Blue Sky Research Project 2017
"Plasticity at different scales: micro to macro"


Principal investigator: Maria Giovanna Mora
Host Institution: Università di Pavia
Duration: 02/10/2017 - 01/10/2019
Funding: 60,000 EUR

Abstract: Plasticity is the property of a material of undergoing permanent deformations in response to an external load. Plastic behaviour is observed in most materials, such as, for instance, ductile metals, clays, and rocks. However, the physical mechanisms that cause plastic deformation can vary widely:
  • In metals, plasticity is considered to be the macroscopic consequence of the presence (and motion) of defects at the microscopic scale, called dislocations;

  • In soils, plasticity is caused by their granular structure: soils are made of many small solid particles, whose irreversible rearrangement, together with the irreversible crushing of individual particles, produces permanent deformation.
The understanding of the plastic mechanism at the microscopic scale and of its implications on the macroscopic response is a necessary step towards the formulation of predictive models of plasticity at the continuum level. The project will investigate several aspects of the plastic response at different scales, ranging from its mechanisms at the microscopic scale to its macroscopic description.


Visitors:
Lucia Scardia (University of Bath), 23-29 October 2017
Lorenzo Freddi (Università di Udine), 27 February - 2 March 2018
Roberto Paroni (Università di Pisa), 27 February - 2 March 2018
Peter Hornung (TU Dresden), 27 February - 2 March 2018
Mark Peletier (TU Eindhoven), 8 - 11 May 2018
Lucia Scardia (University of Bath), 8 -11 May 2018
Carlo Orrieri (Sapienza Università di Roma), 30 May - 9 June 2018
Stefano Almi (TU München), 4 - 8 June 2018
Dorothee Knees (Universität Kassel), 1 - 6 July 2018
Juan Luis Vázquez (Universidad Autónoma de Madrid), 14 - 20 October 2018
Lorenzo Bertini (Sapienza Università Roma), 20 November 2018
Vito Crismale (École Polytechnique), 23 - 17 November 2018
Lucia Scardia (Heriot-Watt University), 13 - 17 December 2018
Elisa Davoli (Universität Wien), 17 - 21 December 2018
Riccardo Cristoferi (Heriot-Watt University), 6 - 11 January 2019
Eurica Henriques (Universidade de Trás-os-Montes e Alto Douro), 20 - 25 January 2019
Vincenzo Vespri (Università di Firenze), 20 - 22 January 2019
Takeshi Fukao (Kyoto University of Education), 4 - 15 February 2019
Giorgio Metafune (Università del Salento), 14 - 17 February 2019
Matteo Focardi (Università di Firenze), 26 - 28 February 2019
Alessandra Pluda (Università di Pisa), 14 - 17 April 2019
Cy Maor (University of Toronto), 5 - 10 May 2019
Jürgen Sprekels (Humboldt-Universität & WIAS Berlin), 12 - 19 May 2019
Gian Paolo Leonardi (Università di Trento), 14 - 15 May 2019
Riccarda Rossi (Università di Brescia), 16 May 2019
Irene Fonseca (Carnegie Mellon University), 27 May - 7 June 2019
Giovanni Leoni (Carnegie Mellon University), 27 May - 7 June 2019
Enea Parini (Aix-Marseille Université), 3 - 7 June 2019
Riccarda Rossi (Università di Brescia), 12 June 2019
Luca Lussardi (Politecnico di Torino), 24 - 26 June 2019
Riccardo Scala (Sapienza Università di Roma), 25 - 28 June 2019
Jean-François Babadjian (Université Paris Sud), 1 - 5 July 2019
Roland Schnaubelt (Karlsruher Institut für Technologie), 16 - 20 September 2019
Giorgio Metafune (Università del Salento), 16 - 20 September 2019
Diego Pallara (Università del Salento), 16 - 21 September 2019


Talks at the Università di Pavia:
05/06/2018 Stefano Almi (München): Energy release rate and stress intensity factors in planar elasticity in presence of smooth cracks
03/07/2018 Dorothee Knees (Kassel): Rate-independent processes with time-discontinuous data
16/10/2018 Juan Luis Vázquez (Madrid): Linear and nonlinear diffusion with nonlocal fractional operators
20/11/2018 Lorenzo Bertini (Roma): Gradient flow formulation of linear Boltzmann equations
27/11/2018 Vito Crismale (Paris): Minimisation and Ambrosio-Tortorelli approximation of the Griffith energy with Dirichlet boundary condition
18/12/2018 Elisa Davoli (Wien): Two-well rigidity and multidimensional sharp-interface limits for solid-solid phase transitions
08/01/2019 Riccardo Cristoferi (Edinburgh): Equilibria configurations for epitaxial crystal growth with adatoms
13/02/2019 Takeshi Fukao (Kyoto): Convergence to equilibrium for the equation and dynamic boundary condition of Cahn-Hilliard type and related topics
26/02/2019 Matteo Focardi (Firenze): The measure and the structure of the free boundary in the lower dimensional obstacle problem
16/04/2019 Alessandra Pluda (Pisa): Long time existence of solutions to an elastic flow of networks
07/05/2019 Cy Maor (Toronto): Elasticity and curvature: the elastic energy of non-Euclidean thin bodies
14/05/2019 Jürgen Sprekels (Berlin): Optimal distributed control of a Cahn-Hilliard-Darcy system with mass sources
15/05/2019 Gian Paolo Leonardi (Trento): Approximate curvatures of a varifold
23/05/1019 Tomáš Roubíček (Prague): Dynamical damage and phase-field fracture models
04/06/2019 Giovanni Leoni (Pittsburgh): A variational approach for water waves
04/06/2019 Irene Fonseca (Pittsburgh): A homogenization result in the gradient theory of phase transitions
05/06/2019 Enea Parini (Marseille): Partizioni di Cheeger: risultati d'esistenza e proprietà qualitative
25/06/2019 Luca Lussardi (Torino): The Kirchhoff-Plateau problem
02/07/2019 Jean-François Babadjian (Paris): Concentration versus oscillation effects in brittle damage


Publications:
  • Equilibrium measure for a nonlocal dislocation energy with physical confinement
    M.G. Mora, A. Scagliotti
    To appear in Adv. Calc. Var.

  • Explicit minimisers of some nonlocal anisotropic energies: a short proof
    J. Mateu, M.G. Mora, L. Rondi, L. Scardia, J. Verdera
    Izv. Math. 85 (2021), 468-482.

  • A maximum-principle approach to the minimisation of a nonlocal dislocation energy
    J. Mateu, M.G. Mora, L. Rondi, L. Scardia, J. Verdera
    Mathematics in Engineering 2 (2020), 253-263.

  • The equilibrium measure for an anisotropic nonlocal energy
    J.A. Carrillo, J. Mateu, M.G. Mora, L. Rondi, L. Scardia, J. Verdera
    Calc. Var. Partial Differential Equations 60, 10 (2021).

  • The ellipse law: Kirchhoff meets dislocations
    J.A. Carrillo, J. Mateu, M.G. Mora, L. Rondi, L. Scardia, J. Verdera
    Commun. Math. Phys. 373 (2020), 507-524.

  • The equilibrium measure for a nonlocal dislocation energy
    M.G. Mora, L. Rondi, L. Scardia
    Comm. Pure Appl. Math. 72 (2019), 136-158.

  • Quasistatic evolution in non-associative plasticity revisited
    G.A. Francfort, M.G. Mora
    Calc. Var. Partial Differential Equations (2018), 57:11.

  • Quasistatic evolution of perfectly plastic shallow shells: a rigorous variational derivation
    G.B. Maggiani, M.G. Mora
    Ann. Mat. Pura Appl. 197 (2018), 775-815.

  • Stress regularity in quasi-static perfect plasticity with a pressure dependent yield criterion
    J.-F. Babadjian, M.G. Mora
    J. Differential Equations 264 (2018), 5109-5151.




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