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

Abstract

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. One such case of probabilistic analysis is considered in this work where the geometry of the phase interface is obtained as the result of the Gibbs random process. Originality/value -The paper confirms that one can make the most appropriate interpretation of the heterogeneous structure properties by taking into account the fine details of the internal structure, along with the related probabilistic aspects with the proper source of randomness, such as the one addressed herein in terms of porosity.

Anisotropic constitutive model of plasticity capable of accounting for details of meso-structure of two-phase composite material

“…October 14,2016 current trend, it has become crucial to have accurate tools that improve the predictive capabilities of macroscopic constitutive equations and furnish a precise description of nonlinear response in structural analysis. At the structural scale, phenomenological models based on macroscopic quantities such as macroscopic stresses and strains and macroscopic laws placed in the thermodynamical framework are widely used.…”

“…The first discontinuity is based upon a weak discontinuity (continuous displacement field and discontinuous strain field) [14]. It is introduced because of the retained meshing process which relies on non-conforming mesh [15] where some truss elements are cut into two parts, each having different elastic properties.…”

“…1(b)): those entirely inside the matrix (in blue) with no weak discontinuity activated, those entirely in the aggregate (in green) with no weak discontinuity activated and those split by a physical interface (in bold red) for which the weak discontinuity is activated. Non-conforming meshes provide the advantage to have a meshing process independent from the microstructure (positions of the aggregates and shapes), as well as the fixed size of the mesh in probability studies [14] of meso-structure for this kind of material. In the present work, this approach is applied to three dimensional domains.…”

Multi-scale failure of heterogeneous materials: A double kinematics enhancement for Embedded Finite Element Method

“…A weak discontinuity (Hautefeuille et al, 2009) (finite jump in the strain field) is introduced into each element in order to take into account this particular kinematics. This technique provides a meshing process that does not depend on the position and the shape of the inclusions.…”

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

“…These enhancements concern both the strain field (in order to represent an elastic modulus jump [18,19]) and the displacement field (in order to model cracks through displacements jumps [6,[20][21][22]). This Section describes these two kinds of discontinuities and shows how the Incompatible Mode Method [15,16] might be used to accommodate both these jumps.…”