Multiscale modelling of propagating material fracture. A continuum approach

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

Buenos Aires

Congreso; 1st Pan-American Congress on Computational Mechanics - PANACM 2015; 2015

IACM

The work presents a new approach for computational multiscale modelling of material failure using finiteelement analysis at two material scales (FE2). Its goal is beyond the simple computational homogenization,and it aims at inserting the resulting, non-smooth, homogenized constitutive model into a computationalscheme for modelling the onset 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 the Hill-Mandel principle and the stress/strain homogenization procedures─ to non-smooth problems, with no fundamental changes.? In both scales, a continuum (stress-strain) constitutive relationship is considered, instead of the mostcommon discrete traction/separation-law, this contributing to provide a unified setting for smooth andnon-smooth problems. This is achieved by resorting to the Continuum Strong Discontinuity Approach(CSDA) to material failure [1].? As for the multiscale modelling issue, it involves a crucial additional entity: an internal (or characteristic)length, which is point wise obtained from the geometrical features of the failure mechanism developed atthe lower scale. As a specific feature of the presented approach, for the non-smooth case this internallength is exported, in addition to the homogenized stresses and the tangent constitutive operator, to themacro-scale, and considered the bandwidth of a propagating strain localization band, at that scale.? Consistently with this internal length, a specific computational procedure, based on the crack-path-fieldand strain injection techniques, recently developed by the authors [2] is then used for modelling the onsetand propagation of this localization band, at the macro-scale.Representative simulations show that the resulting approach provides mesh objective results with respectto, both, size and bias of the upper-scale mesh, and with respect to the size of the lower-scale RVE/failurecell. The continuum character of the approach confers to the formulation a minimally invasive character,with respect to standard procedures for computational one-scale homogenization and modelling ofpropagating material failure. The issue of reducing the computational cost using High PerformanceReduced Order Modelling (HP-ROM) techniques is also considered.