An overview of the modelling of fracture by gradient damage models

Abstract

The paper is devoted to gradient damage models which allow us to describe all the process of degradation of a body including the nucleation of cracks and their propagation. The construction of such model follows the variational approach to fracture and proceeds into two stages: (i) definition of the energy; (ii) formulation of the damage evolution problem. The total energy of the body is defined in terms of the state variables which are the displacement field and the damage field in the case of quasi-brittle materials. That energy contains in particular gradient damage terms in order to avoid too strong damage localizations. The formulation of the damage evolution problem is then based on the concepts of irreversibility, stability and energy balance. That allows us to construct homogeneous as well as localized damage solutions in a closed form and to illustrate the concepts of loss of stability, of scale effects, of damage localization, and of structural failure. Moreover, the variational formulation leads to a natural numerical method based on an alternate minimization algorithm. Several numerical examples illustrate the ability of this approach to account for all the process of fracture including a 3D thermal shock problem where the crack evolution is very complex.

Simple and extensible plate and shell finite element models through automatic code generation tools

“…The present work constitutes an instrumental step in a larger project on the mechanics and physics of shell structures, including the analysis of the nonlinear material behaviour and fracture of isotropic and anisotropic shells [6,8,7] through phase-field variational models [25,45,68], applications to multistable structures with embedded active materials [43,88], and for the understanding of singularities and energy scalings in plates and shells [33]. Current and future technical developments of FEniCS-Shells will be aimed at providing anisotropic adaptive remeshing tools [87,69] and coupling to advanced nonlinear solvers, such as asymptotic numerical continuation methods [93] and deflation techniques [36] to automatically detect multiple solutions of nonlinear systems.…”

Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples

“…if fp ≤ 0 then no plastic increment p k = p k−1 ; else projection: erties have been widely discussed in previous works, when considering damage-gradient model as phase-field approximation of brittle fracture [55,49]. Here we recall and discuss some important facts, useful for later discussions.…”

A novel phase field method for modeling the fracture of long bones

“…Nonetheless, these two classes of methods may be limited when applied to bone fracture. For example, the complex bone geometry and inhomogeneous material properties make the implementation of discrete methods extremely difficult, and on the other hand, damage methods tend to be either mesh dependent (local damage) or spread the damage over large unrealistic domains (nonlocal damage) …”

“…For example, the complex bone geometry and inhomogeneous material properties make the implementation of discrete methods extremely difficult, 31 and on the other hand, damage methods tend to be either mesh dependent (local damage) 32 or spread the damage over large unrealistic domains (nonlocal damage). 33,34 To this end, a so-called phase field method (PFM) for modeling brittle fracture has emerged in the past two decades [35][36][37][38][39][40][41][42][43][44][45][46] and was shown to overcome some of the aforementioned limitations of the other methods. Similar to nonlocal damage mechanics, the PFM is also a regularized continuum-based method that can model crack initiation and propagation in complex 3D geometries.…”

“…37 The PFM was applied to a range of materials, such as polymers, 48 asphalt, 49 concrete, 50 and polycrystalline materials, 51 including brittle and quasi-brittle fracture, 38,52 ductile fracture, 46,53 hydraulic fracture, [54][55][56] interfacial fracture, 57,58 and anisotropic fracture. 59,60 More details and comparisons of the phase field method with traditional damage mechanics could be found in Marigo et al 33 and de Borst and Verhoosel. 61 In this paper, we propose an important modification to the phase field method for modeling the fracture of highly inhomogeneous materials, as the proximal humerus fracture studied in this paper.…”