## Delivered study plan 2021/2022

PhD COURSE 2021/ 2022

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Hands on Continuum Mechanics with COMSOL

Luciano Teresi

Dip. Matematica e Fisica, Università Roma Tre

Schedule: March 2022;

Four lectures on Tue 1, Thu 3, Tue 8, Thu 10, from 15:00 to 18:00

Venue: Lab Informatico, nuovo padiglione aule, Dip. Matematica e Fisica, Università Roma Tre, Largo S. Leonardo Murialdo 1, Roma

Goal: understand the fundamentals of continuum mechanics through worked examples. Participants will tackle some typical problems of continuum mechanics, and will learn to implement a given problem using the weak formulation into the COMSOL software and to discuss the solution.

Synopsis of lectures

1) Browse a model of nonlinear solid mechanics, from the implementation to the solution. A first glance at the fundamentals of continuum mechanics: Kinematics, Constitutive, Balance laws. Differential form (strong) versus Integral form (weak). Worked example: large deformations of a hyperelastic solid under loadings.

2) Material Versus Spatial description. A continuum body as a differentiable manifold. Tell the difference between tensors: strain tensor versus stress tensor. Pull back & push forward of scalar, vector and tensor fields. Geometric elements; change of densities.

3) Solid mechanics versus Fluid mechanics Kinematical constraints; isochoric motion. Reference stress (Piola) & Actual stress (Cauchy). Polar decomposition theorem; eigenspace of the stress tensor and of the strain tensor

4) Non linear solid mechanics Worked example: large deformations of a hyperelastic solid under distortions. Target metric.

5) Material response Worked example: from elastic energy to the constitutive law for the stress. Transversely isotropic materials. Fiber reinforced materials. Worked example: fiber reinforced hyperelastic solid under traction.

6) Fluid dynamics Tackling Navier Stokes equations. Worked examples: fluid in a channel; fluid around an obstacle.

7) Fluid-Structure interactions - theory Worked examples: understand the moving mesh technique; how to write the problem of a beam immersed in a fluid.

8) Fluid-Structure interactions - practice Worked example: implement and solve the problem of an oscillating beam immersed in a fluid.

Practical Info: luciano.teresi@uniroma3.it

How to get here: there are two main entrances, both with a free parking lot. Largo San Leonardo Murialdo 1; best if you are arriving by public transportation https://goo.gl/maps/evgn13joYVmvd2Ux6 Lungotevere Dante; best for private transport https://goo.gl/maps/jCVYgEW6DGwd6B9o6

Software: it is of the essence to have a computer with COMSOL installed, version 5.6 or later. For all participants, it will be possible to install a demo version of the software on their personal computer.

Class Materials: classroom notes, COMSOL models, and other useful material will be distributed with Microsoft Teams through a dedicated Team with private acces. Send an email to luciano.teresi@uniroma3.it to be added to the Team.

Lectures. All lectures will be in hybrid mode, both in presence and in streaming; lectures will be also registered. Due to the "hands-on" approach, participants are recommended to attend in person.

Bio short

Prof. Luciano Teresi holds a MD in Aerospace Engineering, and a Ph.D. in Theoretical and Applied Mechanics from Sapienza, University di Roma, Italy. He is now Prof. of Mathematical Physics at the Dept. of Mathematics and Physics, University of Roma Tre, Italy, where he teaches graduate courses in Finite Elements Methods, and in Mathematics of Machine Learning. His main research activity is in Continuum Physics, with a focus on Active Soft Matter, Hydrogels, and Biological Tissues.

__________________________________________________________________________________________________

-----------------------------------------------------------------------------------------------------------------------------------------------------------------

PhD COURSE 2020 / 2021

-------------------------------------------------------------------------------------------------------------------------------------------------------------------

PhD Course "Nonlinear Elasticity"

The course touches upon all the fundamental aspects of nonlinear elasticity, from the analysis of deformation and stress, to the constitutive response and modelling of soft solids, to the lab experiments required to obtain their material properties, and to the concepts of equilibrium and energy minimisation. The final part of the course is devoted to the analysis of several worked examples, spanning a variety of problems of high technical importance".

Date & durata: 24th May 2021 ( 5 per week).

The teacher will send the link to the e-mails of all PhD students

1. Introduction

1.1. Context

1.2. New notions in algebra

1.3. Vectors

1.4. Tensors

1.5. Eigenvalues and eigenvectors

1.6. Jacobi's identity

1.7. Differential operators

2. Deformations

2.1. Bodies, configurations and deformations

2.2. The deformation gradient

2.3. Differential operators in different configurations

2.4. Deformation of line, area and volume elements

2.5. Further results of tensor algebra

2.6. Stretch, shear and strain of line elements

2.7. Homogeneous deformations

2.8. Integration of tensors

3. Stress

3.1. Balance equations

3.2. The theory of stress: Cauchy's theorem

3.3. Normal and shear stresses

3.4. Principal stresses and principal axes of stress

3.5. Some states of stress

3.6. The nominal stress tensor

3.7. Work

4. Constitutive equations

4.1. Hyperelastic materials

4.2. Objectivity

4.3. Material symmetry

4.4. Isotropic hyperelasticity

4.5. Stress-deformation relations in terms of invariants

4.6. Stress-deformation relations in terms of stretches

4.7. Incompressible hyperelastic solids

4.8. Examples of strain-energy functions

4.9. Simple tension testing

4.10. Simple shear testing

5. Exact solutions of non-linear elasticity

5.1. Universality of homogeneous deformations

5.2. Pure torsion of incompressible materials

5.3. Energy method for the Poynting effect

5.4. Inflation of a spherical membrane

5.5. Energy method for the inflation of spherical membranes

5.6. Electroactive membranes

-----------------------------------------------------------------------------------------------------------------------------------------------------------------

Mechanics and remodeling in anisotropic inelastic materials

Miles Rubin - Technion Israel Institute of Technology (Israel) April 7, 2021

Eulerian formulation of inelasticity

Alain Goriely - University of Oxford (England) April 14, 2021

A field theory for plant tropism

Luigi Preziosi - Politecnico di Torino (Italy) April 21, 2021

Cell reorientation over a stretched substrate: experiments and

mechanical model

Jacopo Ciambella - Sapienza Università di Roma (Italy) April 28, 2021

Remodelling in viscoelastic anisotropic materials

-------------------------------------------------------------------------------------------------------------------------

Mechanical morphing of active gels

Opening lecture: November 13, 2020

Frank Julicher - Max Plank Institute for Complex Systems (Germany)

Self-organization of active surfaces

Taylor Ware - Texas A&M University (TX USA) November 20, 2020

Programmable, Shape-Morphing Hydrogels Enabled

by Liquid Crystals and Living Cells

Luciano Teresi - University Roma Tre (Italy) November 27, 2020

Dynamics of liquid transport in active gels

Mattia Bacca - The University of British Columbia (BC Canada) December 4, 2020

Contraction of Active Gels via Molecular Motor Activity:

A theory based on Transient Microstructural Evolution

Anne Bernheim - Ben Gurion University of the Negev (Israel) December 11, 2020

3D shape transformation in active biological materials

-------------------------------------------------------------------------------------------------------------------------

Calendar of the course “Calculus of variations in mechanics” delivered by Prof. Giuseppe Ruta

Monday September, 9 2019 11: 00-13: 00

Friday September, 13 2019 11: 00-13: 00

Friday September,20 2019 11: 00-13: 00

Monday September,23 2019 11: 00-13: 00

Friday September,27 2019 11: 00-13: 00

Monday September,30 2019 11: 00-13: 00

Sala Multimediale at the Department of Mechanical and Aerospace Engineering.

------------------------------- ------------------------------- ------------------------------- -------------------------------

AA 2018

Stochastic processes and Turbulence delivered by Sergio Chibbaro

The purpose of the course is to provide a general introduction to stochastic processes, which will be presented as modelling tools for various issues in physics, chemistry and engineering, with particular focus on fluid mechanics.

A general overview of probability and stochastic equations will be given. Furthermore, the course will propose a general presentation of key aspects of stochastic processes in relation to numerical simulations (PDF models, Lagrangian models, Monte Carlo methods, etc).

Then, the emphasis of the course will be on fluid mechanical issues, notably on turbulence and two-phase flows with a presentation of the main issues of the stochastic modelling of Turbulence. Large deviations will be presented in a nutshell.

------------------------------- ------------------------------- ------------------------------- -------------------------------

AA 2018

Statistical Mechanics

Calendar of Statistical Mechanics delivered by prof. Emilio Cirillo:

09-apr-18 9:30-13:00

16-apr-18 9:30 -13:00

23-apr-18 9:30 -13:00

07-mag-18 9:30 -13:00

14-mag-18 9:30 -13:00

21-mag-18 9:30 -13:00

28-mag-18 9:30 -13:00

Sala Multimediale at the Department of Mechanical and Aerospace Engineering.

------------------------------- ------------------------------- ------------------------------- -------------------------------

AA 2018

Calendar of Soft mechanics and instabilities delivered by Prof. Paola Nardinocchi and Prof. Giuseppe Ruta

01/10/2018 9:00-12:30

02/10/2018 9:00-12:30

08/10/2018 9:00-12:30

09/10/2018 9:00-12:30

15/10/2018 9:00-12:30

16/10/2018 9:00-12:30

22/10/2018 9:00-12:30

23/10/2018 9:00-12:30

Aula "caveau" (Area Ingegneria Strutturale (AIS), close to the minimarket)

-----------------------------------------------------------------------------------------------------------------------------------------------------------------

Hands on Continuum Mechanics with COMSOL

Luciano Teresi

Dip. Matematica e Fisica, Università Roma Tre

Schedule: March 2022;

Four lectures on Tue 1, Thu 3, Tue 8, Thu 10, from 15:00 to 18:00

Venue: Lab Informatico, nuovo padiglione aule, Dip. Matematica e Fisica, Università Roma Tre, Largo S. Leonardo Murialdo 1, Roma

Goal: understand the fundamentals of continuum mechanics through worked examples. Participants will tackle some typical problems of continuum mechanics, and will learn to implement a given problem using the weak formulation into the COMSOL software and to discuss the solution.

Synopsis of lectures

1) Browse a model of nonlinear solid mechanics, from the implementation to the solution. A first glance at the fundamentals of continuum mechanics: Kinematics, Constitutive, Balance laws. Differential form (strong) versus Integral form (weak). Worked example: large deformations of a hyperelastic solid under loadings.

2) Material Versus Spatial description. A continuum body as a differentiable manifold. Tell the difference between tensors: strain tensor versus stress tensor. Pull back & push forward of scalar, vector and tensor fields. Geometric elements; change of densities.

3) Solid mechanics versus Fluid mechanics Kinematical constraints; isochoric motion. Reference stress (Piola) & Actual stress (Cauchy). Polar decomposition theorem; eigenspace of the stress tensor and of the strain tensor

4) Non linear solid mechanics Worked example: large deformations of a hyperelastic solid under distortions. Target metric.

5) Material response Worked example: from elastic energy to the constitutive law for the stress. Transversely isotropic materials. Fiber reinforced materials. Worked example: fiber reinforced hyperelastic solid under traction.

6) Fluid dynamics Tackling Navier Stokes equations. Worked examples: fluid in a channel; fluid around an obstacle.

7) Fluid-Structure interactions - theory Worked examples: understand the moving mesh technique; how to write the problem of a beam immersed in a fluid.

8) Fluid-Structure interactions - practice Worked example: implement and solve the problem of an oscillating beam immersed in a fluid.

Practical Info: luciano.teresi@uniroma3.it

How to get here: there are two main entrances, both with a free parking lot. Largo San Leonardo Murialdo 1; best if you are arriving by public transportation https://goo.gl/maps/evgn13joYVmvd2Ux6 Lungotevere Dante; best for private transport https://goo.gl/maps/jCVYgEW6DGwd6B9o6

Software: it is of the essence to have a computer with COMSOL installed, version 5.6 or later. For all participants, it will be possible to install a demo version of the software on their personal computer.

Class Materials: classroom notes, COMSOL models, and other useful material will be distributed with Microsoft Teams through a dedicated Team with private acces. Send an email to luciano.teresi@uniroma3.it to be added to the Team.

Lectures. All lectures will be in hybrid mode, both in presence and in streaming; lectures will be also registered. Due to the "hands-on" approach, participants are recommended to attend in person.

Bio short

Prof. Luciano Teresi holds a MD in Aerospace Engineering, and a Ph.D. in Theoretical and Applied Mechanics from Sapienza, University di Roma, Italy. He is now Prof. of Mathematical Physics at the Dept. of Mathematics and Physics, University of Roma Tre, Italy, where he teaches graduate courses in Finite Elements Methods, and in Mathematics of Machine Learning. His main research activity is in Continuum Physics, with a focus on Active Soft Matter, Hydrogels, and Biological Tissues.

__________________________________________________________________________________________________

-----------------------------------------------------------------------------------------------------------------------------------------------------------------

PhD COURSE 2020 / 2021

-------------------------------------------------------------------------------------------------------------------------------------------------------------------

PhD Course "Nonlinear Elasticity"

The course touches upon all the fundamental aspects of nonlinear elasticity, from the analysis of deformation and stress, to the constitutive response and modelling of soft solids, to the lab experiments required to obtain their material properties, and to the concepts of equilibrium and energy minimisation. The final part of the course is devoted to the analysis of several worked examples, spanning a variety of problems of high technical importance".

Date & durata: 24th May 2021 ( 5 per week).

The teacher will send the link to the e-mails of all PhD students

1. Introduction

1.1. Context

1.2. New notions in algebra

1.3. Vectors

1.4. Tensors

1.5. Eigenvalues and eigenvectors

1.6. Jacobi's identity

1.7. Differential operators

2. Deformations

2.1. Bodies, configurations and deformations

2.2. The deformation gradient

2.3. Differential operators in different configurations

2.4. Deformation of line, area and volume elements

2.5. Further results of tensor algebra

2.6. Stretch, shear and strain of line elements

2.7. Homogeneous deformations

2.8. Integration of tensors

3. Stress

3.1. Balance equations

3.2. The theory of stress: Cauchy's theorem

3.3. Normal and shear stresses

3.4. Principal stresses and principal axes of stress

3.5. Some states of stress

3.6. The nominal stress tensor

3.7. Work

4. Constitutive equations

4.1. Hyperelastic materials

4.2. Objectivity

4.3. Material symmetry

4.4. Isotropic hyperelasticity

4.5. Stress-deformation relations in terms of invariants

4.6. Stress-deformation relations in terms of stretches

4.7. Incompressible hyperelastic solids

4.8. Examples of strain-energy functions

4.9. Simple tension testing

4.10. Simple shear testing

5. Exact solutions of non-linear elasticity

5.1. Universality of homogeneous deformations

5.2. Pure torsion of incompressible materials

5.3. Energy method for the Poynting effect

5.4. Inflation of a spherical membrane

5.5. Energy method for the inflation of spherical membranes

5.6. Electroactive membranes

-----------------------------------------------------------------------------------------------------------------------------------------------------------------

Mechanics and remodeling in anisotropic inelastic materials

Miles Rubin - Technion Israel Institute of Technology (Israel) April 7, 2021

Eulerian formulation of inelasticity

Alain Goriely - University of Oxford (England) April 14, 2021

A field theory for plant tropism

Luigi Preziosi - Politecnico di Torino (Italy) April 21, 2021

Cell reorientation over a stretched substrate: experiments and

mechanical model

Jacopo Ciambella - Sapienza Università di Roma (Italy) April 28, 2021

Remodelling in viscoelastic anisotropic materials

-------------------------------------------------------------------------------------------------------------------------

Mechanical morphing of active gels

Opening lecture: November 13, 2020

Frank Julicher - Max Plank Institute for Complex Systems (Germany)

Self-organization of active surfaces

Taylor Ware - Texas A&M University (TX USA) November 20, 2020

Programmable, Shape-Morphing Hydrogels Enabled

by Liquid Crystals and Living Cells

Luciano Teresi - University Roma Tre (Italy) November 27, 2020

Dynamics of liquid transport in active gels

Mattia Bacca - The University of British Columbia (BC Canada) December 4, 2020

Contraction of Active Gels via Molecular Motor Activity:

A theory based on Transient Microstructural Evolution

Anne Bernheim - Ben Gurion University of the Negev (Israel) December 11, 2020

3D shape transformation in active biological materials

-------------------------------------------------------------------------------------------------------------------------

Calendar of the course “Calculus of variations in mechanics” delivered by Prof. Giuseppe Ruta

Monday September, 9 2019 11: 00-13: 00

Friday September, 13 2019 11: 00-13: 00

Friday September,20 2019 11: 00-13: 00

Monday September,23 2019 11: 00-13: 00

Friday September,27 2019 11: 00-13: 00

Monday September,30 2019 11: 00-13: 00

Sala Multimediale at the Department of Mechanical and Aerospace Engineering.

------------------------------- ------------------------------- ------------------------------- -------------------------------

AA 2018

Stochastic processes and Turbulence delivered by Sergio Chibbaro

The purpose of the course is to provide a general introduction to stochastic processes, which will be presented as modelling tools for various issues in physics, chemistry and engineering, with particular focus on fluid mechanics.

A general overview of probability and stochastic equations will be given. Furthermore, the course will propose a general presentation of key aspects of stochastic processes in relation to numerical simulations (PDF models, Lagrangian models, Monte Carlo methods, etc).

Then, the emphasis of the course will be on fluid mechanical issues, notably on turbulence and two-phase flows with a presentation of the main issues of the stochastic modelling of Turbulence. Large deviations will be presented in a nutshell.

------------------------------- ------------------------------- ------------------------------- -------------------------------

AA 2018

Statistical Mechanics

Calendar of Statistical Mechanics delivered by prof. Emilio Cirillo:

09-apr-18 9:30-13:00

16-apr-18 9:30 -13:00

23-apr-18 9:30 -13:00

07-mag-18 9:30 -13:00

14-mag-18 9:30 -13:00

21-mag-18 9:30 -13:00

28-mag-18 9:30 -13:00

Sala Multimediale at the Department of Mechanical and Aerospace Engineering.

------------------------------- ------------------------------- ------------------------------- -------------------------------

AA 2018

Calendar of Soft mechanics and instabilities delivered by Prof. Paola Nardinocchi and Prof. Giuseppe Ruta

01/10/2018 9:00-12:30

02/10/2018 9:00-12:30

08/10/2018 9:00-12:30

09/10/2018 9:00-12:30

15/10/2018 9:00-12:30

16/10/2018 9:00-12:30

22/10/2018 9:00-12:30

23/10/2018 9:00-12:30

Aula "caveau" (Area Ingegneria Strutturale (AIS), close to the minimarket)