A two-scale failure model for heterogeneous materials: numerical implementation based on the Finite Element Method

S. TORO; P.J. SÁNCHEZ; A.E. HUESPE; S.M. GUISTI; P.J. BLANCO; R.A. FEIJÓO

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

JOHN WILEY & SONS LTD

Lugar: Londres; Año: 2014 vol. 97 p. 313 - 351

0029-5981

In a first part of this contribution, a compact theoretical revision of the mechanical and variational foundations of a Failure-Oriented Multi-scale Formulation (FOMF) devised for modeling failure in heterogeneous materials is described.The proposed model considers two well separated physical length scales, namely: (i) the macro scale where nucleation and evolution of a cohesive surface is considered as a medium to characterize the phenomenon taking place at the lower scale of length, and (ii) The micro scale where some mechanical processes that leads to the material failure are taking place, such as strain localization, damage, shear band formation, etc. These processes are modeled using the concept of Representative Volume Element (RVE).In the macro scale, the traction separation response, characterizing the mechanical behavior of the cohesive interface, is a result of the simulated failure processes taking place in the micro scale, and it is obtained by a particular homogenization technique applied on specific RVE sub-domains. Standard, as well as, Non-Standard boundary conditions are consistently derived in order to preserve ?objectivity? of the homogenized response with respect to the micro-cell size.In a second part of the paper, and as an original contribution, the detailed numerical implementation of the two-scale model based on the Finite Element Method is presented. Special attention is devoted to the topics which are distinctive of the FOMF, such as: (i) the finite element technologies adopted in each scale along with their corresponding algorithmic expressions, (ii) the generalized treatment given to the kinematical boundary conditions in the RVE and (iii) how these kinematical restrictions affect the capturing of macroscopic material instability modes and the posterior evolution of failure at the RVE level.Finally, a set of numerical assessments is performed in order to show the potentialities of the proposed methodology, as well as, to compare and verify the numerical solution provided by the two-scale model with respect to a mono-scale Direct Numerical Simulation (DNS) approach