Two-scale model for failure analysis of heterogeneous materials: numerical validation

SEBASTIAN TORO; PABLO SÁNCHEZ; PABLO BLANCO; ALFREDO HUESPE; RAÚL FEIJÓO

Praga

Congreso; Third International Conference on Computational Modeling of Fracture and Failure of Materials and Structures (CFRAC 2013); 2013

ECCOMAS

In recent works ([1] and [2]), the authors have presented a new variational multi-scale formulation devised to modeling the failure of heterogeneous materials (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).The traction T is defined as a function of B by means of a computational homogenization technique that considers two transfer operators: i) a non homogeneous strain injection operator that transfers the crack opening B, from the macro to the micro scale; ii) as consequence of a well established variational principle and the adopted approach, it is derived a stress homogenization operator which determines T as a results of a homogenization of the stress field at the RVE level.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.The numerical implementation of the multi-scale model is presented. At the macroscopic scale, an E-FEM technique (finite elements with embedded strong discontinuities) is adopted to simulate the cohesive interfaces. At the RVE scale, continuum damage or elasto-plastic models with softening are used. Then, strain localization solutions act as the precursor mechanism leading to failure. A smeared crack approach is taken to circumvent the deficiencies of standard finite element approaches with this kind of continuum constitutive models.Specific boundary conditions, imposed on the RVE, are given in order to satisfy: i) objective 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. Boundary conditions similar to that presented in [3] are taken in order to satisfy the second requirement. In this paper, emphasis is given to the numerical assessments of the model. In particular, we compare and verify the numerical solution provided by the two-scale variational formulation with respect to a mono-scale Direct Numerical Simulation (DNS) approach.References[1] P.J. Sánchez, P.J. Blanco, A.E. Huespe, R.A. Feijóo, Failure-Oriented Multi-scale Variational Formulation: micro-structures with nucleation and evolution of softening bands, Comp. Meth. Appl. Mech. Engrg., in press, 2012.[2] S. Toro, P.J. Sánchez, A.E. Huespe, S. Giusti, P.J. Blanco, R.A. Feijóo, A two-scale failure model for heterogeneous materials: numerical implementation based on the Finite Element Method, Int. J. Num. Meth. Engrg., submitted, 2013.[3] E. W. C. Coenen, V. G. Kouznetsova, M. G. D. Geers, Novel boundary conditions for strain localization analyses in microstructural volume elements, Int. J. Num. Meth. Engrg., 90, 121, 2012.