Mechanics of solids and structures

This course trains specialists of solid mechanics with a thorough understanding of the concepts and tools involved in modeling and simulating mechanical structures and their constituent materials. The course covers the non-linear behavior of materials, micro-mechanical modeling, homogenization, structural dynamics, numerical calculation methods (finite elements) in linear and non-linear contexts, and the modeling of fracture, damage, fatigue and instability phenomena in solids. These subjects are at the core of current industrial concerns, short- and medium-term research and technological development issues, and long-term research issues for the sector.

The courses offered include both fundamental and more specialized units, enabling students to enter the workforce or pursue a doctorate. The aim of the course is twofold:

• To train specialists in structural design, with an excellent command of industrial software, to meet the modern needs of large and medium-sized companies responsible for designing or controlling mechanically stressed industrial structures.
• Enable students to join the most advanced research teams in the fields of materials behavior and structural design, whether in university laboratories or in industry, by providing them with modern, advanced conceptual training.

Application fields are extremely varied, including transport, aeronautics, aerospace, energy, civil engineering, biomechanics and robotics.

The program is organized in partnership with the École Nationale des Ponts et Chaussées and is supported by major industrial research centers. The teaching team is made up of teacher-researchers, researchers from the Institut Jean le Rond d'Alembert (Unité Mixte de Recherche Sorbonne University - CNRS 7190) attached to the SMAER doctoral school (Sciences mécaniques, acoustique, électronique et robotique de Paris) of Sorbonne University, as well as industrialists specializing in the design and calculation of mechanical structures, and international partners.

First year:

• Hold a general bachelor's degree in Mechanics, Physics or Mathematics.

Second year:

• Hold a Master 1 in Mechanics, Physics or Mathematics,
• Hold an engineering degree with proven knowledge of Mechanics, Physics or Mathematics.

Applications from atypical backgrounds, which do not fall within the above-mentioned categories, will also be considered with particular attention paid to the excellence of the applicant's expertise in Mechanics, Physics or Mathematics.

The course comprises a common first year. Three subjects are offered in the second year:

• M2 - Modeling and Simulation (MS)
• M2 - Durability of Materials and Structures (DMS)
• M2 - Multi-scale Analysis for Materials and Structures (AMMS)

For detailed information, please see the following documents:

• Detailed presentation of the Master 2 Solid Mechanics: Materials and Structures
• Master 2 Solid Mechanics: Materials and Structures course catalog

An international pathway is also offered with Computational Mechanics.

First-year courses (M1) take place at Sorbonne University's Pierre et Marie Curie campus (Jussieu). They include a core curriculum shared with the other courses in the Mechanics specialization.

The Master's program boasts extensive computing resources, with computer rooms running several operating systems and featuring major scientific computing codes and libraries (Matlab, Abaqus, Castem, FEniCS, etc.). Students will also benefit from a high quality library.

Primary career opportunities include:

• Computation, Structures or Mechanics departments of the R&D divisions of major industrial groups in the aeronautics, automotive, civil engineering, space, nuclear, transport, energy sectors, etc. (EDF, CEA, Safran, Framatome, Renault, PSA, EADS, Dassault Aviation, Technip, IFP, SNCF, CETIM, Lafarge, ANDRA, Total, etc.);
• Medium-sized companies or high-tech start-ups needing experts in calculation and modeling of materials and structures for product design and optimization, development of innovative materials, and tools for physical investigation of materials;
• Cement industry, design offices specializing in construction and civil engineering works;
• IT service companies specializing in the development of numerical simulation software and/or subcontracting to major groups;
• Pursuit of a thesis for a career in academic or industrial research. Theses are carried out within the framework of partnerships between university laboratories and major industrial groups, under CIFRE funding, or with thesis grants offered by the French Ministry of Research, the CNRS or major research centers (IFSTTAR, CEA, ONERA, IFREMER, etc.).

Master 1

Master 2

In the first year, the curriculum covers the basics of continuum mechanics, material behavior, wave and vibration propagation phenomena, and numerical methods associated with mechanical models. After these core mechanical courses, introductory courses in Master 1 provide a broad perspective that prepares students for specific subjects of the specialization presented in Master 2.

First semester S1 (30 ECTS)

Second semester S2 (30 ECTS)

For details about the various teaching units, please refer to the document below:

• Master 1 Solid Mechanics: Materials and Structures course catalog

Planning

The Modeling and Simulation subject provides advanced training in the modeling and numerical simulation of physical phenomena encountered in the field of solid mechanics. Graduates will have a solid grasp of the concepts of continuum mechanics and the main classes of materials, be trainined in advanced methods of fracture and damage mechanics, have a good knowledge of methods for digitally solving linear and non-linear problems, and operational experience of computer simulation.

Among the specialization courses, the Structural Code Practice and Applications module (compulsory) develops the digital practice of the concepts and methods introduced in the core courses, and trains students in the advanced use of structural codes used in an industrial context (Abaqus) on problems of plasticity, homogenization, fracture, multiphysics couplings and non-linear calculations. This module will run in parallel with the core courses. The other specialization options comprise subjects specific to the theme (composites or structural stability), a supervised group project on an industrial or academic subject, or an introduction to fluid-structure coupling in biomechanics, shared with the Master in Fluid Mechanics and Computational Mechanics at Sorbonne University.

Program

15 ECTS core curriculum

• Fracture mechanics (3 ECTS, TC)
• Nonlinear behavior of solids (3 ECTS, TC)
• Digital computation of non-linear solids and structures (3 ECTS, TC)
• Introduction to homogenization in continuum mechanics (3 ECTS, TC)
• Image-based experimental analysis of materials and structures (3 ECTS, TC)

9 ECTS for specialization, including

• Structural design code practices and applications (6 ECTS, MS)
• One 3 ECTS unit to choose from:
  • - Composite structures: design and optimization (3 ECTS, MS)
  • - Structural stability (3 ECTS, MS)

6 elective ECTS

• Elasticity and strength of heterogeneous materials (AMMS - 3 ECTS)
• Multiscale approaches to metal plasticity (DMS - 3 ECTS)
• Damage (TC - 3 ECTS)
• Fatigue of materials and structures (TC - 3 ECTS)

Legends: (TC) Common Core courses; (MS) Courses specific to the MS theme; (AMMS) Courses specific to the AMMS theme; (DMS) Courses specific to the DMS theme.

Planning

The Modeling and Simulation theme provides advanced training in the modeling and digital simulation of physical phenomena encountered in the field of solid mechanics. Graduates will have a strong grasp of the concepts of continuum mechanics and the main classes of materials, be trained in advanced methods of fracture and damage mechanics, have a good knowledge of methods for digitally solving linear and non-linear problems, and operational experience of computer simulation.

Among the specialization courses, the Structural Code Practice and Applications module (compulsory) aims to develop digital practice of the concepts and methods introduced in the core courses, and to train students in the advanced use of structural codes used in an industrial context (Abaqus) on problems of plasticity, homogenization, fracture, multiphysics couplings and non-linear calculations. This module will run in parallel with the core courses. The other specialization options comprise of subjects specific to the theme (composites or structural stability), a supervised group project on an industrial or academic subject, or an introduction to fluid-structure coupling in biomechanics, shared with the Master in Fluid Mechanics and Computational Mechanics at Sorbonne University.

Program

15 ECTS core curriculum

• Fracture mechanics (3 ECTS, TC)
• Nonlinear behavior of solids (3 ECTS, TC)
• Numerical computation of non-linear solids and structures (3 ECTS, TC)
• Introduction to homogenization in continuum mechanics (3 ECTS, TC)
• Image-based experimental analysis of materials and structures (3 ECTS, TC)

9 ECTS for specialization, including:

• Structural design code practices and applications (6 ECTS, MS)
• One 3 ECTS unit to choose from:
  • Composite structures: design and optimization (3 ECTS, MS)
  • Stability of structures (3 ECTS, MS)

6 elective ECTS

• Elasticity and strength of heterogeneous materials (AMMS - 3 ECTS)
• Multiscale approaches to metal plasticity (DMS - 3 ECTS)
• Damage (TC - 3 ECTS)
• Fatigue of materials and structures (TC - 3 ECTS)

Legends: (TC) Common Core courses; (MS) Courses specific to the MS theme; (AMMS) Courses specific to the AMMS theme; (DMS) Courses specific to the DMS theme.

The Durability of Materials and Structures theme trains professionals with the highest level of scientific expertise, who are capable of dealing with the durability of future installations and identifying the condition of existing installations, in order to determine their residual lifespan and decide on possible reinforcements or optimize a maintenance policy. Particular attention is paid to potential hazards and analyzing the possible consequences of an accident. Applications will include engineering structures (bridges, tunnels, roads, etc.), energy production and storage structures (dams, STEPs, pressurized water nuclear reactors, offshore or onshore wind turbines, etc.) and buildings. At the end of the course, students will have mastered the main models of material and structural ageing, know how  to identify the state of an old structure, be familiar with methods of recognizing the hazards of materials and loads, or hazards linked to ignorance of the precise state of a structure. Students will be able to determine the probability of an accident or the lifespan of a structure, and rationally predict a problem to optimize a reinforcement or maintenance policy. This training could lead to a thesis in a research laboratory, or a position in a research center or an industrial or civil engineering design office responsible for studying the residual lifespan of structures, reinforcing structures or optimizing maintenance policies.

See also the ENPC website: http://www.enpc.fr/master-dms-durabilite-materiaux-structures

Program

12 ECTS common core. The TC courses required for this theme are :

• Fracture mechanics (3 ETCS, TC)
• Damage (3 ETCS, TC)
• Fatigue of materials and structures (3 ETCS, TC)
• Introduction to homogenization in continuum mechanics (3 ETC, TC)

12 ECTS for specialization

• Challenges of severe nuclear accidents / Seminar Challenges of electricity in energy systems (3 ECTS, DMS)
• Physics and operation of PWRs (3 ECTS, DMSE)
• In-service identification and monitoring of civil engineering structures and large systems (3 ECTS, DMS)
• Uncertainty in engineering and mechanics (3 ECTS, DMS)

6 elective ECTS

• Multiscale approaches to metal plasticity/concrete durability (3 ECTS, DMS)
• Modeling and simulation of structural equipment: application to seismic analysis (3 ECTS, DMS)
• Other AMMS, MS and TC courses.

Legend: (TC) Common Core courses; (MS) Courses specific to the MS theme; (AMMS) Courses specific to the AMMS theme; (DMS) Courses specific to the DMS theme.