Representative elementary volume

About: Representative elementary volume is a research topic. Over the lifetime, 4105 publications have been published within this topic receiving 86863 citations.

Effective response of classical, auxetic and chiral magnetoelastic materials by use of a new variational principle

Abstract: This work provides a rigorous analysis of the effective response, i.e., average magnetization and magnetostriction, of magnetoelastic composites that are subjected to overall magnetic and mechanical loads. It clarifies the differences between a coupled magnetomechanical analysis in which one applies a Eulerian (current) magnetic field and an electroactive one where the Lagrangian (reference) electric field is usually applied. For this, we propose an augmented vector potential variational formulation to carry out numerical periodic homogenization studies of magnetoelastic solids at finite strains and magnetic fields. We show that the developed variational principle can be used for bottom-up design of microstructures with desired magnetomechanical coupling by properly canceling out the macro-geometry and specimen shape effects. To achieve that, we properly treat the average Maxwell stresses arising from the medium surrounding the magnetoelastic representative volume element (RVE), while at the same time we impose a uniform average Eulerian and not Lagrangian magnetic field. The developed variational principle is then used to study a large number of ideal as well as more realistic two-dimensional microstructures. We study the effect of particle volume fraction, particle distribution and particle shape and orientation upon the effective magnetoelastic response at finite strains. We consider also unstructured isotropic microstructures based on random adsorption algorithms and we carry out a convergence study of the representativity of the proposed unit cells. Finally, three-phase two-dimensional auxetic microstructures are analyzed. The first consists of a periodic distribution of voids and particle chains in a polymer matrix, while the second takes advantage of particle shape and chirality to produce negative and positive swelling by proper change of the chirality and the applied magnetic field.

Computational modeling of dual-phase steels based on representative three-dimensional microstructures obtained from EBSD data

Abstract: The microstructure of dual-phase steels consisting of a ferrite matrix with embedded martensite inclusions is the main contributor to the mechanical properties such as high ultimate tensile strength, high work hardening rate, and good ductility Due to the composite structure and the wide field of applications of this steel type, a wide interest exists in corresponding virtual computational experiments For a reliable modeling, the microstructure should be included For that reason, in this paper we follow a computational strategy based on the definition of a representative volume element (RVE) These RVEs will be constructed by a set of tomographic measurements and mechanical tests In order to arrive at more efficient numerical schemes, we also construct statistically similar RVEs, which are characterized by a lower complexity compared with the real microstructure but which represent the overall material behavior accurately In addition to the morphology of the microstructure, the austenite–martensite transformation during the steel production has a relevant influence on the mechanical properties and is considered in this contribution This transformation induces a volume expansion of the martensite phase A further effect is determined in nanoindentation test, where it turns out that the hardness in the ferrite phase increases exponentially when approaching the martensitic inclusion To capture these gradient properties in the computational model, the volumetric expansion is applied to the martensite phase, and the arising equivalent plastic strain distribution in the ferrite phase serves as basis for a locally graded modification of the ferritic yield curve Good accordance of the model considering the gradient yield behavior in the ferrite phase is observed in the numerical simulations with experimental data