Fracture propagation in brittle materials as a standard dissipative process: General theorems and crack tracking algorithms

Salvadori, Alberto; Fantoni, Francesca

doi:10.1016/j.jmps.2016.04.034

Cited by 19 publications

(7 citation statements)

References 34 publications

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“…In view of these original features and focusing on infinitesimal deformations we provided thorough derivations, differing advection to a companion paper. Similar reasoning holds for the analysis of mechanical failure [60,61,62,63,64], of numerical accuracy, stability, and convergence, which although deserving careful investigations fall out of the scope of the present paper.…”

Section: Discussionsupporting

confidence: 54%

A coupled model of transport-reaction-mechanics with trapping. Part I – Small strain analysis

Salvadori

McMeeking

Grazioli

et al. 2018

Journal of the Mechanics and Physics of Solids

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A fully coupled model for mass and heat transport, mechanics, and chemical reactions with trapping is proposed. It is rooted in non-equilibrium rational thermodynamics and assumes that displacements and strains are small. Balance laws for mass, linear and angular momentum, energy, and entropy are stated. Thermodynamic restrictions are identified, based on an additive strain decomposition and on the definition of the Helmholtz free energy. Constitutive theory and chemical kinetics are studied in order to finally write the governing equations for the multi-physics problem. The field equations are solved numerically with the finite element method, stemming from a three-fields variational formulation. Three case-studies on vacancies redistribution in metals, hydrogen embrittlement, and the charge-discharge of active particles in Li-ion batteries demonstrate the features and the potential of the proposed model.

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Section: Discussionsupporting

confidence: 54%

A coupled model of transport-reaction-mechanics with trapping. Part I – Small strain analysis

Salvadori

McMeeking

Grazioli

et al. 2018

Journal of the Mechanics and Physics of Solids

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“…fracturing in many small parts, caused by large deformations during lithiation [196]. Cracks have been observed even in active materials that undergo small deformations when lithiated, as for LiCoO 2 , LiMn 2 O 4 , and LiFePO 4 [197] To predict the onset of fracture in electrode particles, many authors [198,199,196,200,201,202,197,203] resorted to linear-elastic fracture mechanics [204,205,206,207]. A pre-existing flaws population in the particles was assumed and Griffith's criterion used to investigate the effects of charging rate and fracture toughness on the failure of particles of different sizes.…”

Section: The Modeling Of Micro-mechanical Effectsmentioning

confidence: 99%

Computational modeling of Li-ion batteries

2016

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This review focuses on energy storage materials modeling, with particular emphasis on Li-ion batteries. Theoretical and computational analyses not only provide a better understanding of the intimate behavior of actual batteries under operational and extreme conditions, but they may tailor new materials and shape new architectures in a complementary way to experimental approaches. Modeling can therefore play a very valuable role in the design and lifetime prediction of energy storage materials and devices. Batteries are inherently multi-scale, in space and time. The macro-structural characteristic lengths (the thickness of a single cell, for instance) are order of magnitudes larger than the particles that form the microstructure of the porous electrodes, which in turn are scale-separated from interface layers at which atomistic intercalations occur. Multi-physics modeling concepts, methodologies, and simulations at different scales, as well as scale transition strategies proposed in the recent literature are here revised. Finally, computational challenges toward the next generation of Li-ion batteries are discussed.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

A phase field approach for damage propagation in periodic microstructured materials

et al. 2019

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In the present work, the evolution of damage in periodic composite materials is investigated through a novel finite element-based multiscale computational approach. The methodology is developed by means of the original combination of homogenization methods with the phase field approach of fracture. This last is applied at the macroscale level on the equivalent homogeneous continuum, whose constitutive properties are obtained in closed form via a two-scale asymptotic homogenization scheme. The formulation allows considering different assumptions on the evolution of damage at the microscale (e.g., damage in the matrix and not in the inclusion/fiber), as well as the role played by the microstructural topology. Numerical results show that the proposed formulation leads to an apparent tensile strength and a postpeak branch of unnotched and notched specimens dependent not only on the internal length scale of the phase field approach, as for homogeneous materials, but also on the inclusion volumetric content and its shape. Down-scaling relations allow the full reconstruction of the microscopic fields at any point of the macroscopic model, as a simple post-processing operation.

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Fracture propagation in brittle materials as a standard dissipative process: General theorems and crack tracking algorithms

Cited by 19 publications

References 34 publications

A coupled model of transport-reaction-mechanics with trapping. Part I – Small strain analysis

A coupled model of transport-reaction-mechanics with trapping. Part I – Small strain analysis

Computational modeling of Li-ion batteries

A phase field approach for damage propagation in periodic microstructured materials

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