Determination of the size of the representative volume element for random composites: statistical and numerical approach

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

X-ray computer tomography (CT) is fast becoming an accepted tool within the materials science community for the acquisition of 3D images. Here the authors review the current state of the art as CT transforms from a qualitative diagnostic tool to a quantitative one. Our review considers first the image acquisition process, including the use of iterative reconstruction strategies suited to specific segmentation tasks and emerging methods that provide more insight (e.g. fast and high resolution imaging, crystallite (grain) imaging) than conventional attenuation based tomography. Methods and shortcomings of CT are examined for the quantification of 3D volumetric data to extract key topological parameters such as phase fractions, phase contiguity, and damage levels as well as density variations. As a non-destructive technique, CT is an ideal means of following structural development over time via time lapse sequences of 3D images (sometimes called 3D movies or 4D imaging). This includes information nee...

https://www.tandfonline.com/doi/pdf/10.1179/1743280413Y.0000000023

Quantitative X-ray tomography

https://hal.archives-ouvertes.fr/hal-00858028/document

Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing

A gradient-enhanced computational homogenization procedure, that allows for the modelling of microstructural size effects, is proposed within a general non-linear framework. In this approach the macroscopic deformation gradient tensor and its gradient are imposed on a microstructural representative volume element (RVE). This enables us to incorporate the microstructural size and to account for non-uniform macroscopic deformation fields within the microstructural cell. Every microstructural constituent is modelled as a classical continuum and the RVE problem is formulated in terms of standard equilibrium and boundary conditions. From the solution of the microstructural boundary value problem, the macroscopic stress tensor and the higher-order stress tensor are derived based on an extension of the Hill-Mandel condition. This automatically delivers the microstructurally based constitutive response of the higher-order macro continuum and deals with the microstructural size in a natural way. Several examples illustrate the approach, particularly the microstructural size effects.

http://www.mate.tue.nl/mate/pdfs/2091.pdf

Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme

A unifying thermomechanical framework is presented that reconciles several classes of gradient elastoviscoplasticity and damage models proposed in the literature during the last 40 years . It is based on the introduction of the micromorphic counterpart ϕχ of a selected state or internal variable ϕ in a standard constitutive model. In addition to the classical balance of momentum equation, a balance of micromorphic momentum is derived that involves generalized stress tensors. The corresponding additional boundary conditions are also deduced from the procedure. The power of generalized forces is assumed to contribute to the energy balance equation. The free energy density function is then chosen to depend on a relative generalized strain, typically ϕ- ϕχ , and the microstrain gradient ∇ ϕχ . When applied to the deformation gradient itself, ϕ≡ F , the method yields the micromorphic theory of Eringen and Mindlin together with its extension to finite deformation elastoviscoplasticity by Forest and Sievert. If...

Samuel Forest

Papers

Determination of the size of the representative volume element for random composites: statistical and numerical approach

Micromorphic Approach for Gradient Elasticity, Viscoplasticity, and Damage

Cosserat overall modeling of heterogeneous materials

Nonlinear microstrain theories

Intergranular and intragranular behavior of polycrystalline aggregates.Part 2: Results