M2 Advanced Materials, Structure and Energy for sustainable construction

Mechanics of Materials, finite-element method, statistics, probability theory

Lectures on Digital Image Correlation (DIC)

• Imaging devices (photons, electrons, and all the rest, Atomic Force Microscopy, resolution in space and time, 2D/3D, scanning/full field ...)
• Images (grey-level histograms, and encoding depth, color coding, distortions ...)
• Subpixel interpolation (pixel meaning from square box to cardinal splines, all are splines), correlation length, noise
• Optical flow (description of what is conserved in images and what is not). Brightness / Contrast / Temperature / Elevation (Atomic Force Microscopy)
• Kinematic basis (starting from translation and intercorrelation to finite-element)
• Least squares formulation, and numerical solution; 1) gradient descent; 2) multiscale. Discussion on the Hessian matrix (eigenvalue spectrum, eigenmodes)
• Uncertainty quantification, relation with Hessian matrix (motivation for regularization)

Specific challenges and applications of Digital Image Correlation for Civil Engineering structures, mini-structures and specimens

• Examples will illustrate applications of DIC in civil engineering, in particular for the detection and quantification of damage.

This course is devoted to the introduction of the general principles of Digital Image Correlation (DIC) as an inverse problem. It also deals with the quantification of measurement uncertainties.

• The students will master the theoretical and implementation aspects of DIC. They will be able to measure displacement fields via DIC, evaluate the measurement uncertainties, criticize the results, and choose advanced strategies for performing DIC measurements.

• Mesures de champs et identification en mécanique des solides, M. Grédiac, F Hild, Hermes science, 2011.
• Full-field measurements and identification in solid mechanics, M. Grédiac, F. Hild, John Wiley & Sons, 2012
• Comprehensive full-field measurements via Digital Image Correlation, S. Roux, F. Hild, in V. Silberschmidt (Edt.). Comprehensive Mechanics of Materials, 2, Elsevier, pp. 3-56, 2024.

Linear finite-element method, mechanics of materials for non-linear behavior, fundamentals on transfer, fundamentals on numerical methods (numerical integration, interpolation and solving a linear system)

• Architecture of a finite-element code for non-linear behavior, subroutine for the time integration of constitutive equations
• Computational techniques for the solution of non-linear and time-dependent constitutive equations within the framework of the finite-element method
• Consistent tangent operator
• Explicit and implicit time integration for the evolution equations
• Application to non-linear thermal transfer
• Application to elasto-plasticity
• Application to continuum damage mechanics
• Individual projects for own implementation

• This course introduces the application of the finite-element method for the numerical prediction of the response of a structure composed of materials with non-linear constitutive behavior. Students learn how to derive systematically the algorithm for any material behavior. The course emphasizes conceptual development for a variety of non-linear constitutive equations. Thermal and mechanical applications are considered. Various temporal schemes are studied to solve evolution equations.

• By the end of the course, students are able to derive their own non-linear finite element program for the material behavior of interest, in particular to implement new material models into a finite-element code.

• E.A. de Souza Neto, D. Peric, D.R.J. Owen, Computational Methods for Plasticity: theory and applications, 2008.

Continuum Mechanics, elasticity, anisotropy, tensor calculus

The thermodynamics of irreversible processes is presented for solid materials, starting from thermo-poroelasticity up to the framework of standard generalized materials. Associated and non-associated elastoplasticity models are described in a general manner, applicable to both metals and geomaterials.

• Shear/hydrostatic elastic energy density, deviatoric/hydrostatic stress, von Mises stress, anisotropy.
• State variables, poro-elasticity.
• 3D visco-elasticity (elastic energy density, dissipation potential, viscosity larger for shear moduli than for bulk modulus) as a toy model for general constitutive equations. 
• Thermodynamics of solid materials: 1st and 2nd principle of thermodynamics, Clausius-Duhem Inequality, intrinsic dissipation.
• Local state method, internal variables (including isotropic and kinematic hardening state variables).
• Infinitesimal strain framework of standard generalized materials (associated / non-associated models), positivity of the intrinsic dissipation, heat equation for local states described by internal variables.
• Associated elasto-plasticity: elasto-plasticity of metallic materials, elasto-plasticity of soils and rocks, poro-elasto-plasticity.

• The primary objective is to derive, within a thermodynamic framework that incorporates internal variables, the constitutive equations that describe the mechanical behavior of solids and soils throughout their lifetime.
• By the end of the course, students will have mastered three-dimensional formulations of elasto- (visco-) plasticity models.

• J. Lemaitre, J.-L. Chaboche, Mechanics of Solid Materials, Cambridge University Press, 1991 (3rd Edition in French 2020).

• Thermodynamics, heat transfer, and fluid mechanics
• Basic numerical methods
• Fundamentals of materials science or environmental processes

• Heat and mass transfer in porous and composite materials
• Diffusion, advection, and phase change mechanisms
• Sorption, capillarity, condensation, and chemical coupling
• Governing equations and constitutive relationships
• Multiphase modeling and micro–macro coupling
• Thermodynamic equilibrium and non-equilibrium processes
• Applications: insulation, energy storage, drying, geothermal systems, and remediation

This course provides an advanced understanding of heat, mass, and momentum transfer in porous and composite materials. It combines theoretical, modeling, and experimental approaches to study phenomena such as diffusion, advection, phase change, and interfacial interactions. The course emphasizes the link between micro- and macro-scale processes and develops advanced skills to model, simulate, and optimize multiphase and multiscale systems using computational tools and sustainability-driven design principles. It enables evaluation of material performance, improvement of energy efficiency, safety, and durability, and supports the development of sustainable technologies and resilient infrastructures in renewable energy, building physics, and environmental engineering. Furthermore, the course integrates a research-oriented perspective, fostering expertise in the design, analysis, and validation of innovative experimental setups, numerical models, and theoretical frameworks for investigating complex transport phenomena in porous media, preparing for contributions to cutting-edge scientific research.

Students will be able to:

• Formulate and analyze transport equations in porous media. 
• Model multiphase and multiscale processes. 
• Link micro- and macro-scale phenomena to optimize systems. 
• Evaluate energy and environmental system performance. 
• Propose sustainable, efficient engineering solutions.

• Nield & Bejan – Convection in Porous Media (Springer)
• Kaviany – Principles of Heat Transfer in Porous Media (Springer)
• Whitaker – The Method of Volume Averaging (Kluwer)
• Bennacer, R. – Research articles on heat/mass transfer and sustainability

• Basic modeling of mechanical and energy systems
• Elementary thermodynamics, heat transfer, or fluid mechanics (recommended)

• Introduction to controlled energy, mechanical, and transport systems
• Dynamic responses and stability analysis of active and reactive systems
• Principles of feedback and basic optimization
• Coupling of system components under varying boundary conditions
• Case studies: adaptive building systems, active damping, and others
• Research perspectives: design and validation of adaptive strategies

This course introduces the theoretical and practical fundamentals of active and reactive systems that adapt to time-varying conditions. It covers the principles of dynamic system behavior, system stability, regulation, and feedback control. Students learn how system components interact and respond to changes in boundary conditions and external inputs. The course emphasizes conceptual understanding of optimization strategies, control law design, and the theoretical foundations necessary for modeling adaptive systems, preparing for more advanced control applications in Control of active and Reactive Systems - Part II.

Students will be able to:

• Describe active and reactive system behavior under dynamic conditions; 
• Understand feedback, stability, and basic optimization principles;
• Analyze system responses to changing environments;
• Identify applications for adaptive strategies in engineering systems.

• Åström, K.J., Murray, R.M. – Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press
• Ogata, K. – Modern Control Engineering, Prentice Hall
• Bennacer, R. – Selected research articles on adaptive control and energy system optimization

Recommended to have followed “Coupled energy and mass transfers in porous media”, “Thermodynamics of solid materials – part II porous media”, and “Continuum damage mechanics for quasi-brittle materials”.

• Hydration and heat release
• Development of the microstructure and physical/mechanical properties
• Autogenous and drying shrinkage
• Basic and drying creep
• Modelling of thermal, chemical, hydric, and mechanical behavior at early-age and long-term

This course deals with the delayed behavior of construction materials under both environmental (relative humidity, temperature) and mechanical loadings from early age to long-term (hydration, shrinkage, creep). The experimental behavior and the role of the formulation are studied. Chemo-physical mechanisms and existing models are developed to predict material behavior.

• Understand the mechanisms of hydration, shrinkage, and creep in relation to the mix design and the ambient conditions
• Model the early-age and long-term behavior of cement-based materials:
• Analyze the cracking risk by shrinkage restraint through analytical calculations and numerical simulations.

• Ollivier J.-P., Torrenti J.-M., Carcasses M. (2012) Physical Properties of Concrete and Concrete Constituents, Wiley
• Benboudjema F., Carette J., Delsaute B., Honorio de Faria T., Knoppik A., Lacarrière L., Neiry de Mendonça Lopes A., Rossi P., Staquet S. (2018), Chapter 4, « Mechanical properties », dans Thermal Cracking of Massive Concrete Structures, Rilem Technical Committee CMS, Springer International Publishing, ISBN 978-3-319-76617-1, 2019

Thermodynamics of irreversible processes, three-dimensional elasto-(visco)plasticity.

• Chimio-elasticity, early age concrete.
• Third invariant, Lode angle, general expression of an isotropic criterion function
• Rankine, Hershey-Hosford, (Modified-)Mohr-Coulomb, Willam-Warnke, Mazars criterion functions.
• Marigo (1981) damage model and Lemaitre-Mazars (1980, 1984) damage model for concrete.
• Non associated elasto-plasticity: dilatancy of geo-materials, Drucker-Prager and Willam-Warnke elasto-plasticity.
• Plastic modulus, tangent operator for rate independent Drucker-Prager plasticity.
• Poro-elasto-plasticity, drained and undrained tangent operators.
• Elasto-visco-plasticity of soils.

• The students will master the three-dimensional, nonlinear material models used for the design of 3D Civil Engineering structures and/or soils subjected to complex loadings. 
• Specific constitutive equations are detailed, with a focus on non-isothermal loading conditions and poro-elasto-plasticity. The positivity of the intrinsic dissipation and the fulfillment of the second principle of thermodynamics are checked systematically.

• J. Lemaitre, J.-L. Chaboche, Mechanics of Solid Materials, Cambridge University Press, 1991 (3rd Edition in French, 2009). 
• J. Lemaitre, Materials Behavior Models, Volume III: Multiphysics Behaviors, Academic Press (2001). 
• O. Coussy, Poromechanics, Wiley, Edition Technip (2004).

To have followed the course “Digital Image Correlation and Identification (part I)”

Lectures on advanced Digital Image Correlation

• Optimal extractor (noise weighting, covariance, ...)
• Optimal Space-time Digital Image Correlation, Poisson noise
• Mechanical regularization
• Multiview correlation

Lectures on identification based on Digital Image Correlation

• Identification using the Finite-Element Method Updating (FEMU)
• Identification using the integrated Digital Image Correlation (iDIC).
• Integrated Digital Image Correlation for Linear Elastic Fracture Mechanics: measurement of the stress intensity factors KI, KII, supersingular terms

Application to Construction Engineering

• The identification of material parameters using temperature / displacement fields is performed via Finite Element Model Updating (FEMU) for heat transfer applications and/or Continuum Damage Mechanics. Different cost functions are discussed and their relationship to measurement uncertainties is established.

The course integrates research-oriented procedures dealing with advanced DIC techniques, such as mechanical regularization for robust DIC, space-time DIC, multiview and multimodal correlation for 3D surface and volumetric analyses. The students will also learn how to extract model parameters from measured displacement fields, or directly from images via integrated approaches.

• Mesures de champs et identification en mécanique des solides, M. Grédiac, F Hild, Hermes science, 2011.
• Full-field measurements and identification in solid mechanics, M. Grédiac, F. Hild, John Wiley & Sons, 2012
• Comprehensive full-field measurements via Digital Image Correlation, S. Roux, F. Hild, in V. Silberschmidt (Edt.). Comprehensive Mechanics of Materials, 2, Elsevier, pp. 3-56, 2024.

Continuum mechanics, engineering mathematics, fundamental/advanced Finite-Element Method

• 3D Wave and Shock wave propagation
• Dynamics experimental tests: Split Hopkinson Bar, spalling experiments, impact and penetration tests.
• Impact structural modeling: simplified approach and Finite-Element modeling
• ⁠Physical aspects of explosions and evaluation of their effects on structures: simplified formulations and Finite-Element modeling.
• Structures subjected to fire: phenomenological analysis and thermo-poro-mechanical modeling of concrete spalling
• ⁠Numerical methods for interface couplings (fluid–structure interaction) and volumetric couplings (coupled processes in porous media).

This course explores the scientific principles of extreme loads, such as impacts, blasts, fire, and other extreme events, with an emphasis on their effects on structures. Key topics include 3D wave propagation in solids, experimental and numerical modeling techniques, and the behavior of structures under impact and blast conditions. Students will gain theoretical knowledge to analyze and model the dynamic response of structures under extreme conditions.

• L. Davison, Fundamentals of Shock Wave Propagation in Solids, Springer, 2008 
• M.Y.H. Bangash, Shock, Impact and Explosion: Structural Analysis and Design, Springer; 2009.

mechanics of materials, non-linear finite element method, fundamentals on structural dynamics

• Parametrized partial differential equations and the challenges of their finite element approximation. Motivation of reduced-order and surrogate/approximated modeling (real-time, high-dimension, multi-query). 
• Traditional engineering approaches: static condensation, modal decomposition.
• Various reduced-order and surrogate modeling methods, such as Proper Orthogonal Decomposition (POD), reduced basis methods.
• Sampling strategies.
• Application to non-linear, transient, dynamic responses to parametric or/and random loads.

• Non-linear finite element analyses often entail significant computational costs, particularly in realistic civil, mechanical, and thermal engineering applications. To enable efficient parametric studies and large-scale simulations, Model Order Reduction (MOR) and surrogate modeling techniques have emerged as essential tools for reducing computational complexity while preserving the essential features of the underlying physical phenomena. 
• The course emphasizes both the mathematical foundations and computational implementation of reduced-order and surrogate models, i.e. smart approximated models, with particular focus on their application to computational mechanics and structural dynamics in Construction Engineering.

Students will gain the ability to develop, implement, and critically assess model-order reduction and surrogate modeling strategies designed to address high-fidelity problems at reduced computational cost, while developing awareness of the theoretical limitations and practical challenges inherent to these approaches.

• B. Haasdonk: Reduced Basis Methods for Parametrized partial differential equations - A Tutorial Introduction.
• F. Chinesta et al.: Model Order Reduction, Encyclopedia of Computational Mechanics.

Continuum Mechanics, elasto-plasticity, thermodynamics of irreversible processes

Three-dimensional isotropic (scalar) damage models are first described, such as those proposed by Marigo and Mazars. These models will be criticized from the points of view both of thermodynamics soundness and of representativity of multiaxial responses of cementitious materials.

The question of the tensorial nature of damage is then addressed. Effective stresses are defined, and the principle of strain equivalence is used to couple both elasticity and (visco-)plasticity with damage. A sound thermodynamics formulation of the loading-induced damage anisotropy of quasi-brittle materials is then provided. 

• Sought properties of a damage variable
• Effective stress concept (1D, 3D, isotropic damage, anisotropic damage).
• First damage models (Marigo 1981, Lemaitre-Mazars 1980, Mazars 1984).
• Thermodynamics of damage, on the difficulties of ensuring the positivity of the intrinsic dissipation in Continuum Damage Mechanics.
• Loading-induced anisotropic damage of quasi-brittle materials such as concrete.
• Permanent strains due to damage, coupling or not coupling with (visco-)plasticity
• Elements of modeling of cyclic mechanical responses of quasi-brittle materials.
• Visco-damage.
• Quasi-implicit numerical schemes for anisotropic damage models.
• Nonlocal, Eikonal Nonlocal, Gradient damage models, Phase field regularization.

• The main objective is to derive, in the thermodynamics framework of Continuum Damage Mechanics, three-dimensional constitutive equations for quasi-brittle materials such as concrete.
• The student will become fluent in Continuum Damage Mechanics. They will acquire the necessary insight to propose relevant tests and procedures for identifying the material parameters.

• J. Lemaitre, A course on damage mechanics, Springer Verlag, 1992.
• J. Lemaitre, R. Desmorat, Engineering damage mechanics: ductile, creep, fatigue and brittle failures, Springer, 2005.
• J. Lemaitre, J.-L. Chaboche, R. Desmorat, A. Benallal, Mécanique des matériaux solides, 3e éd. 2020.

Fundamentals/advanced Finite-Element Method, background in structural modeling, Engineering mathematics

This course focuses on the advanced application of the finite element method and non-linear material constitutive models in Construction Engineering. Emphasis is placed on the assessment of resilience under complex loading, up to failure. Key topics include simplified modeling approaches, advanced finite-element techniques, and resilience assessment methods tailored to extreme loading scenarios.

• Multi-fiber beam finite element
• Crack modeling in finite-element simulations of quasi-brittle material and structures: continuous damage model, embedded discontinuities, discrete elements
• Multiscale modeling
• Measures of Robustness and Resilience of structures: Risk-Oriented, Reliability-Based, Energy-Based, Accumulative Damage models… resilience Measures.

Built on the bases of engineering mathematics, mechanics, and structural analysis, the course “Advanced Structural Modeling” enables students to meet the growing challenges of modeling complex civil constructions up to failure.

By the end of the course, students will have the expertise to apply sophisticated numerical models that represent the mechanical degradation of Construction Engineering structures in both research and professional settings.

de Borst R., “Fracture and damage in quasi-brittle materials: A comparison of approaches”, Theoretical and Applied Fracture Mechanics, 2022

Bodnar B., Larbi W., Titirla, M., Deü J.-F., Gatuingt F., Ragueneau F., “Hyper-reduced order models for accelerating parametric analyses on reinforced concrete structures subjected to earthquakes", Computer-Aided Civil and Infrastructure Engineering, 2024

Desmorat R., Gatuingt F. and Ragueneau F., “Non standard thermodynamics framework for robust computations with induced anisotropic damage”, Int. J. Damage Mechanics., 2010.

Kotronis P, Davenne L & Mazars J (2004). Poutre multifibre Timoshenko pour la modélisation de structures en béton armé. Revue Française de Génie Civil, 2004.

Continuum Mechanics

• Geometric reformulation of Continuum Mechanics: configurations as embedding, the body as a manifold with border, stresses as powers/1-forms. Strain rate, finite strain, and stress tensors defined by pullback/pushforward operations. 
• Conservation laws are formulated using the Lie derivative.
• Differential forms, and their application to modern 4D formulation of electromagnetism.
• Primary and secondary field variables in physics and mechanics, a general Lagrangian framework for couplings formulation, and elements of variation calculus.

• The main objective is to introduce advanced geometry concept (Riemannian geometry, exterior calculus…) to formulate modern Continuum Mechanics and its coupling with electromagnetism.

• Kolev B., Desmorat R., An intrinsic geometric formulation of hyper-elasticity, pressure potential and non-holonomic constraints, Journal of Elasticity, 146(1), 29-63, 2021.
• Kolev B., Desmorat, R., Objective rates as covariant derivatives on the manifold of Riemannian metrics, Archive for Rational Mechanics and Analysis, 248(4), 66, 2024.
• Kolev K., Éléments de géométrie différentielle à l'usage des mécaniciens. 2020. hal-03330418

Probability theory, Continuum Mechanics, Structural analysis

• Review of the fundamentals of probability theory: random variables, information entropy, estimation, statistical analysis, stochastic fields
• Probabilistic modeling tools and uncertainty propagation methods, polynomial chaos, Monte Carlo simulation
• Description of random fields from Karhunen-Loève expansion, parametric studies from kriging approaches
• Machine learning: supervised learning for classification and regression, stochastic gradient, universal approximation theorem, two-layer neural networks, deep networks and convolutional networks, unsupervised and semi-supervised learning, autoencoders, generative adversarial networks (GANs)
• Risk assessment by combining a probabilistic approach and machine learning
• Application to a nonlinear structural response in civil engineering.

Unlike traditional deterministic design methods, which rely on fixed safety factors, probabilistic approaches explicitly account for uncertainty in loads, material properties, geometry, and environmental conditions. Students will learn how to quantify, model, and manage these uncertainties to make more informed and resilient engineering decisions.

In particular, this course explores how probabilistic mechanics and machine learning are combined to enhance risk assessment, reliability analysis, and decision-making in civil engineering. Traditional deterministic design approaches are being transformed by data-driven methods that can better capture uncertainty, complexity, and interdependence in infrastructure systems. Students will learn to apply probabilistic and machine learning techniques to predict performance, assess risk, and support resilient, adaptive engineering design.

• This course reviews the fundamentals of probability, statistics, and information theory to account for Uncertainty Modeling, Quantification, and Propagation in structural and material mechanics
• Reliability analysis for non-linear response.
• Statistical and Machine learning to build efficient surrogate models for structures or materials, taking advantage of extensive databases originating from either advanced experiments or numerical simulations.

• The stochastic finite element method: Past, present and future. G. Stefanou, 2009
• Sto chastic Finite Element Methods and Reliability. A State-of-the-Art Report. B. SUDRET, A. DER KIUREGHIAN, 2000

cement-based materials microstructure, basic statistics

• Presentation and discussion on experimental characterization of microstructure and porosity of construction materials: SEM, XRD, TGA, X-ray tomography, MIP etc.. 
• Analysis of research experimental devices for diffusion and permeation in reactive porous materials.
• Sensor principles used in thermal, diffusion, permeation etc. 
• Analysis of real experimental results: influence of Representative Elementary Volume (REV), material parameters variability and sensors uncertainties
• Practical works (4) realized by the students: durability analysis, accelerated chloride diffusion, permeation and micromorphology.

This course explores different experimental techniques on civil engineering materials in relation to their durability from the microscopic scale to the scale of the materials. Microstructural analysis (mineral phases, liquids and porosity) testing devices used in research applications are described and analyzed (SEM, XRD, TGA, X-ray tomography, MIP etc.). Sensors for the measurements of temperature, relative humidity, pressure etc. are also studied. Effect of Representative Elementary Volume (REV), material parameters variability and sensors uncertainties are discussed. 4 practical works will be realized by the students: durability analysis, accelerated chloride diffusion, permeation and micromorphology.

V.S. Ramachandran, James J. Beaudoin, Handbook of Analytical Techniques in Concrete Science and Technology, William Andrew Publishing, 2001, ISBN 9780815514374.

Nicolas BURLION, "Test techniques and experimental characterization", edited by Jean-Michel Torrenti, GillesPijaudier-Cabot and Jean-Marie Reynouard, Wiley, 2010, p. 3-55.

Recommended to have followed courses on Eco-conception, on Life Cycle Analysis, on durability of materials, and to have followed the two M2 courses “Durability of building materials” and “Coupled energy and mass transfers in porous media”.

• This module aligns with the objectives of sustainable development by studying the reduction of the environmental impact of construction through the vision of materials. 
• The aim of current research is to develop new cementitious materials that do not require clinker to form a cementitious paste, to recycle steels and concretes from deconstruction, or to recover waste or end-of-life products. 
• An introduction to the impact of construction and public works, the challenges and solutions for reducing the sector's carbon footprint, will provide an understanding of current and future issues. Then, the course proposes for the student an overview of the eco-friendly materials with regard to their properties (thermophysical, chemical, mechanical, and hygric properties...), their potential applications, in structures, for public works or in building (new, renovation, and rehabilitation), and their life-cycle analysis or carbon impact. The module will draw on notions of mechanics and structure, deferred behavior and durability, transfers in porous media, and the physical chemistry of reactions.
• Topics covered include: mineral and bio-based additions and substitutions for binders to reduce the use of clinker, which has a high carbon impact; concretes made from recycled aggregates; waste from deconstruction is a major issue; the management of sediments and products from aquaculture; wood as an element of sustainable development; and the use of renewable energies.

• This module aligns with the objectives of sustainable development by studying the reduction of the environmental impact of construction through the vision of materials. 
• The aim of current research is to develop new cementitious materials that do not require clinker to form a cementitious paste, to recycle steels and concretes from deconstruction, or to recover waste or end-of-life products. 
• An introduction to the impact of construction and public works, the challenges and solutions for reducing the sector's carbon footprint, will provide an understanding of current and future issues. Then, the course proposes for the student an overview of the eco-friendly materials with regard to their properties (thermophysical, chemical, mechanical, and hygric properties...), their potential applications, in structures, for public works or in building (new, renovation, and rehabilitation), and their life-cycle analysis or carbon impact. The module will draw on notions of mechanics and structure, deferred behavior and durability, transfers in porous media, and the physical chemistry of reactions.
• Topics covered include: mineral and bio-based additions and substitutions for binders to reduce the use of clinker, which has a high carbon impact; concretes made from recycled aggregates; waste from deconstruction is a major issue; the management of sediments and products from aquaculture; wood as an element of sustainable development; and the use of renewable energies.

• Ecostructures en béton: Comment diminuer l'empreinte carbone des structures en béton, Pierre-Claude Aïtcin, Sidney Mindess, Editions Eyrolles, 2013 - 276 pages
• Achour R., 2013. Valorisation et caractérisation de la durabilité d’un matériau routier et d’un béton à base de sédiments de dragage
• Amziane Sofiane, Arnaud Laurent, Les bétons de granulats d'origine végétale : Application au béton de chanvre, Ed Lavoisier, 2013 - 352 pages
• Sallé-Hoyet, Nadia. Matériaux et architecture durable fabrication et transformations, propriétés physiques et architecturales, approche environnementale. Ed Dunod, 2013.
• Fernando Pacheco Torgal, Said Jalali, Eco-efficient Construction and Building Materials, Springer London, 2011 - VIII, 247 pages
• Amziane, Sofiane, Sonebi, Mohammed. Bio-Based Building Materials - Trans Tech Publications Ltd, Switzerland, 2022.
• Federico Orsini, Paola Marrone, Approaches for a low-carbon production of building materials: A review. Journal of Cleaner Production 241 (2019) 118380.
• Julia L.K. Nußholza, Freja Nygaard Rasmussen, Leonidas Milios. Circular building materials: Carbon saving potential and the role of business model innovation and public policy. Resources, Conservation & Recycling 141 (2019) 308–316

cement-based materials microstructure, Coupled energy and mass transfers in porous media, basics in mechanical behavior of structures

• Presentation and discussion on chemo-physical mechanisms controlling the durability of reinforced concrete structures
• Analysis of the effects of temperature, relative humidity, chemical environment and mix design on the main pathologies of concrete and rebar
• Experimental measurements in laboratory and on field (destructive and nondestructive techniques) 
• Modelling of transport phenomena regarding leaching, CO2, chloride and sulfate transports, internal swelling
• Analysis of structural behavior of degraded reinforced concrete structures due to internal swelling

This course deals with the prediction of durability of building construction materials and structure. Main chemical attacks are analyzed in regards to environmental conditions (temperature, relative humidity and chemical environments) and material mix design :carbonation, chloride and (internal and external) sulphatic attacks, Alkali-silica reaction and leaching. Chemo-physical mechanisms from the nanostructure to the mesoscopic scales are detailed, in relation to the effects on the structure level. Experiments, multiscale and Multiphysics modeling approaches and design recommendations are analyzed and discussed.

Marios Soutsos, ICE Handbook of Concrete Durability. A practical guide to the design of resilient concrete structures, ICE Publishing, 576 pages

Kefei Li, Durability Design Of Concrete Structures, 2016 John Wiley & Sons Singapore Pte. Ltd.

heat transfer, thermodynamics of materials, basic image processing

• Part 1: Multiscale Thermo-Hygro-Morphic Behavior

The first part of the course focuses on the physical mechanisms and multiscale interactions governing the thermo-hygro-morphic behavior of porous and bio-based materials. The lectures address the coupling between heat, moisture, and deformation processes, as well as the influence of material structure and morphology across different observation scales. Special attention is given to the impact of these coupled phenomena on material aging and biodeterioration, highlighting how environmental conditions accelerate degradation and alter performance over time. Emphasis is placed on understanding experimental characterization methods and their integration into predictive models.

• Part 2: Morphological Characterization and Numerical Simulation

The practical sessions introduce digital tools for analyzing and simulating the behavior of real materials. Students first use ImageJ to perform morphological analysis of material microstructures (e.g., porosity, texture, orientation). Based on these results, a 3D simulation using COMSOL Multiphysics is carried out to model the thermo-hygro-morphic responses on an actual material geometry.

• The course aims to study, through innovative approaches, the hygro-morphic behavior in porous materials in general, and bio-based materials in particular. Several scales of observation are considered, from the cell wall scale of the plant component of these materials to the envelope scale.
• In terms of modeling, the aim is to improve current knowledge of existing models by considering the real 3D morphology of the material, including its hygro-morphic behavior. Particular attention is devoted to integrating the hysteresis phenomenon and the dimensional variation of the materials.

• Rima A., Abahri K., Bennai F., El Hachem & Bonnet M. (2021). Microscopic estimation of swelling and shrinkage of hemp concrete in response to relative humidity variations, Journal of Building Engineering
• Kosiachevskyi D., El-Hachem C., Abahri K., Bennacer R. & Chaouche M. (2021). Biomaterials heterogeneous displacement, strain and swelling under hydric sorption/desorption: 2D image correlation on spruce wood, Construction and Building Materials
• El Hachem C., Abahri K., Leclerc S. & Bennacer R., (2020). NMR and XRD quantification of bound and free water interaction of spruce wood fibers, Construction and Building Materials

• Fundamentals of thermodynamics and heat transfer
• Basic building physics and materials science
•  Elementary knowledge of renewable energy systems (recommended)

• Thermodynamic behavior of building envelopes and high-performance components, including multi-layered insulation and glazing
• Passive and hybrid strategies: free cooling, natural ventilation, thermal mass, daylighting, and energy management
• Integration of renewable energy systems and energy storage for net-zero and positive-energy objectives
• Modeling, simulation, evaluation, and research applications in sustainable and energy-positive building systems

This course provides an advanced understanding of building energy performance, with a focus on thermal dynamics, energy efficiency, and integration of renewable energy systems. It combines theoretical and applied perspectives on heat transfer, thermodynamic behavior of building envelopes, and dynamic interactions between building components and environmental conditions. The course investigates strategies to achieve net-zero or energy-positive buildings, including passive cooling, free cooling, thermal storage, and active energy management. Emphasis is placed on modeling, simulation, and optimization of energy flows, integrating component-level efficiency with system-level performance, and evaluating the interactions between renewable energy sources and building operation. The course also adopts a research-oriented approach, enabling students to develop scientific expertise in the analysis, design, and performance evaluation of sustainable building systems.

• Fabbri, K., et al. – Energy Efficiency in Buildings, Springer
• Bennacer, R. – Selected research articles on building energy performance and renewable integration

• Basic numerical methods and simulation tools
• Completion of Part I 
• Dynamics and control theory (recommended))

• Advanced modelling and simulation of controlled energy, mechanical, and transport phenomenon
• Optimization of component parameters and material responses under dynamic conditions
• Coupling control with heat, mass, and energy transfer processes
• Stability analysis and design of predictive, adaptive, and robust control laws
• Case studies: adaptive building systems, active damping, 
• Research applications: design and validation of innovative control strategies for multi-physics systems

This part (II) emphasizes advanced theoretical and applied aspects of active and reactive systems. It covers modeling of dynamic multi-physics systems, predictive, adaptive, and robust control strategies, and stability analysis under time-varying boundary conditions. The course develops skills in optimization of building system components and material responses, integrating control theory with energy, mechanical, and transport processes. It fosters research-oriented expertise in designing, simulating, and validating complex control strategies, bridging theory with practical applications in engineering and smart infrastructure.

Students will be able to:

• Model and simulate active and reactive systems using advanced theoretical and computational tools; 
• Apply predictive, adaptive, and robust control strategies; 
• Optimize system performance under dynamic conditions; 
• Integrate control with energy and mechanical system design; 
• Contribute to research and innovation in adaptive and resilient engineering systems.

• Åström, K.J., Murray, R.M. – Feedback Systems: An Introduction for Scientists and Engineers, Princeton University Press
• Ogata, K. – Modern Control Engineering, Prentice Hall
• Bennacer, R. – Selected research articles on adaptive control and energy system optimization

Experimental methods, durability, life cycle analysis, cement-based materials microstructure, modelling of transport phenomena in porous materials (energy and mass), numerical methods

• Analysis of experimental results in steady state and transient conditions. Identification of material parameters (diffusivity, permeability).
• Several projects will be proposed to students, and each group will have to choose a topic.
• Proposal of an ionic (chlorides) or gaseous (CO2) diffusion model taking into account porosity, then composition parameters. Numerical implementation in the linear then nonlinear case. Multi-criteria analysis to identify the optimal composition and geometry.
• Proposal of a model taking into account liquid water permeation (drying) and gas tightness. Coupling between the two models. Application to a containment building for nuclear reactors, to predict its service-life.

The objectives of this course are to apply the skills acquired in the field of experimental methods and modeling of transport phenomena in porous materials, as well as in the field of numerical methods. The experimental results (permeability and ion diffusion) obtained during the practical work in the experimental methods module will be used to predict the lifespan of a reinforced concrete structure (bridges, nuclear power plants, dams, etc.). A model will be developed by proposing hypotheses on transport mechanisms and analyzing boundary conditions. The solution of parabolic partial differential equations (PDE) in the linear and nonlinear domains will be implemented. A multi-criteria analysis (price, environmental impact: greenhouse gas emissions, resource depletion, etc.) will be carried out to identify the optimal geometry and composition of the material to be used.

• Kumar, P. - Mehta – Monteiro, P.: Concrete Microstructure, Properties, and Materials, McGraw Hill, third edition, http://dx.doi.org/10.1036/0071462899.
• Ababneh A., Benboudjema F., Xi Y., Chloride penetration in nonsaturated concrete, Journal of Materials in Civil Engineering, ASCE journal, 2003, 2(15), p. 183-191.

Basic heat transfer, basic coding

• Part 1: Direct Simulation.

After a brief review of heat transfers, various numerical methods used to solve the heat equation are reviewed, followed by a presentation of modal methods. The course alternates lectures and practical classes during which students code methods covered in class.

• Part 2: Inverse Problems.

The inverse problem is presented. Using the previously obtained reduced model, the objective is to identify a parameter of the problem, either a material property or a time-varying boundary condition.

• In addition to its obvious applications, heat transfer is omnipresent for the design of systems, whether in thermomechanics or metrology. Its precise consideration involves the numerical solution of the heat equation, which might require significant memory space and computation time. This often prohibits its implementation in iterative process encountered in inverse problems. These latter aim to determine causes or parameters from observed effects, and are crucial in various scientific and mathematical fields.
• The course is a numerical/code module applied to heat transfer. Its objective is to present modal reduction methods for the numerical solution of the heat equation, as well as their application to inverse problems such as parameter identification.

F. Joly, Y. Rouizi, O. Quéméner, Type of inverse problem, model reduction, model identification, Part B, Advanced Automn School in Thermal Measurements and Inverse Techniques METTI8, 24-29 september, Ile d’Oléron, France.

Mécanique des fluides élémentaire (bilans de masse, de quantité de mouvement, d'énergie. Théorème de Bernoulli).

- Aérogénération : historique, développement actuel et principes de base
- Eolienne standard : fonctionnement, rendement instantané et production annuelle
- Energies marines : éolien off-shore, hydroliennes et dispositifs houlo-moteurs

Des études de cas et des dimensionnement sont proposés sous forme d'exercices de TD et d'une séance de TP numérique encadré.

Le cours présente les grands principes, éprouvés ou émergents, sur lesquels les machines de production d'énergie renouvelable éolienne et marine sont conçus, avec un accent mis sur la modélisation en aérodynamique des rotors et sur la prédiction de l'énergie annuelle produite. Continuellement remis à jour, il aborde aussi l'actualité très fournie dans ces domaines.

- Compréhension et prévision de la conversion mécanique dans une machine de production d’énergie renouvelable éolienne ou marine

- Dimensionnement et design d’une machine de production d’énergie renouvelable éolienne ou marine

- Prévision de l’énergie produite annuellement par une machine de production d’énergie renouvelable éolienne ou marine.

HAU, E. (2006) Wind turbines, Fundamentals, technologies, application, economics, second edition, Springer. 

LE GOURIERES, D. (2008) Les éoliennes, Editions du Moulin Cadiou. Journal des Energies Renouvelables.

Base de la programmation (Python), maitrise d'un environnement sous Unix.

- Introduction générale sur le calcul haute performance
- Bases de l'utilisation d'un super-calculateur (Slurm)
- Fonctionnement de la bibliothèque MPI pour l'écriture d'un programme parallèle
- Etude de la performance.

Ce cours est une introduction à la programmation parallèle appliquée au domaine scientifique. Les ressources de calcul nécessaire à la résolution de nombreux problèmes physiques nécessitent l’utilisation de super-calculateurs. Les super-calculateurs sont des machines parallèles composées d’un grand nombre d’unités de calcul (processeur, GPU) connectées au travers d'un réseau extrêmement rapide. Le défi du Calcul Haute Performance est de faire travailler efficacement ensemble toutes ces unités de calcul.

L'UE s'organise autour de 4 séances de 3h45 avec une alternance de cours et de TD. L'UE est évalué par un projet.

- Cours de l'IDRIS sur MPI : https://www.idris.fr/formations/mpi/

Méthodes numériques (interpolation, différenciation, analyse de stabilité, ordre & consistance, différences finies)
Résolution de systèmes linéaires (méthodes directes, méthodes itératives)
Bases de la programmation (Fortran ou C, Python)

- Introduction à la méthodes des Volumes Finis et principes de base
- Résolution de problèmes modèles : équation de Laplace, équation d'Helmholtz
- Problème de convection-diffusion : schémas Upwind, Power-Law, Quick, TVD, ...
- Problèmatique du couplage vitesse-pression : introduction des spécifités des écoulements incompressibles, maillages décalés, méthodes stationnaires (SIMPLE, PISO) et instationnaires (méthode de projection)
- Méthodes de résolution des systèmes linéaires : méthodes directes (algorithme de Thomas), méthode itératives (multi-grille)
- Introduction aux méthodes de maillage adaptatif
- Implémentation d'un schéma de résolution de l'équation de Navier-Stokes pour des configurations académiques (cavité entraînée, cavité différentiellement chauffée).

La méthode des Volumes Finis est une méthode classique pour discrétiser les équations régissant les écoulements de fluide. Lors de ce cours, une introduction à cette méthode sera donnée, en présentant les principales caractéristiques et propriétés de la méthode, d'abord sur des équations modèles (transfert de la chaleur, stationnaire puis instationnaire, sans transport puis avec, mono-dimensionnel puis 2D, puis vers les équations de Navier-Stokes).
Ces techniques seront ensuite appliquées à de nombreux exemples pour discrétisation dans des Travaux Dirigés puis implémentation algorithmique et informatique dans des Travaux Pratiques.

Ce cours se restreint aux écoulements incompressibles. Une brève ouverture sera mentionnée vers les écoulements compressibles et leurs spécificités de résolution.

Cours. Travaux Dirigés pour travailler sur la discrétisation des équations. Projet pour l'implémentation de la méthode : accompagnement en Travaux Pratiques et travail personnel.

- Fletcher, C.A.J., Computational techniques for fluid dynamics, Vol. 1& 2, Springer Berlin Heidelberg. ed, 1991 

- Hirsch, C., Numerical computation of internal and external flows, Vol. 2, Wiley ed, 1990 

- Versteeg & Malalasekera, An Introduction to
Computational Fluid Dynamics, 2ème édition, éd.
Pearson, 2007

Mécanique des milieux continus, méthodes des éléments finis, analyse fonctionnelle, notions de programmation.

La modélisation et la simulation numérique sont au coeur des activités modernes en recherche et ingénierie. De ce fait, et pour assurer la fiabilité des résultats de simulation, la maîtrise des modèles et des calculs est une problématique fondamentale. L’objectif est de calculer juste au juste coût. Le cours vise à présenter les concepts de base utilisés pour atteindre cet objectif, ainsi que leur mise en œuvre pratique.
Les outils d’estimation d’erreur de discrétisation et d’adaptation de maillage dans le cadre de la méthode des éléments finis apparaissent comme précurseurs pour la vérification des modèles numériques. Cependant, la thématique englobe à présent un spectre beaucoup plus large d’outils impactant toute la chaine de modélisation. On peut citer par exemple la modélisation multi-fidélité, avec contrôle de l’erreur du modèle mathématique dans les techniques de réduction de modèle et de couplage multiéchelle par exemple, ou la modélisation pertinente en lien avec la richesse de l’information expérimentale (quantité et niveau de bruit des mesures) dans la résolution de problèmes inverses et l’assimilation de données. Toutes ces composantes sont abordées dans le cours.

Le cours présente d’abord les techniques classiques d’estimation d’erreur (basées sur les résidus d’équilibre, les techniques de lissage, ou l’erreur en relation de comportement) et d’adaptation de maillage dans le cadre de la méthode des éléments finis. Des extensions au contrôle de quantités d’intérêt (via la technique de l’adjoint) et aux problèmes non-linéaires (à partir d’arguments de dualité) sont faites. Ensuite, le contrôle de l’erreur de modèle est abordé pour les approches multiéchelles et de réduction de modèle (PGD, bases réduites). Enfin, la sélection des modèles en cohérence avec les données expérimentales est traité. Des développements récents de recherche sont montrés tout au long du cours et une sensibilisation aux challenges scientifiques actuels dans la thématique est apportée. Le cours est accompagné d’un projet numérique durant lequel les étudiants mettent en œuvre et analysent certaines méthodes de contrôle et d’adaptation pour en mesurer leurs performances.

Mécaniques des milieus continus, formulations variationnelles, méthodes des éléments finis, algèbre linéaire, méthodes numériques pour la résolution des systèmes linéaires

Dans ce cours sont présentées les stratégies de calcul multiéchelles par méthodes de décomposition de domaine (DDM) sans recouvrement. Les approches primales, duales et mixtes sont présentées dans le cadre de la mécanique des structures en élasticité linéaire. Les formulations continue et discrétisée correspondantes ainsi que leur mise en œuvre technique sont détaillées :

Présentation du problème et enjeux : problème de référence sous-structuré, généralités sur les DDM (mise en donnée, enjeux, environnement matériel) ;
Approches primale, duale et mixte : approches de Schur primale et duale, approches mixtes basées sur un Lagrangien augmenté ou sur un algorithme à deux directions de recherche ;
Stratégies de calcul multiéchelle par DDM, introduction du problème grossier : tests de qualification d’une DDM, préconditionnement du problème d’interface (BDD, FETI, DDM mixte basée sur la LATIN), résolution du problème grossier (solveur de Krylov, gradient conjugué projeté…) ;
Introduction au traitement par DDM des problèmes non-linéaires : approches classiques, méthode de Newton Krylov Schur, technique de relocalisation non-linéaire, approche globale en temps de type LATIN.

Le cours est accompagné d’un projet numérique durant lequel les étudiants mettrons en œuvre et coderont certaines des méthodes de décomposition de domaine vues en cours afin d’examiner et de comparer leurs performances sur un cas académique.

[1] P. Gosselet and C. Rey. Non-overlapping domain decomposition methods in structural mechanics. Archives of Computational Methods in Engineering, 13(4): 515-572, 2006 [2] C. Farhat and F.-X. Roux. A method of finite tearing and interconnecting and its parallel solution algorithm. International Journal for Numerical Methods in Engineering, 32: 1205-1227, 1991 [3] J. Mandel. Balancing domain decomposition. Communications in Numerical Methods in Engineering, 9: 233-241, 1993 [4] P. Ladevèze and A. Nouy. On a multiscale computational strategy with time and space homogeneization for structural

Disciplinary courses in the M2 program

Autonomous Learning instruction of a scientific thematic in the skills of a University Professor of the M2 program

Disciplinary courses of the M2 program

Each student carries out individual bibliography research on a scientific subject, under the guidance of a member of Laboratoire de Mécanique Paris-Saclay (LMPS), UMR CNRS  9026.

Students are trained in scientific methodology, including bibliographic analysis and the presentation of scientific results.

Disciplinary courses of the M2 program

This project aims to prepare students to communicate scientific results related to cutting-edge topics (writing an abstract,  a list of hihlights, a graphical abstract).

Disciplinary courses of the M2 program

Research internship

The internship enables the student to gain initial research experience within a research group. A research project, including a bibliography and own investigation (analytical development, modeling, or experiment), is carried out. A few collective and individual guidance sessions are organized by the Master program.

After agreement with the heads of the M2 programs, the opening course(s) can be chosen either among the Master programs lists of courses, or can be chosen from another M2 or among those proposed by the Graduate School Engineering and System Science. 

Examples of Opening Courses are:

• Course “UE Sport” (2.5 ECTS)
• Autonomous-Learning course (3 ECTS)
• Course from other M2 programs.

After agreement with the heads of the M2 programs, the opening course(s) can be chosen either among the Master programs lists of courses, or can be chosen from another M2 or among those proposed by the Graduate School Engineering and System Science. 

Examples of Opening Courses are:

• Course “UE Sport” (2.5 ECTS)
• Autonomous-Learning course (3 ECTS)
• Course from other M2 programs.