Abstract
The numerical simulation of two-dimensional fracture processes of quasi-brittle materials by means of the Embedded Finite Element Method is dealt with. Attention is paid to the coupling with the global crack-tracking strategy, which has been proposed in the literature in the form of a heat conduction-like problem. It turns out that the stiffness-like matrix associated with this formulation is singular and a numerical perturbation has to be introduced in order to overcome the ill-posedness of the problem. The dependence of the solution on this parameter may represent a limitation for the global tracking approach. Furthermore, it is found that if the root of each discontinuity is not updated during an incremental analysis, a loss of continuity of the crack path may appear when principal stress directions rotate. This paper aims to provide a solution to the aforementioned issues. An alternative mathematical formulation of the problem is thus given in terms of Navier-Stokes equations, linking the diffusive contribution to a characteristic mesh length. Additionally, a modified crack-tracking algorithm, considering the evolution of the root for the identification of the crack path, is proposed. The numerical assessment of the proposed tracking strategy is reported by means of benchmark tests at the structural level.
Highlights
In the last decade, the Embedded Finite Element Method (E-FEM) has gained wide popularity for the description of cracking phenomena [1,2,3,4,5,6]
Due to the local nature of the kinematic enrichment, this approach presents some advantages concerning the computational effort with respect, for example, to the Extended Finite Element Method (X-FEM) [7,8,9,10,11]
Since no information is available in the vicinity of cracked elements, the continuity of the crack path is not intrinsically guaranteed and a loss in objectivity may be encountered in numerical simulations [12,13]
Summary
The Embedded Finite Element Method (E-FEM) has gained wide popularity for the description of cracking phenomena [1,2,3,4,5,6]. Local tracking techniques are able to reproduce continuous crack paths in a robust manner by exploiting the informations of nearby elements Their implementation in the case of multiple crack problems may be cumbersome and this strategy can loose much of its robustness. It is found out that the capability of the thermal-like isovalues to envelop the vector tangent field is reduced as soon as cracking occurs This fact, due to the rotation of the principal stress directions outside the region crossed by the discontinuity, may lead to a loss of continuity of the crack path and, in the worst case, to a wrong evaluation of the enriched shape functions whenever the element domain is not decomposed properly [12,25].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
