Mean-field Homogenization Method Research Articles

Quantum-Mechanical Study of Single-Crystalline and Polycrystalline Elastic Properties of Mg-Substituted Calcite Crystals

We use quantum-mechanical calculations to study single-crystalline elastic properties of (Ca,Mg)CO3 crystals with concentrations ranging from calcite CaCO3 to magnesite MgCO3. By analyzing results for a dense set of distributions of Ca and Mg atoms within 30-atom supercells, our theoretical study shows that those atomic configurations, that minimize the total energy for a given concentration, are characterized by elastic constants that either increase with the Mg content or remain nearly constants. Employing these ab initio calculated single-crystalline elastic parameters, the polycrystalline elastic properties of (Ca,Mg)CO3 aggregates are determined using a mean-field self-consistent homogenization method. The computed integral elastic moduli (bulk and shear) show a significant stiffening impact of Mg atoms on calcite crystals. Our analysis also demonstrates that it is not advantageous to use a granular two-phase composite of stoichiometric calcite and magnesite instead of substituting individual Ca and Mg atoms. Such two-phase aggregates are not significantly thermodynamically favorable and do not offer any strong additional stiffening effect.

Nonlinear modeling of carbon nanotube composites dissipation due to interfacial stick–slip

A nonlinear constitutive theory is proposed to describe and characterize the hysteretic elastoplastic response of nanocomposite materials caused by the inelastic shear stick–slip between carbon nanotubes and the surrounding matrix. The theory combines the mean-field homogenization method based on the Eshelby equivalent inclusion theory, the Mori–Tanaka homogenization approach, and the concept of inhomogeneous inclusions affected by inelastic eigenstrains. The shear stick–slip is accounted for as an incremental plastic eigenstrain in the inclusions. The evolution of the introduced plastic eigenstrain is regulated by a constitutive law based on a micromechanical adjustment of the von Mises function based on the interfacial stress discontinuity. Parametric studies show that the investigated carbon nanotube composites can exhibit superior damping capacities by determining optimal nano/micro-scale constitutive parameters to maximize the nanofrictional energy dissipation.

A combined incremental-secant mean-field homogenization scheme with per-phase residual strains for elasto-plastic composites

This paper presents an incremental secant mean-field homogenization (MFH) procedure for composites made of elasto-plastic constituents. In this formulation, the residual stress and strain states reached in the elasto-plastic phases upon a fictitious elastic unloading are considered as starting point to apply the secant method. The mean stress fields in the phases are then computed using secant tensors, which are naturally isotropic and enable to define the Linear–Comparison-Composite. The method, which remains simple in its formulation, is valid for general non-monotonic and non-proportional loading. It is applied on various problems involving elastic, elasto-plastic and perfectly-plastic phases, to demonstrate its accuracy compared to other existing MFH methods.

A multiscale mean-field homogenization method for fiber-reinforced composites with gradient-enhanced damage models

In this work, a gradient-enhanced homogenization procedure is proposed for fiber reinforced materials. In this approach, the fibers are assumed to remain linear elastic while the matrix material is modeled as elasto-plastic coupled with a damage law described by a non-local constitutive model. Toward this end, the mean-field homogenization is based on the knowledge of the macroscopic deformation tensors, internal variables and their gradients, which are applied to a micro-structural representative volume element (RVE). The macro-stress is then obtained from a homogenization procedure. The methodology holds for 2-phase composites with moderate fiber volume ratios, and for which, at the RVE size, the matrix can be considered as homogeneous isotropic and the ellipsoidal fibers can be considered as homogeneous transversely isotropic. Under these assumptions, the method is successfully applied to simulate the damage process occurring in unidirectional carbon-fiber reinforced epoxy composites submitted to different loading conditions.

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

Grain size reduction in single phase alloys is generally accompanied by a loss of ductility related to a decrease in the strain hardening capacity. The flow behaviour of fine-grained dual-phase steels produced by swaging was investigated in order to address the couplings between grain size reduction and incorporation of a second phase towards optimizing microstructures with different objectives. A physically based grain size dependent strain hardening model has been developed for the ferrite matrix, involving specific laws for the accumulation and saturation of dislocations along grain boundaries and for their net back stress contribution. The back stress increases with the dislocation density, reaches a maximum and finally decreases due to screening effects. The overall behaviour of the ferrite–martensite composite is then evaluated using a mean field homogenization method. After identification of the material parameters, a parametric study provides, for a given carbon content and grain size of the ferrite matrix, the optimum martensite volume fraction, leading either to the maximum strength ductility product or to the maximum strength under the constraint of a minimum ductility.