Martin Hautefeuille

Failure model for heterogeneous structures using structured meshes and accounting for probability aspects

Purpose – The purpose of this paper is to discuss the inelastic behavior of heterogeneous structures within the framework of finite element modelling, by taking into the related probabilistic aspects of heterogeneities.Design/methodology/approach – The paper shows how to construct the structured FE mesh representation for the failure modelling for such structures, by using a building‐block of a constant stress element which can contain two different phases and phase interface. All the modifications which are needed to enforce for such an element in order to account for inelastic behavior in each phase and the corresponding inelastic failure modes at the phase interface are presented.Findings – It is demonstrated by numerical examples that the proposed structured FE mesh approach is much more efficient from the non‐structured mesh representation. This feature is of special interest for probabilistic analysis, where a large amount of computation is needed in order to provide the corresponding statistics. On...

Probability Based Size Effect Representation for Failure in Civil Engineering Structures Built of Heterogeneous Materials

In this work we discuss the failure analysis of civil engineering structures built of heterogeneous materials. The material heterogeneities call for a detailed representation of typical micro or meso-structure, which can be provided with the structured FE mesh representation as illustrated herein for 2D case and two-phase material. The building-block of such a representation is the constant stress triangular element that can contain two different phases and phase interface, along with all modifications needed to account for inelastic behavior in each phase and the corresponding inelastic failure modes at the phase interface. We further show by numerical simulations that the proposed structured FE mesh approach is much more efficient than the non-structured mesh representation. This feature is of special interest for probabilistic analysis, where a large amount of computation is needed in order to provide the corresponding statistics. One such case of probabilistic failure analysis is also considered in this work, where the geometry of the phase interface remains uncertain since it is obtained as the result of the Gibbs random process. This computation is further used to provide the appropriate probabilistic description of material parameters of phenomenological model of localized failure in terms of correlated random fields. Subsequent Monte Carlo computations of failure phenomena in simple tension test performed with such probabilistic phenomenological model clearly show the capability of presented approach to recover the size effects anywhere within a range between the two classical bounds which are Continuum Damage Mechanics and Linear Fracture Mechanics.

Stochastic analysis of coupled nonlinear thermo-mechanical problems : SFEM model

Dealing with the modelling of brittle and quasi-brittle materials requires to be able to take into account of some special features of such materials, among them is the so-called size-effect. This effect leads to an important uncertainty about the yield or maximum stress in a structure, depending on its size.Moreover this effect is mostly due to the heterogeneity of these materials, at a microscopic scale.