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Master mention Mécanique – M2 track: Solids… (‘S’)


 Multiphysics and Multiscale Modeling of Materials and Structures (or M4S)

Contact: Ziad Moumni & Michel Jabbour



In a scientific, technological, and industrial environment in which increasingly innovative solutions are constantly pursued, it is vital to describe the mechanical response of materials and structures in ever greater detail. This requires models that capture multiple length scales, which are coupled to each other. The fast developing research field of multiscale modeling of materials and structures is inherently multidisciplinary: physicists contribute their knowledge of the behaviour of condensed matter at small scales, solid mechanicians their expertise of the larger scales, and applied mathematicians their techniques for bridging scales. The M4S track is a master-level program that is situated at the interface between these three fields. It provides advanced training in the fundamentals of the mechanics of materials and structures, highlights the multiscale and multiphysics dimensions of the state-of-the-art research in solid mechanics, and emphasises a mathematical approach to the field.



Language of instruction: English

ECTS: 60

Oriented: Research and Industry

Duration: 1 year

Courses Location: École Polytechnique, ENSTA-Paris


Educational objectives of the track:

The M4S track trains students to become experts in the development and implementation of models that efficiently predict a wide range of physical phenomena observed in structures and materials. Pedagogically speaking, we aim at providing our students with the multidisciplinary scientific culture that would enable them to interact with physicists, mechanicians, applied mathematicians, and engineers. Our scientific goal is to prepare students for the fundamental research in solid mechanics that is likely to develop in the decades to come, and introduce them to its present and potential applications in state-of-the-art technologies. Finally, students will acquire the skills to work and communicate with ease in English-speaking environments.


Program structure:

Each of the courses below amounts to 3 ECTS

  • Fracture mechanics: classical theory and variational approach
  • Fracture mechanics: numerical and experimental projects
  • Materials modeling: from atomistic to macroscopic
  • Smart materials and structures
  • Modeling of heterogeneous materials and composites
  • Numerical methods in nonlinear mechanics
  • Multiphysics couplings: from thin-film growth to electromagnetic continua
  • Mechanics of inelastic materials and structures
  • Experimental methods in solid mechanics
  • Metamaterials, with applications in elastodynamics, acoustics and electromagnetism
  • Mechanics of slender structures


IP Paris labs involved :

  • LMS - UMR7649
  • IMSIA - UMR9219
  • LPMC - UMR7643

Career prospects:


The M4S track aims to train students for research in mechanics, and to a lesser degree for a career in industry. At the end of the master program, our students are expected to pursue a Ph.D., or alternatively to launch a career in research-and-development, be it in industry or in one of the several public research institutions of France.


Industrial partners:


  • CEA

  • PSA


  • EDF




Academic Prerequisites

Application files are reviewed by an admission committee, in particular to ensure that the prerequisites are met. Please note that admission is not automatic for students holding an M1 diploma. 

Language prerequisites : english

Procedure "TO APPLY"