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.

Numerical modelling of the elastic properties of 3D-printed specimens of thermoplastic matrix reinforced with continuous fibres

Abstract: Numerical modelling of 3D-printed Fused Filament Fabrication (FFF) specimens with thermoplastic matrices reinforced with continuous fibres is still in its infancy. The existing numerical work is mostly related to the adhesion between printed filaments and not to the mechanical properties. However, the latter are one of the most important parameters that define the structural behaviour of the material. A numerical three-step multi-scale model is introduced in the present study, concentrating on the fundamental aspect of the elastic properties. The most encountered reinforced Nylon FFF structures with continuous fibres of glass, carbon and, Kevlar, are examined. The concept of Representative Volume Element (RVE) is utilized for the combination of matrix and fibres at the micro-scale and the addition of voids at the meso-scale. Finally, at the macro-scale, tension simulations are performed for specimens with various lay-ups. The results of the numerical model are validated using analytical models and experimental data. A new analytical micro-mechanical model is developed as an alternative to the more cumbersome Mori–Tanaka model. A series of experimental testing is performed for Kevlar-reinforced Nylon specimens to accompany the limited existing data and aid the validation process. The comparison reveals a good correlation with the analytical models for the micro- and meso-scale and to the experimental data for the macro-scale, leading to a robust conclusion for its validity and efficiency.

An advanced approach for the generation of complex cellular material representative volume elements using distance fields and level sets

Abstract: A general and widely tunable method for the generation of representative volume elements for cellular materials based on distance and level set functions is presented. The approach is based on random tessellations constructed from random inclusion packings. A general methodology to obtain arbitrary-shaped tessellations to produce disordered foams is presented and illustrated. These tessellations can degenerate either in classical Voronoi tessellations potentially additively weighted depending on properties of the initial inclusion packing used, or in Laguerre tessellations through a simple modification of the formulation. A versatile approach to control the particular morphology of the obtained foam is introduced. Specific local features such as concave triangular Plateau borders and non-constant thickness heterogeneous coatings can be built from the tessellation in a straightforward way and are tuned by a small set of parameters with a clear morphological interpretation.

Use of composite cylinder model as representative volume element for unidirectional fiber composites

Abstract: The present work is concerned with the theoretical study of the elastic properties of unidirectional fiber composites. The approach to calculate the effective moduli of composite materials is generally based upon the premise of a representative volume element, or an element in which the strain and stress averages taken over large enough subregions of the specimen are the same for any such subregion. For purposes of computation, some model of a fiber composite must be assumed. The objective of this study is to demonstrate that the composite cylinder model can provide a good simulation for the representative volume element to define the response of a unidirectional composite for a wide range of elastic moduli and volume fraction provided the displacements are prescribed on the external surfaces. Results of the effective elastic moduli and microstresses within the constituents are compared with existing numerical solutions, both with and without partial interphase failure, to demonstrate the effectiveness of...

A study of the unloading behaviour of dual phase steel

Abstract: It is important to understand the strain recovery of a steel sheet in order to predict its springback behaviour. During strain recovery, the stress–strain relation is non-linear and the resulting unloading modulus is decreased. Moreover, the unloading modulus will degrade with increasing plastic pre-straining. This study aims at adding new knowledge on these phenomena and the mechanisms causing them. The unloading behaviour of the dual-phase steel DP600 is characterised experimentally and finite element (FE) simulations of a representative volume element (RVE) of the microstructure are performed. The initial stress and strain state of the micromechanical FE model is found by a simplified simulation of the annealing processes. It is observed from the experimental characterisation that the decrease of the initial stiffness of the unloading is the main reason for the degrading unloading modulus. Furthermore, the developed micromechanical FE model exhibits non-linear strain recovery due to local plasticity caused by interaction between the two phases.

Derivation of anisotropic flow curves of ferrite–pearlite pipeline steel via a two-level homogenisation scheme

Abstract: In order to calculate the effective macroscopic stress–strain curves of a pearlitic–ferritic pipeline steel, a multi-scale approach based on the homogenisation method is presented. Starting from an experimental material characterisation after the cooling process, material models involving microstructural features (e.g. grain size, carbon content) are derived for each phase. Since pearlite is a eutectoid phase mixture, embedded in a ferrite matrix, three length scales are introduced: the nano-scale of a ferrite–cementite bi-lamella of pearlite, the mesoscopic pearlite/ferrite microstructure and the macro-scale of the component. Firstly homogenisation techniques are applied to a bi-lamella Representative Volume Element (RVE) of pearlite. Initial predictions based on the assumption of a hard, elastic cementite phase are further improved by considering its yield behaviour. The present study outlines that cementite is not only anisotropic in elasticity but also in plasticity. Due to uncertainties about the yield behaviour of cementite, a sensitivity analysis has been performed. Secondly pearlite is treated at the micro-scale as an effective phase in an elasto-plastic ferrite matrix. Virtual tensile and shear tests are performed in order to derive the effective flow curves of the pearlite/ferrite microstructures. Comparisons with experimental stress–strain curves in rolling and transverse directions illustrate the accuracy and entitlement of the two-level homogenisation scheme.