Multiscale analysis of brittle failure in heterogeneous materials

Abstract

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Thermodynamically-consistent derivation and computation of twinning and fracture in brittle materials by means of phase-field approaches in the finite element method

“…Having the capability to model the microstructural evolution, phase-field modeling has been successfully adopted in the simulation of martensitic phase transformations (Levitas and Preston, 2002;Javanbakht et al, 2021), reconstructive phase transformations (Denoual et al, 2010), phase transformations in liquids (Slutsker et al, 2006), dislocations (Albrecht et al, 2020), twinning (Clayton and Knap, 2011), damage (Loew et al, 2019), and their interactions (Ruffini and Finel, 2015;Mozaffari and Voyiadjis, 2016;Schmitt et al, 2015). Initiated with the celebrated work by Francfort and Marigo (1998) on the variational approach to brittle fracture, where the total energy is minimized simultaneously with respect to the crack geometry and the displacement field, the concept of applying the phase-field method in fracture mechanics has gained significant interest in the literature (Bourdin et al, 2000(Bourdin et al, , 2008Farrahi et al, 2020;Levitas et al, 2018;Jafarzadeh et al, 2019;Kuhn and Müller, 2010;Placidi et al, 2020;Sargado et al, 2018;Eid et al, 2021;Msekh et al, 2015;Shanthraj et al, 2017;Aldakheel et al, 2018;Seleš et al, 2021). Due to the thermodynamic driving forces, the evolution of interfaces (e.g., merging and branching of multiple cracks) is predicted with no additional effort (Wu et al, 2018).…”

An efficient matrix-free preconditioned conjugate gradient based multigrid method for phase field modeling of fracture in heterogeneous materials from 3D images

“…Because the best performance is already achieved with a simple average. But for equation (14), as presented in Figure 9b, the advanced technique can distinctly improve the convergence performance, i.e. the simulation is 2 times cheaper.…”

“…Many papers can be found both on extensions and applications of this model e.g. [7,8,9,10,11,12,13,14,15].…”

Thermodynamically-consistent derivation and computation of twinning and fracture in brittle materials by means of phase-field approaches in the finite element method

“…Having the capability to model the microstructural evolution, it has been successfully adopted in the simulation of martensitic phase transformations [42,43], reconstructive phase transformations [44], phase transformations in liquids [45], dislocations [46], twinning [47], damage [48], and their interactions [49,50,51]. Initiated with the celebrated work by Francfort and Marigo on the variational approach to brittle fracture [52], where the total energy is minimized simultaneously with respect to the crack geometry and the displacement field, the concept of applying the phase-field method in fracture mechanics has gained significant interest in the literature [53,54,55,56,57,58,59,60,61,62,63,64,65]. Due to the thermodynamic driving forces, the evolution of interfaces (e.g., merging and branching of multiple cracks) is predicted with no additional effort [66].…”