Fracture propagation in brittle materials as a standard dissipative process: Effective crack tracking algorithms based on a viscous regularization

A phase field approach for damage propagation in periodic microstructured materials

“…Regarding the prediction of failure events in engineering materials and structures, the advent of new computational capabilities has promoted the generation of different numerical tools including diffusive crack methods (Bazant and Jirasek, 2002;Comi, 1999;Peerlings et al, 2001;Dimitrijevic and Hackl, 2011), strong discontinuity procedures (Moes et al, 1999;Linder and Armero, 2007;Oliver et al, 2006) and cohesive-like crack approaches (Camacho and Ortiz, 1996;Ortiz and Pandolfi, 1999;Paggi and Wriggers, 2012;Turon et al, 2018), among many others, where most of them rely on the exploitation of finite element(FE)-based procedures. Recent variational formulations and crack tracking algorithms based on the analogy between linear elastic fracture mechanics and standard dissipative systems can be found in (Salvadori and Fantoni, 2016;Salvadori et al, 2019). Derived from its versatility for the estimation of failure mechanisms due to crack initiation and growth, the seminal variational approach of fracture developed by Francfort and Marigo (1998), being denominated as the phase field approach of fracture, endows a smeared crack idealization that permits overcoming most of the limitations of alternative numerical methods.…”

A novel hydraulic fractures growth formulation

“…Crack tracking algorithms are formulated in terms of so-called fundamental kernels [92], whose values depend exclusively upon the shape of the crack front and whose analytical expression or even an accurate approximation is still missing for generic crack front shapes. To overcome the issue, novel theoretical studies and resulting explicit in time crack tracking algorithms have been recently proposed in [56] for LEFM: they are grounded on a viscous regularization of the quasi-static fracture propagation problem and allow computing finite elongations of the crack front without fundamental kernels.…”

“…In the formulation, which stems from a standard dissipative picture of crack propagation in brittle materials [49,50,51,52,53,54,55], the fracturing fluid is allowed to lag behind the fracture front and the algorithm is capable of tracking both the moving crack and fluid edges concurrently. While the fluid front velocity is computed in a closed form from the mass balance equation, the adopted crack tracking algorithm is grounded on a novel viscous regularization of the quasi-static crack propagation problem as a standard dissipative system recently presented in [56].…”

“…The influence of such a parameter upon the performances of the crack tracking algorithm is discussed at large in[56]: the lower the value of η, the lower the number of iteration requested to satisfy a Griffith condition (G = G C ) at the crack front.…”

A two-mechanism and multiscale compatible approach for solid state electrolytes of (Li-ion) batteries

“…In spite they have been mostly investigated experimentally, digital twins can guide and even partially replace experimental campaigns. Computational simulations easily and rapidly allow selecting constituents and tailoring architectures, providing meaningful insights on the evolution of ionic concentrations during operation [4][5][6][7] and predicting limiting factors together with material degradation in SSBs charge/discharge cycles [3,[8][9][10].…”