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**Localised failure mechanism as the basis for constitutive modelling of geomaterials.**
*(English)*
Zbl 1423.74598

Summary: Localised failure of geomaterials in the form of cracks or shear bands always requires special attention in constitutive modelling of solids and structures. This is because the validity of classical constitutive models based on continuum mechanics is questionable once localised inelastic deformation has occurred. In such cases, due to the fact that the macro inelastic responses are mainly governed by the deformation and microstructural changes inside the localisation zone, internal variables, representing these microstructural changes, should be defined inside this zone. In this paper, the localised failure mechanism is identified and employed as an intrinsic characteristic upon which a constitutive model is based on at the first place, instead of being dealt with after developing the model using various regularisation techniques. As a result, inelastic responses of the model are correctly associated with the localisation bands, and not smeared out over the whole volume element as in classical continuum constitutive models. It is shown that this inbuilt localisation mechanism in a constitutive model can naturally capture important features of the material and possess intrinsic regularisation effects while minimising the use of additional phenomenological treatments, and also possessing intrinsic regularisation effects. The development of the proposed model is based on an additional kinematic enhancement to account for high gradient of deformation across the localisation band. This enrichment allows the introduction of an additional constitutive relationship for the localisation band, which is represented in the form of a cohesive-frictional model describing traction-displacement jump relationship across two sides of the localisation band. The model, formulated within a thermodynamically consistent approach, possesses constitutive responses of the bulk material and two localisation bands connected through internal equilibrium conditions. Its key characteristics are demonstrated and validated against experimental data from different types of geomaterials under different loading conditions at both material and structural levels.

### MSC:

74L05 | Geophysical solid mechanics |

74R10 | Brittle fracture |

74S05 | Finite element methods applied to problems in solid mechanics |

86A60 | Geological problems |

### Keywords:

constitutive modelling; geomaterials; localised failure; lode angle; size effect; localisation band; cohesive-frictional
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\textit{L. A. Le} et al., Int. J. Eng. Sci. 133, 284--310 (2018; Zbl 1423.74598)

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