## Onglets principaux

### Contact

**Bureau :**3:20-02&C

**Département/Laboratoire/Service :**CA/DER/LAB/LMS

### Bibliographie & travail en cours

PHD title: **Thermomechanical couplings during cyclic chemical fronts propagation**

PHD abstract: Many industrial topics intimately couple chemical reactions with mechanics (mechanical behaviour, strength, damage, fracture). One can cite, for example, corrosion, oxidation, lixiviation, hydrogen embrittlement, electrochemical reactions, which correspond, more generally, to the mechanochemistry framework. Some key applications concern the lifetime of Li-ion battery under charge-discharge cycles or of macro- and microelectronic systems under high frequency loadings, both conducting to the fatigue and fracture of components (anode, cathode, actuators, …) for which silicon is one of the more employed constitutive material. In these cases, respectively, cyclic lithiation and oxidation phenomena are coupled with irreversible behaviours as plasticity.

Though the fatigue and fracture mechanisms in metals or metalloids are studied since decades, which conducts to many models and criteria, the influence of chemical reactions on these mechanisms and the way to integrate them in a more general modelling framework need more efforts.

A common way in mechanochemistry consists in introducing a swelling strain contribution associated to the variation of local concentrations of chemical species. Then, this strain is added to elastic and/or plastic strains and this problem, coupling chemistry through a kinetic equation and mechanics, can be analytically and/or numerically solved. Within this framework, for example, the cyclic plasticity and shakedown in Li-ion electrodes during charge and discharge cycles.

However, during chemical reactions coupled with mechanics, in order to verify local energy balance separating reversible and irreversible processes, the later conducting to damage and fracture, a more general thermodynamics framework is needed. Some recent works conducted by Freidin’s team are going in this way, based on chemical potentials and affinity tensors. They recently proposed first analytical and numerical results in case of a viscoelastic constitutive law and simple plane and spherical problems, subjected to monotonic chemical reactions.

The objective of the PhD work is:

- to extend such a framework to elasto(visco)plasticity,

- to extend the studied cases to cyclic loadings,

- to generalize the shakedown concept in pure mechanical cyclic loadings to to

mechanochemistry,

- to propose a complete numerical framework, coupling chemisty and mechanics,

- to derive new fatigue criteria in presence of chemical reactions based on this

extended shakedown concept

In order to validate this approach, original experiments under cyclic loadings (tension, flexion) will be conducted on silicon specimens in presence of oxidation reaction front. The objective of such experiments will be to study the kinetics of such a front by using coupled full-field measurements (displacements and temperatures) at local scales and to compare the obtained results with analytical and/or numerical results.

### Publications et Liens

A. Freidin, N. Morozov, S. Petrenko, E. Vilchevskaya. Chemical reactions in spherically-symmetric problems of mechanochemistry, Acta Mech. (2016) 227: 43. https://doi.org/10.1007/s00707-015-1423-2

### Hal

{{ type="webpage_from_hal" url="http://hal.univ-grenoble-alpes.fr/Public/afficheRequetePubli.php?auteur_exp=boris,morel&CB_auteur=oui&CB_titre=oui&CB_article=oui&langue=Francais&tri_exp=annee_publi&tri_exp2=typdoc&tri_exp3=date_publi&ordre_aff=TA&Fen=Aff&css=../css/VisuRubriqueEncadre.css}}

### Cours :

#### PHY201 - Classical Mechanics (2018-2019)

This course introduces students to mechanics of complex system. After a reminder of the classical concepts of point mechanics (covered in PHY101), the course extends these concepts to more general systems. Using energy-based formalisms, it provides a comprehensive approach to the concepts of force balance and moments, leading to the equations of the movement. This permits students to approach the concepts of oscillators, stabilities and behavior law. The energy-based approach that is at the heart of this course is also found in many other fields of physics: relativity, quantum physics, electromagnetism, etc.

#### PHY207 - Advanced Lab II (2018-2019)

In Advanced Lab II, students have the opportunity to apply their physics knowledge they have acquired over the course of 7 distinct lab sessions of 4 hours each. PHY207 provides an in-depth study of a wide range of physical phenomena such as fundamental and applied optics (Fourier optics, optical fiber communication), atomic and nuclear physics (Balmer series, Nuclear magnetic resonance), thermodynamics (low temperature physics, SF6 critical point) and the mechanics of deformable bodies.

Upon completion of this course, students will have acquired advanced experimental skills allowing them to set up, carry out and to critically analyze experiments in physics and mechanics.

#### PHY201 - Classical Mechanics (2019-2020)

This course introduces students to mechanics of complex system. After a reminder of the classical concepts of point mechanics (covered in PHY101), the course extends these concepts to more general systems. Using energy-based formalisms, it provides a comprehensive approach to the concepts of force balance and moments, leading to the equations of the movement. This permits students to approach the concepts of oscillators, stabilities and behavior law. The energy-based approach that is at the heart of this course is also found in many other fields of physics: relativity, quantum physics, electromagnetism, etc.

#### PHY207 - Advanced Lab II (2019-2020)

In Advanced Lab II, students have the opportunity to apply their physics knowledge they have acquired over the course of 7 distinct lab sessions of 4 hours each. PHY207 provides an in-depth study of a wide range of physical phenomena such as fundamental and applied optics (Fourier optics, optical fiber communication), atomic and nuclear physics (Balmer series, Nuclear magnetic resonance), thermodynamics (low temperature physics, SF6 critical point) and the mechanics of deformable bodies.

Upon completion of this course, students will have acquired advanced experimental skills allowing them to set up, carry out and to critically analyze experiments in physics and mechanics.

#### Exemple d'un cours

#### Plan de continuité d'activité d'enseignement

#### PHY201 - Classical Mechanics (2020-2021)

This course introduces students to the Lagrangian and Hamiltonian mechanics.

Starting from the concepts of Newtonian mechanics, the course extends these

concepts to a more systematic description of the mechanics, adapted to complex

systems. The course will mostly use examples from the dynamics and vibrations of

mechanical systems, with progressively increasing complexity. Examples from

other fields of physics will be also proposed (electromagnetism, astrophysics,

chaos,...)

After a reminder of the classical concepts of point mechanics, the course

extends these concepts to the Lagrangian formalism and to the least action

principle. The Lagrangian formalism will be used to describe the mechanics of

rigid bodies. Lagrangian formalism will then be extended to the Hamiltonian

mechanics which is at the core of quantum physics and other modern theories in

physics. We will also present some extensions of Lagrangian and Hamiltonian

mechanics to other fields of physics.

Upon completion of this course, students master equations and principles in

analytical mechanics. They will be able to discuss the relevance of the chosen

model, as well as derive and solve simple models taken from their environment.

Main concepts covered: Fundamental law of dynamics; kinetic and potential

energy. Linearized equations of motion, dynamics of linear coupled oscillators.

Constraints and generalized coordinates, D'Alembert principle, Hamilton

principle, Euler-Lagrange equations of motion, conservation of energy and

momentum. Rigid body, center of mass, Euler angles, Moment of inertia and

inertia tensor, Euler equation of motion. Equations of Hamilton, conservation

theorem, canonical transformation, Poisson brackets.

This course introduces students to mechanics of complex system. After a reminder of the classical concepts of point mechanics (covered in PHY101), the course extends these concepts to more general systems. Using energy-based formalisms, it provides a comprehensive approach to the concepts of force balance and moments, leading to the equations of the movement. This permits students to approach the concepts of oscillators, stabilities and behavior law. The energy-based approach that is at the heart of this course is also found in many other fields of physics: relativity, quantum physics, electromagnetism, etc.