck

Numerical exercices using Zset

D. Ryckelynck


February 16th

Reduced variational inequalities

J. Salomon

Numerical exercices using Matlab

J. Salomon

Model reduction in material science

F. Fritzen

Numerical exercices using Python


February 17th

(French session)

POD en mécanique des fluides

A. Hamdouni

Modes non linéaires en mécanique des vibrations

O. Thomas




Download Matlab files
Download Python files
Chicago 2017



Thèmes de recherche

Mécanique des structures: réduction adaptative de modèles non linéaires, modèles d'ordre réduit non linéaires pour la propagation d'incertitudes et les simulations multidimensionnelles (surfaces de réponse, aide à la décision,...), hyper réduction, interface 4D et transfer de champs, contact, calcul parallèle, modèles d'ordre réduit non linéaires pour le développement durable de la simulation numérique en science des matériaux. Développement de modèles multiphysiques pour la maîtrise des procédés. Modélisation simplifiée des procédés à sollicitation localisée mobile (soudage, frittage laser, cold spray, coupe, ...). Recalage de modèles. Résultats scientifiques récents (novembre 2011). CSDL (janvier 2012).

Hyper-reduction in nonlinear mechanics of solid materials. Reduced-order models reveal common features between solutions of parametric partial differential equations (PDE). They aim to save computational time when modelling complex mechanical phenomena, as setting-up convenient nonlinear constitutive equations or boundary conditions for instance.The Garlerkin weak form of nonlinear reduced equations do not provide sufficient speed-up, mainly because the computation of the reduced-residual can’t be performed offline. Hence, this computation remains affected by the complexity of the original model. Hyper-reduction methods aim to generate reduced-order model whose complexity does not depend on the complexity of the original model by introducing a reduced integration domain (RID). This domain contains only few elements of the original mesh.We propose both an explicit hyper-reduced scheme and implicit hyper-reduced schemes applied to nonlinear mechanics of solid materials. The explicit approach aims to interpolate missing boundary conditions on the boundary of the RID. The implicit approach predicts the reduced coordinate of the displacement field by using balance conditions restricted to the RID.


Revues à comité de lecture
  • Estimation of the validity domain of hyper-reduction approximations in generalized standard elastoviscoplasticity, D. Ryckelynck, L. Gallimard, S. Jules, AMSES, (2015),
  • POD of IR thermal data to assess heat source distributions, N. Ranc, A. Blanche, D. Ryckelynck, A. Chrysochoos, Special issue, Experimental Mechanics, (2014), DOI 10.1007/s11340-014-9858-2.
  • A priori hyper-reduction method for coupled viscoelastic-viscoplastic composites, B. Miled, D. Ryckelynck, S. Cantournet, Computer & Structures, 119, (2013), p 95-103.
  • Bimodal Beremin-type model for brittle fracture of inhomogeneous ferritic steels : Theory and applications, Andrieu, A., Pineau, A., Besson, J., Ryckelynck, D., Bouaziz, O., Engineering Fracture Mechanics, 95, (2012), p 84-101.
  • Beremin model : Methodology and application to the prediction of the Euro toughness data set, Andrieu, A., Pineau, A., Besson, J., Ryckelynck, D., Bouaziz, O., Engineering Fracture Mechanics, 95, (2012), p 102-117.
  • Multidimensional a priori hyper-reduction of mechanical models involving internal variables, D. Ryckelynck, F. Vincent, S. Cantournet, Computer Methods in Applied Mechanics and Engineering, Volumes 225–228, Pages 28–43, (2012).
  • Numerical simulation of the cooling-down of high-zirconia fused-cast refractories, Petroni, L. Boussuge, M., Ryckelynck, D., Journal of the european ceramic society, Vol. 32 , Issue: 15, Special Issue: SI , (2012), p 3941-3947.
  • Reduced-order modelling for solving linear and non-linear equations,Verdon, N, Allery, C, Beghein, C, Hamdouni, A., Ryckelynck, D., International Journal for Numerical Methods in Biomedical Engineering, Volume: 27  Issue: 1  Pages: 43-58, (2011).
  • A priori reduction method for solving the two-dimensional Burger’s equations, C. Allery, A. Hamdouni, D. Ryckelynck, N. Verdon, Applied Mathematics and Computation, Volume 217, Issue 15, 1 (2011), Pages 6671-6679.
  • A robust adaptive model reduction method for damage simulations, D. Ryckelynck, D. Missoum Benziane, S. Cartel, J. Besson, Computational Materials Science, Volume 50, Issue 5, March (2011), Pages 1597-1605.
  • Toward "green" mechanical simulations in materials science: hyper-reduction of a polycrystal plasticity model, David Ryckelynck, Djamel Missoum Benziane, Andrey Musienko, and Georges Cailletaud, EJCM, Volume 19, N°4, pp. 365-388, (2010).
  • B. Sarbandi, S. Cartel, J. Besson, D. Ryckelynck, Truncated Integration for Simultaneous Simulation of Sintering Using a Separated Representation, Achives of Computational Methods in engineering, accepté.

  • D. Ryckelynck, D. M. Benziane, Multi-level a priori hyper-reduction of mechanical models involving internal variables, Computer Methods in Applied Mechanics and Engineering, en ligne (2010).
  • N. Verdon, C. Allery, A. Hamdouni, D. Ryckelynck, Reduced-Order Modelling for solving linear and non-linear equations, Communications in Numerical Methods in Engineering, en ligne (2010).
  • D. Ryckelynck, Hyper reduction of mechanical models involving internal variables, International Journal for Numerical Methods in Engineering, Volume 77, Issue 1, Pages: 75-89, (2009).
  • D. Missoum Benziane, D. Ryckelynck, F. Chinesta, A new fully coupled two-scales modelling for mechanical problems involving microstructures: the 95/5 technic, Computer Methods in Applied Mechanics and Engineering, Volume 196, Issues 21-24, Pages 2325-2337, 2007.
  • J. Yvonnet, G. Coffignal, D. Ryckelynck, Ph. Lorong et F. Chinesta. A simple error indicator for meshfree methods based on natural neighbors. Computers & Structures, Vol. 84, Issue 21, pp 1301-1312, 2006.
  • D. Ryckelynck, F. Chinesta, E. Cueto et A. Ammar. On the ÒA PrioriÓ Model Reduction: Overview and Recent Developments. Archives of Computational Methods in Engineering, State of the Art Reviews, Special issue, Vol. 13, n¡1, pp 91-128, 2006.
  • A. Ammar, D. Ryckelynck, F. Chinesta and R. Keunings, On the reduction of kinetic theory models related to finitely extensible dumbells, Journal of Non-Newtonian Fluid Mechanics, 134, pp 136-147, 2006.
  • N. Sukumar, J. Dolbow, A. Devan, J. Yvonnet, F. Chinesta, D. Ryckelynck, Ph. Lorong, I. Alfaro, M.A. Martinez, E. Cueto et M. Doblarè, Meshless Methods and Partition of Unity Finite Elements. International Journal of Forming Processes, Vol. 8 Ðn¡4, pp. 409-427, 2005.
  • J. Yvonnet, F. Chinesta, Ph. Lorong, D. Ryckelynck, The constrained natural element method (C-NEM) for treating thermal models involving moving interfaces, International Journal of thermal sciences, 44:559-569, 2005.
  • D. Ryckelynck, L. Hermanns, F. Chinesta et E. Alarc—n, An Efficient A Priori Model Reduction for Boundary Element Models. Engineering Analysis with Boundary Elements, Volume 29, Issue 8, pp 796-801, 2005.
  • D. Ryckelynck, A priori hypereduction method : an adaptive approach, Journal of Computational Physics, Vol. 202 , N¡1 , pp 346 - 366, (2005).
  • J. Yvonnet, D. Ryckelynck, Ph. Lorong and F. Chinesta, A new extension of the natural element method for non-convex and discontinuous problems : the constrained natural element method (C-NEM), Int. J. Numer Meth. Engng, 60 :1451-1474, 2004.
  • F. Chinesta, Ph. Lorong, D. Ryckelynck, M. A. Martinez, E. Cueto, M. Doblare, G. Coffignal, M. Touratier, J. Yvonnet, Thermomecanical cutting model discretisation : eulerian or lagrangian, mesh or meshless ?, International Journal of forming processes, 7 (2) : pp. 83 Ð 98, 2004
  • D. Ryckelynck, Réduction a priori de modèles thermomécaniques, Comptes Rendus Mécanique, Volume 330, Issue 7, Pages 499-505, 2002.
  • J-P. Pelle et D. Ryckelynck, An Efficient Adaptive Strategy to Master the Global Quality of Viscoplastic Analysis , Computers & Structures, Ed. Elsevier Science, vol. 78, N¡1-3,pp. 169-184, 2000.
Publications spéciales des journaux scientifiques
  • J. Yvonnet, Ph. Lorong, D. Ryckelynck et F. Chinesta. Simulating Dynamic Thermo-Elasto-Plasticity in Large Transformations with Adaptative Refinement in the Natural Element Method: Application to Shear Banding. International Journal of Forming Processes, IJFP/Special Issue, Material Forming Process Optimization, pp 317-345 2005.
Livres et chapitres dans des ouvrages
  • J. Yvonnet, D. Ryckelynck, Ph. Lorong et F. Chinesta, The C-NEM for Dicontinuous Natural Element Galerkin Interpolation and Moving Interfaces. Springer, 43, 255-270, 2005
  • J. Yvonnet, D. Ryckelynck, Ph. Lorong, F. Chinesta et G. Coffignal. Piotr Breitkopf (eds.) Nouvelles Avancées dans les Méthodes sans Maillage Basées sur les Eléments Naturels Contraints pour la Simulation des Procédés., Extensions et alternatives à la méthode des éléments finis, Collection Mécanique et Ingénierie des Matériaux, Hermes Science, pp.21-68, 2006.


  • Cycle ingénieurs civils, Mécanique des Matériaux Solides
  • Deuxième cycle : Méthode des Eléments Finis. (ES Eléments Finis)
  • Master Recherche : Réduction de modèles, Méthodes numériques.

Organisation de congrès

  • Organisateur de WORM2014 et WORM2013 avec Felix Fritzen
  • Membre du comité scientifique de la conférence internationale "10th. International Conference on Modelling of Machining Operations" (University of Calabria) (2007).
  • Co-organisateur d'une session (invited session) "Model Reduction Strategies: Fundamentals and Applications" lors de la conférence ECCOMAS 2007, Computational Methods for Coupled Problems.
  • Membre du comité d'organisation d'un minisymposium intitulé "Machining and cutting technologies and modelling" , dans le cadre des conférences Esaform 2005 et 2006.
  • Membre du comité d'organisation d'un minisymposium intitulé "New and Advanced Numerical Strategies in Forming Process Simulation" , dans le cadre de la conférence Esaform à Salerno en avril 2003 et celle de Trondeim en avril 2004.



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