Mesh objective modeling of cracks using continuous linear strain and displacement interpolations.

*(English)*Zbl 1242.74101Summary: The paper addresses the problem of tensile and mixed-mode cracking within the so-called smeared crack approach. Because lack of point-wise convergence on stresses is deemed as the main difficulty to be overcome in the discrete problem, a (stabilized) mixed formulation with continuous linear strain and displacement interpolations is used. The necessary convergence rate can be proved for such a formulation, at least in the linear problem. Two standard local isotropic Rankine damage models with strain-softening, differing in the definition of the damage criteria, are used as discrete constitutive model. Numerical examples demonstrate the application of the proposed formulation using linear triangular P1P1 and bilinear quadrilateral Q1Q1 mixed elements. The results obtained do not suffer from spurious mesh-bias dependence without the use of auxiliary tracking techniques.

##### MSC:

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

74R10 | Brittle fracture |

74R05 | Brittle damage |

##### Keywords:

mesh independence; tensile cracking; mixed-mode cracking; mixed finite elements; stabilization; local damage models
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\textit{M. Cervera} et al., Int. J. Numer. Methods Eng. 87, No. 10, 962--987 (2011; Zbl 1242.74101)

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