Strain localization, strong discontinuities and strain injection procedures in computational modeling of material failure

I.F.DIAS; J. OLIVER; A.E. HUESPE

Viena

Congreso; ECCOMAS 2012, 6th European Congress on Computational Methods in Applied Sciences and Engineering; 2012

ECCOMAS

In the first part of the work, attention is focused on the connections of strain localization modeling ofmaterial failure [1] and discrete fracture mechanics. The main idea is to discern whether the finiteelement solutions of material failure problems based on strain localization techniques, using standardcontinuum stress-strain constitutive models equipped with strain softening, have physical sense assolutions of de-cohesive fracture mechanics problems. Based on the well-established links betweenthe continuum strong discontinuity approach and the cohesive fracture mechanics [2], the ability ofthe standard finite element solutions to represent discrete fractures is analyzed in the sense that thesolution in terms of the displacement field might be interpreted as a regularized strong discontinuityembedded into the localization band. To assess this equivalence, several objective indicators areproposed. These indicators can be computed without a-priori knowledge of the exact fracturemechanics solution of the problem, and used as error indicators in a large variety of material failuresituations. Representative numerical applications are presented, being pointed out the relationbetween the limited ability of strain localization methods to reproduce a regularized strongdiscontinuity with the classical flaws of these methodologies (stress locking and mesh biasdependence).Giving the limited capacity of strain localization methods to represent cohesive fracture, in thesecond part of the work, a combination of those methods and the strong discontinuity approach isexplored, in order to remove the flaws of the former, and simultaneously abdicate of global trackingalgorithms, that are usually used in conjunction with the later. The strong discontinuity concept isthen initially substituted by that of a weak discontinuity capturing the displacement jump through itsdistribution (smearing) in a finite length: the oriented with of a finite element through which thefracture passes in a rather diffuse manner. In other words, the classical strain localization concept isbrought to the approach, no strong discontinuity enrichment is made and standard constitutive modelsare used in a classical strain localization setting. However, in order to remove the spurious meshorientation dependence, constant strain localization modes are injected, via mixed finite elementsformulations, to the path of elements that are going to capture the cracks. Moreover, in a secondstage, and in order to minimize stress locking, the elemental kinematics of those finite elements thatbelong to the localization band, is enhanced with the injection of an weak/strong discontinuity mode,see (Figure 1).Figure 1: Continuum body, subdivided in three different regions. Binj stands for the injection domain and BSDfor the strong discontinuity domain where a constant strain and a strong discontinuity mode, respectively, areinjected . \ B Binj stands for the remaining part of the body where a standard formulation is used, S fordiscontinuity line and n for the unit vector orthogonal to the discontinuity.The obtained approach enjoys the benefits of the strong discontinuities approach, at a complexitysimilar to the classical and simpler localization methods. Representative numerical simulationsvalidate the proposals made in the work.