Continuum Approach to Computational Multi-scale Modeling of Material Failure

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

Barcelona

Congreso; COMPLAS XII, Int. Conf. on Comp. Plasticity, Fundamentals and Applic.,; 2013

Two-scale computational modelling of materials is a subject of increasing interest in computationalmechanics. When dealing with materials displaying a spatially smooth behaviour, there is wideconsensus on the suitable mechanical approaches to the problem. The so called FE2 methods, basedon the hierarchical, bottom-up one-way coupled, description of the material using the finite elementmethod in both scales, and computational homogenization procedures at the fine scale, is nowadaysone of the most popular approaches. At the heart of this direct computational homogenizationprocedures lies the notion of representative volume element (RVE) defined as the smallest possibleregion representative of the whole heterogeneous medium on average. Two-scale computationalmodelling of material failure exhibits additional complexity; either if discrete approaches, based onnon-linear decohesive traction-separation laws, or continuum approaches, using stress-strainsoftening constitutive models combined with strain localization techniques, are used at the lowerscale, the kinematic description of some, or both, scales cannot be considered smooth anymore, andthe existence of the RVE can be questioned arguing that, in this case, the material loses the statisticalhomogeneity. A crucial consequence of this issue is the lack of objectivity of the results with respectto the size of the RVE. In [1] a recent attempt to overcome this flaw, for regularized non-localmodels, can be found.The present work is an attempt to address this issue in a continuum setting i.e.: the propagatingfailure mechanisms, at both scales, are captured by means of continuum (stress-strain) models. Theessentials of the method are: 1) at the microscopic level material failure is captured on a failurecell/RVE via strain-localization on cohesive bands equipped with a strain-softening continuumconstitutive model, 2) stress homogenization, at the failure-cell/RVE level returns a macroscopicstrain-softening continuum constitutive model exhibiting a characteristic length, which stemsnaturally from the size of the chosen RVE and the type and measure of the activated material failuremechanisms at the failure-cell, 3) the macrostructure is then equipped with finite elements withembedded, regularized, strain-localization bands and displacement-discontinuity bands, whosebandwidth is consistent with the aforementioned characteristic length, that capture the onset andpropagation of the resulting macroscopic material failure mechanisms i.e.: cracks or slip lines.Through this method, insensitivity of the structural macroscopic response, with respect to the RVEsize and the macroscopic and microscopic finite element meshes, is achieved, and material failureproperties, like the fracture energy, are consistently up-scaled.