Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications

Various multiscale methods are reviewed in the context of modelling mechanical and thermomechanical responses of composites. They are developed both at the material level and at the structural analysis level, considering sequential or integrated kinds of approaches. More specifically, such schemes like periodic homogenization or mean field approaches are compared and discussed, especially in the context of non linear behaviour. Some recent developments are considered, both in terms of numerical methods (like FE2) and for more analytical approaches based on Transformation Field Analysis, considering both the homogenization and relocalisation steps in the multiscale methodology. Several examples are shown.

Multiscale Methods for Composites: A Review

Mean-field homogenization of multi-phase thermo-elastic composites: a general framework and its validation

Structure–property optimization of ultrafine-grained dual-phase steels using a microstructure-based strain hardening model

Micromechanics of room and high temperature fracture in 6xxx Al alloys

Homogenization of two-phase elasto-plastic composite materials and structures: Study of tangent operators, cyclic plasticity and numerical algorithms

This article presents a Study of steel fiber-reinforced concrete (SFRC). In its first part, it four-point bending test performed oil both plain concrete and SFRC is investigated. The collected nonlinear load-deflection curves are transformed into stress-strain curves with the help of all incremental method, which the authors developed in the nonlinear regime. In the second part of this article, the authors present a micromechanical approach based oil Mori-Tanaka/Voigt mean-field homogenization schemes in order to model the effective nonlinear behavior of the three-phase brittle composite materials. The first phase (concrete matrix) is assumed to obey Ju's brittle damage model. The second phase (fibers) is modeled with classical J(2) plasticity, while the third phase represents cavities. Numerical algorithms enable the simulation of SFRC within reasonable CPU time and memory requirements. The homogenization module is interfaced to the finite element package ABAQUS. A two-scale simulation of the bending test is validated against the experimental results.

/pdf/micromechanics-of-the-deformation-and-damage-of-steel-fiber-40jtjjz91n.pdf

Micromechanics of the deformation and damage of steel fiber-reinforced concrete

Two issues of the XFEM method are adressed. The first one is the clip to vertex algorithm when a node is too close to the iso zero of the levelset that requires the definition of a treshold. The second one is the numerical integration in high order elements cut by the levelset. A solution to these two problems is presented.

Amine Ouaar

Papers

Homogenization of two-phase elasto-plastic composite materials and structures: Study of tangent operators, cyclic plasticity and numerical algorithms

Micromechanics of the deformation and damage of steel fiber-reinforced concrete

Discontinuous fields integration in a structured mesh using the level set method