Strain Injection Techniques in Numerical Modeling of Propagating Material Failure

Abstract

The methodology proposed in this research work explores the use of the straininjection concept in a combination of classical strain localization methods andembedded strong discontinuities, to remove the flaws (stress locking and meshbias dependence) of the former, and simultaneously abdicate of the global trackingalgorithms usually required by the later. The basic idea is to use, after thebifurcation instant, i.e. after the time that elements are amenable to develop discontinuities,a mixed continuous displacements - discontinuous constant strainscondensable finite element formulation (Q1/ e0 ) for quadrilaterals in 2D. Thisformulation provides improved behavior results, specially, in avoiding mesh biasdependence. In a first, very short, stage after the bifurcation the concept of strongdiscontinuity is then left aside, and the apparent displacement jump is capturedacross the finite element length (smeared) like in classical strain localization settings.Immediately after, in a second stage, the kinematics of those finite elementsthat have developed deep enough strain localization is enriched with the injectionof a weak/strong discontinuity mode that minimizes the stress locking defects.The necessary data to inject the discontinuity (the discontinuity direction and itsposition inside the finite element) is obtained by a post process of the strain-likeinternal variable field obtained in the first stage, this giving rise to a local (elementalbased) tracking algorithm (the crack propagation problem) that can belocally and straightforwardly implemented in a finite element code in a non invasivemanner. The obtained approach enjoys the benefits of embedded strong discontinuitymethods (stress locking free, mesh bias independence and low computationalcost), at a complexity similar to the classical, and simpler, though lessaccurate, strain localization methods. Moreover, the methodology is applicable toany constitutive model (damage, elasto-plasticity, etc.) without apparent limitations.Representative numerical simulations validate the proposed approach.