Matteo Negri - Università di Pavia - Dipartimento di Matematica

Prof. Matteo Negri

Università degli Studi di Pavia

Via Ferrata 1 - 27100 Pavia - Italy

Ufficio E21

email matteo {dot} negri [at] unipv {dot} it
email prof {dot} matteo {dot} negri [at] universitadipavia {dot} it

Analisi Matematica 1 (Laurea in Matematica e in Fisica)
Analisi Funzionale ed Equazioni Differenziali (Laurea Magistrale in Matematica)
Phase-field Models for Brittle Fracture (PhD in Computational Mathematics and Decision Sciences - Mathematics - Design, Modeling and Simulation in Engineering)

Ricevimento studenti: su appuntamento.

"In the modern world the stupid are cocksure while the intelligent are full of doubts" [B. Russel]

Field: Calculus of Variations.
Subjects: Free Discontinuity Problems, Γ- convergence, BV and BD spaces, Rate-Independent Evolutions, Gradient Flows, Finite Element Methods.
Applications: Fracture Mechanics, Finite and Linearized Elasticity, Image Segmentation.

"Simplicity is not the goal. It is the by-product of a good idea and modest expectations." [P. Rand]

M. Negri: A unilateral L²- gradient flow and its quasi-static limit in phase-field fracture by alternate minimization.
Adv. Calc. Var. 12(1) (2019) 1-29
[preprint] [journal]
S. Almi, S. Belz, M. Negri: Convergence of discrete and continuous unilateral flows for Ambrosio-Tortorelli energies and application to mechanics.
ESAIM Math. Model. Numer. Anal. 53(2) (2019) 659-699
[preprint] [journal]
M. Negri: Γ- convergence for high order phase field fracture: continuum and isogeometric formulation.
Comput. Methods Appl. Mech. Engrg. 362 (2020) 112858
[arXiv] [journal]
M. Montardini, M. Negri, G. Sangalli, M. Tani: Space-time least-squares isogeometric method and efficient solver for parabolic problems.
Math. Comp. 89 (2020) 1193–1227
[arXiv] [journal]
S. Almi, M. Negri: Analysis of staggered evolutions for nonlinear energies in phase field fracture.
Archive Rational Mech. Anal. 236 (2020) 189–252
[arXiv] [journal]
M. Negri: A quasi-static model for craquelure patterns.
In Mathematical Modeling in Cultural Heritage. Springer INdAM Series 41 (2021) 147-164
[arXiv] [publication]

M. Kimura, M. Negri: Weak solutions for unidirectional gradient flows: existence, uniqueness, and convergence of time discretization schemes.
NoDEA Nonlinear Differential Equations Appl. 28 (2021) #59
[arXiv] [journal]
A.Marengo, A.Patton, M.Negri, U.Perego, A.Reali: A rigorous and efficient explicit algorithm for irreversibility enforcement in phase-field finite element and isogeometric modeling of brittle crack propagation.
Comput. Methods Appl. Mech. Engrg. 387 (2021) 114137
[journal]
M. Negri, R. Scala: Existence, energy identity and higher time regularity of solutions to a dynamic visco-elastic cohesive interface model.
SIAM J. Math. Anal. 53 (2021) 5682-5730
[arXiv] [journal]
M. Negri: Homogenization of Griffith's Criterion for brittle Laminates.
[arXiv]
B. Grossman-Ponemon, A. Lew, M. Negri: Analysis of a Method to Compute Mixed-Mode Stress Intensity Factors for Non-Planar Cracks in Three-Dimensions.
ESAIM Math. Model. Numer. Anal.

Constraints and penalties for phase-field flows in ℝ² and ℝ^N
Phase-Field Models of Fracture (BIRS, Banff, 2019)
Quasi-static evolutions for layered brittle materials and applications to craquelure
Mathematical modeling and Analysis of degradation and restoration in Cultural Heritage (Rome, 2019)

Convergence of evolutions generated by staggered minimization schemes
Recent advances in phase-field modeling: from engineering to biology (Pavia, 2019)

Characterization of quasi-static evolutions generated by alternate minimization
SIMAI 2020+2021 (Parma, 2021)

Homogenization of quasi-static crack propagation in brittle layered materials
Mathematical modeling and Analysis of degradation and restoration in Cultural Heritage (Rome, 2021)

Effective toughness of brittle composite laminates
WPI Math Colloquium (online)

Homogenization of Griffith's criterion for brittle laminates
Beyond Elasticity: Advances and Research Challenges (Luminy, 2022)

Gradient flows for separately convex phase-field energies
PHAME 2022 (Rome, 2022)

Effective toughness of brittle composite laminates
(Oberseminar Angewandte Mathematik, Freiburg, 2022)

Segmentation of a noisy image (a detail from "La dama dell'ermellino" by L. Da Vinci) using Mumford-Shah functional.

Craquelure patterns in pottery (simulations of local qualitative features developed in FreeFem++)