Failure of heterogeneous materials: 3D meso‐scale FE models with embedded discontinuities

Abstract

SUMMARYWe present a meso-scale model for failure of heterogeneous quasi-brittle materials. The model problem of heterogeneous materials that is addressed in detail is based on two-phase 3D representation of reinforced heterogeneous materials, such as concrete, where the inclusions are melt within the matrix. The quasibrittle failure mechanisms are described by the spatial truss representation, which is defined by the chosen Voronoi mesh. In order to explicitly incorporate heterogeneities with no need to change this mesh, some bar elements are cut by the phase-interface and must be split into two parts. Any such element is enhanced using both weak and strong discontinuities, based upon the Incompatible Mode Method. Furthermore, a dedicated operator split solution procedure is proposed to keep local any additional computation on elements with embedded discontinuities. The results for several numerical simulations are presented to illustrate the capabilities of the proposed model to provide an excellent representation of failure mechanisms for any different macroscopic loading path.

Meso-macro modelling of crack-induced diffusivity in heterogeneous materials

“…For the readers interested in more details, a complete description of the model, its numerical implementation and a number of illustrative examples of the model predictive capabilities can be found in [1].…”

“…(17) where D 1 and D 2 are the diffusion coefficient in the mortar matrix and in the aggregates, respectively and θ, the spatial position of the interface in an element computing in the meshing process (see ( [1]) for details). Note that when an element is in the mortar matrix, D 1 is equal to D 2 and the original expression of ( [6]) is found again.…”

“…In this paper, we model concrete at the mesoscale as an heterogeneous quasi-brittle two-phase material based upon the work of ( [1]). This model is presented in Section 2.…”

Performance Based Earthquake-Resistant Design: Migrating Towards Nonlinear Models and Probabilistic Framework

“…However, it is only since recent times that we have acquired the modelling capabilities; e.g. see (Benkemoun et al 2010;Dominguez et al 2005;Ibrahimbegovic and Brancherie 2003;Ibrahimbegovic and Delaplace 2003;Ibrahimbegovic and Markovic 2003;Ibrahimbegovic and Melnyk 2007;Ibrahimbegovic 2009;Ibrahimbegovic et al 2008Ibrahimbegovic et al , 2010Jehel et al 2010;Markovic and Ibrahimbegovic 2004) to provide a more refined interpretation of the local failure mechanisms rather than the global, push-over-type models. We have also very well advanced in the long process, from early works (Ibrahimbegovic andWilson 1990, 1992) to more recent works (Ibrahimbegovic and Markovic 2003) or (Ibrahimbegovic et al 2008) in development of the robust computational procedure that is able to isolate the most severely damaged zone and deliver the corresponding scenario on the interplay of different local mechanisms in building the global failure mechanisms for structures and systems of any complexity.…”

A Stochastic Multi-scale Approach for Numerical Modeling of Complex Materials—Application to Uniaxial Cyclic Response of Concrete

“…In [24], heterogeneities are represented by random fields introduced at a mesoscale, which defines so-called Statistical Volume Elements that tends to become RVEs as mesoscale grows; effective properties at macroscale are retrieved according to two hierarchies of scale-dependent bounds obtained from either homogenous displacements or homogenous tensions applied on the boundary of the mesoscale. In [2], a mesoscale is explicitly constructed for representing the macroscopic behavior of heterogeneous quasi-brittle materials. This mesoscale consists of a 3D finite element mesh composed of truss elements cut by inclusions.…”