Smeared crack approach: back to the original track

By Miguel Cervera, Michele Chiumenti. 2006

164 citations recorded by the source corpus.

This paper briefly reviews the formulations used over the last 40 years for the solution of problems involving tensile cracking, with both the discrete and the smeared crack approaches. The paper focuses on 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 the strong discontinuity (discrete cracks) approaches are analysed 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 stability of the solution, attaining the necessary convergence properties of the corresponding discrete finite element formulation. Numerical examples show that the formulation derived is stable and remarkably robust. As a consequence, the results obtained do not suffer from spurious mesh‐size or mesh‐bias dependence, comparing very favourably with those obtained with other fracture and continuum mechanics approaches. Copyright © 2006 John Wiley & Sons, Ltd.

Subfields: Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f06bca4a4712012fd288d75c6ac85da8b4c8c4ad

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mechanics of Materials

Citations in the corpus

A comparative study on the modelling of discontinuous fracture by means of enriched nodal and element techniques and interface elements (2009, background): “Explanations for the differences could be the consideration of incorrect material parameters as well as spurious bending, leading to different crack paths at the front and rear faces of the specimen (Cervera and Chiumenti 2006; Pivonka et al. 2004; Gasser and Holzapfel 2006).”
Mixed stabilized finite element methods in nonlinear solid mechanics: Part II: Strain localization (2010, background): “Cervera and Chiumenti ([33,34]) have reported in the reciprocal sense that if tracking is used, the weak discontinuity formulation produces results that do not suffer from mesh bias dependence in an evident spurious way.”
Extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids (2015, result): “The deviation of the numerical results from the experimental observation is mainly caused by some critical differences between the simulations and experiments as discussed in Cervera [57].”
An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks (2015, background): “To the best knowledge of the authors, only References [7, 49, 78] reported success in modeling this curious result.”