Localisation issues in local and nonlocal continuum approaches to fracture

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Dynamic crack propagation analysis of orthotropic media by the extended finite element method (2009, methodology): “Later, Peerlings et al. (2002) and Oliver et al. (2003) further studied the loss of hyperbolicity and added this technique into equilibrium equations.”
Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment (2003, background): “[18] have discussed the relationship between crack formation and loss of ellipticity in damage models.”
Discrete vs smeared crack models for concrete fracture: bridging the gap (2004, unknown): “Higher-order continua Continuum damage models, including the class of smeared crack models described in Section 2, suffer from loss of ellipticity beyond a certain level of accumulated damage [39].”
An evaluation of higher-order plasticity theories for predicting size effects and localisation (2006, background): “k !1 ). This reflects the ill-posedness of the problem and the pathological localisation which results from it ( Peerlings et al., 2002 ).”