CESS Seminar: Fracture propagation in brittle or embrittled materials as a standard dissipative process
Event details
Date | 15.11.2019 |
Hour | 12:15 › 13:00 |
Speaker | Prof. Alberto Salvadori, DIMI, University of Brescia, Italy |
Location | |
Category | Conferences - Seminars |
Abstract:
Recent publications framed the problem of three-dimensional quasi-static crack propagation in brittle materials into the theory of standard dissipative processes [1, 2]. Variational formulations, stated therein, characterize the three-dimensional crack front quasi-static velocity as the minimizer of constrained quadratic functionals. An implicit in time crack tracking algorithm, that computationally handles the constraint via a penalty method was developed and implemented in [3]. Although the theoretical setting is sound, the derived crack tracking methods suffered from a major drawback that limited the interest in the method to its theoretical content. Specifically, the need of still currently unavailable accurate approximations for weight functions made the approach of minor interest from a numerical standpoint. Such a drawback was overcome in [4], where a viscous regularization of the fracture propagation in brittle materials as a standard dissipative process was formulated. Rate-dependency provided a simple and accurate approximation of the crack front velocity, thus allowing to formulate effective crack tracking algorithms. That idea is further developed here to model hydraulic fracture processes [5]. Although limited to a penny shaped crack benchmark, the novel set of differential equations that are here proposed are capable to model the evolution of the lag and of the crack advancing in a straightforward way. The formulation can be easily extended to account for fractures pressurized by gas or other substances.
[1] A. Salvadori. A plasticity framework for (linear elastic) fracture mechanics. J Mech Phys Sol. (2008)
[2] A. Salvadori and F. Fantoni. Minimum theorems in 3D incremental linear elastic fracture mechanics. Int J Frac (2013)
[3] A. Salvadori and F. Fantoni. Fracture propagation in brittle materials as a standard dissipative process: general theorems and crack tracking algorithms. J Mech Phys Sol. (2016)
[4] A. Salvadori, P.A. Wawrzynek, and F. Fantoni. Fracture propagation in brittle materials as a stan dard dissipative process: Effective crack tracking algorithms based on a viscous regularization J Mech Phys Sol. (2019)
[5] E. Detournay. Mechanics of hydraulic fractures. Ann. Rev. Fluid Mech. (2016)
Bio:
Prof. Alberto Salvadori received his M.S. in Civil Engineering from the University of Brescia in 1995 and Ph.D. degrees in Engineering Science from Politecnico di Milano, in 2000. At present, he is Associate Professor at the University of Brescia. He has been Research Assistant Professor at the University of Notre Dame, USA from Jan. 2015 to June 2017. He was also recipient of a Marie-Curie IEF fellowship, that he spent at the Technical University of Eindhoven (The Netherlands). He founded the Multiscale Mechanics and Multiphysics of Materials Lab and is currently Director of the CeSiA (Centro di Studio e Ricerca di Sismologia applicata e dinamica strutturale - Applied Seismology and Structural Dynamics Research Center) at the University of Brescia. Professor Salvadori's research is focused on the multiscale and multiphysics modeling in the green and white economy, as well as on understanding of failure in continua. He is particularly interested in Mechanobiology, energy-storage materials, (computational) homogenization, diffusion and migration of species in solids and in the induced fracturing processes (especially for Li-ion batteries modeling, Hydrogen Embrittlement in metals, Environmentally assisted cracking, Solid Oxide Fuel Cells, Hydraulic fracturing and gas/oil shale extraction), variationally modeled in two- and three-dimensions via standard dissipative systems and approximated via ad-hoc numerical schemes.
Recent publications framed the problem of three-dimensional quasi-static crack propagation in brittle materials into the theory of standard dissipative processes [1, 2]. Variational formulations, stated therein, characterize the three-dimensional crack front quasi-static velocity as the minimizer of constrained quadratic functionals. An implicit in time crack tracking algorithm, that computationally handles the constraint via a penalty method was developed and implemented in [3]. Although the theoretical setting is sound, the derived crack tracking methods suffered from a major drawback that limited the interest in the method to its theoretical content. Specifically, the need of still currently unavailable accurate approximations for weight functions made the approach of minor interest from a numerical standpoint. Such a drawback was overcome in [4], where a viscous regularization of the fracture propagation in brittle materials as a standard dissipative process was formulated. Rate-dependency provided a simple and accurate approximation of the crack front velocity, thus allowing to formulate effective crack tracking algorithms. That idea is further developed here to model hydraulic fracture processes [5]. Although limited to a penny shaped crack benchmark, the novel set of differential equations that are here proposed are capable to model the evolution of the lag and of the crack advancing in a straightforward way. The formulation can be easily extended to account for fractures pressurized by gas or other substances.
[1] A. Salvadori. A plasticity framework for (linear elastic) fracture mechanics. J Mech Phys Sol. (2008)
[2] A. Salvadori and F. Fantoni. Minimum theorems in 3D incremental linear elastic fracture mechanics. Int J Frac (2013)
[3] A. Salvadori and F. Fantoni. Fracture propagation in brittle materials as a standard dissipative process: general theorems and crack tracking algorithms. J Mech Phys Sol. (2016)
[4] A. Salvadori, P.A. Wawrzynek, and F. Fantoni. Fracture propagation in brittle materials as a stan dard dissipative process: Effective crack tracking algorithms based on a viscous regularization J Mech Phys Sol. (2019)
[5] E. Detournay. Mechanics of hydraulic fractures. Ann. Rev. Fluid Mech. (2016)
Bio:
Prof. Alberto Salvadori received his M.S. in Civil Engineering from the University of Brescia in 1995 and Ph.D. degrees in Engineering Science from Politecnico di Milano, in 2000. At present, he is Associate Professor at the University of Brescia. He has been Research Assistant Professor at the University of Notre Dame, USA from Jan. 2015 to June 2017. He was also recipient of a Marie-Curie IEF fellowship, that he spent at the Technical University of Eindhoven (The Netherlands). He founded the Multiscale Mechanics and Multiphysics of Materials Lab and is currently Director of the CeSiA (Centro di Studio e Ricerca di Sismologia applicata e dinamica strutturale - Applied Seismology and Structural Dynamics Research Center) at the University of Brescia. Professor Salvadori's research is focused on the multiscale and multiphysics modeling in the green and white economy, as well as on understanding of failure in continua. He is particularly interested in Mechanobiology, energy-storage materials, (computational) homogenization, diffusion and migration of species in solids and in the induced fracturing processes (especially for Li-ion batteries modeling, Hydrogen Embrittlement in metals, Environmentally assisted cracking, Solid Oxide Fuel Cells, Hydraulic fracturing and gas/oil shale extraction), variationally modeled in two- and three-dimensions via standard dissipative systems and approximated via ad-hoc numerical schemes.
Practical information
- Informed public
- Free
Organizer
- Profs Brice Lecampion & Alexandre Alahi
Contact
- Prof. Brice Lecampion