Multiscale modeling for material failure

S. TORO; P.J. SÁNCHEZ; P.J. BLANCO; E.A. DE SOUZA NETO; A.E. HUESPE; R.A. FEIJÓO

Río de Janeiro

Simposio; 52th SNP meeting of the Society for Natural Philosophy, Scale bridging in the Mathematical and Mechanical Science; 2014

Universidad Federal de Río de Janeiro, Dpto de mecánica

Material fracture problems involve physical phenomena observed at different length scales, with strong coupling effects between them. Multiscale models, making use of scale bridging techniques, are showing to be an important tool of analysis to understand with more details such phenomena involving a wide range of scales and their coupling. In this contribution, we show a number of issues related to the mechanical approach of fracture problems, but more specifically, we address to the mathematical formulation of a multiscale fracture model that considers the coupling between scales of length. The main application of this model points out to understand and describe fracture problems in heterogeneous materials at the macro and meso or microscale. Recent works of the authors (Sánchez et al. (2012), Toro et al. (2013), Toro et al. (2014), Blanco et al. (2014)) have presented a new variational multiscale formulation addressed to modeling failure of heterogeneous materials from a purely mechanical point of view. The formulation is called (Failure-Oriented Multi-scale Formulation (FOMF)). Two well-separated length scales are considered in the FOMF. The macro model describes the failure processes that are taking place at the micro model by means of a cohesive interface which is mechanically characterized through a traction T vs. separation B relation. The failure processes at the microscopic level are modeled using a Representative Volume Element (RVE). One of the main characteristics of this technique is its full variational consistency, as well as, that the vector T is objective with respect to the micro-cell size taken to perform the material failure analysis at the microscopic level. Computational homogenization techniques have also been developed to implement this formulation. A number of issues arise, but mainly we remark: specific boundary conditions should be imposed on the RVE according to satisfy: i) objectivity of the macroscopic relations (T vs. B) with respect to the micro-cell size, and, ii) full degradation of the RVE model in the sense that the homogenized material response reaches a completely exhausted state. Numerical assessment of the model is given in the contribution, and particularly, it is validated through Direct Numerical Simulation (DNS) procedures.