This paper reviews briefly the formulations used over the last 40 years for the solution of problems involving tensile cracking, both with the discrete and smeared crack approaches. The paper focuses in the smeared approach, identifying as its main drawbacks the observed mesh-size and mesh-bias spurious dependence when the method is applied “straightly”. A simple isotropic local damage constitutive model is considered, and the (exponential) softening modulus is regularized according to the material fracture energy and the element size. The continuum and discrete mechanical problems corresponding to both the weak discontinuity (smeared cracks) and strong discontinuity (discrete cracks) approaches are analyzed and the question of propagation of the strain localization band (crack) is identified as the main difficulty to be overcome in the numerical procedure. A tracking technique is used to ensure uniqueness of the solution, attaining the necessary stability and convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is well posed, stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious meshsize or mesh-bias dependence, comparing very favorably with those obtained with other fracture and continuum mechanics approaches.

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Published on 03/12/19

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