Multiscale modelling of propagating fracture in quasi-brittle materials: a continuum approach

J. OLIVER,; M. CAICEDO; E. ROUBIN; A E. HUESPE

Paris

Conferencia; International Conference on Computational Modeling of Fracture and Failure (ECCOMAS thematic conference); 2015

ECCOMAS

The work presents an approach to computational multiscale modelling of materialfailure using finite element analysis at two material scales (FE2). Its goal is beyond thesimple computational homogenization, and it aims at inserting the resulting, nonsmooth, homogenized constitutive model into a computational scheme for modelling theonset and propagation of the material failure at the structural macro-scale. In thiscontext, the main features of the approach are the following:? Extends the homogenization paradigms for smooth problems ─typically theHill-Mandel principle and the stress/strain homogenization procedures─ to nonsmooth problems, with no fundamental changes.? In both scales, a continuum (stress-strain) constitutive relationship is considered,instead of the most common discrete traction/separation-law, this contributing toprovide a unified setting for smooth and non-smooth problems. This is achieved byresorting to the Continuum Strong Discontinuity Approach (CSDA) to materialfailure [1].? As for the multiscale modelling issue, it involves a crucial additional entity: aninternal (or characteristic) length, which is point wise obtained from the geometricalfeatures of the failure mechanism developed at the lower scale. As a specific featureof the presented approach, for the non-smooth case this internal length is exported,in addition to the homogenized stresses and the tangent constitutive operator, to themacro-scale, and considered the bandwidth of a propagating strain localizationband, at that scale.? Consistently with this internal length, a specific computational procedure, basedon the crack-path-field and strain injection techniques, recently developed by theauthors [2] is then used for modelling the onset and propagation of this localizationband, at the macro-scale.