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• RVE method to homogenize an elasto-plastic spheres-reinforced FGM composite. • Implementation of the homogenization technique in VUMAT-VUSFLD into Abaqus/Explicit. • Formability of elasto-plastic spheres-reinforced FGM composite using a single point incremental forming process. • Effect of power-law index on Von Mises distributions, plastic deformation, and vertical forming force is investigated. In the present paper, as a first endeavor, homogenization of elasto-plastic functionally graded material (FGM) is investigated based on representative volume element (RVE) and used for the first time in the single point incremental forming (SPIF) process. The effective properties of elasto-plastic spheres-reinforced FGM composite are determined using the numerical RVE method and Mori-Tanaka model. In order to implement the homogenization equations and numerical algorithm into Abaqus Software, user-defined material, (VUMAT) and (VUSFLD) subroutines are employed. The accuracy of the proposed homogenization methodology is highlighted through comparisons of the present results with those taken from the literature and an excellent agreement is found. During SPIF process, the effect of the power-law index on the formability, plastic deformation, forming force along Z_direction and Von Mises distribution is analyzed. Parametric studies are conducted to show the influence of cone wall angle and sheet thickness on the formability and the thinning along the SPIF process. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Based on experimental investigations on the influence of water content on time-dependent behaviour of flax reinforced epoxy composites, this paper proposes to model the viscoelastic–viscoplastic behaviour with hygromechanical coupling. From a rheological point of view, the proposed model is a combination of a linear spring (elasticity), a Kelvin–Voigt model (viscoelasticity) and a viscoplastic model described by kinematic hardening in which the evolution of the internal variable is collinear with the plastic deformation. The hygromechanical coupling is obtained via the dependence on water content of all the model parameters according to a power law. The developed model shows a good correlation between experimental data (tensile, creep and relaxation) and numerical predictions of the mechanical behaviour for low water contents (below 4.90%). However, the model shows its limits for high water contents ( w c ≥ 4. 90 %) and high loadings. Indeed, tensile tests have revealed the emergence of a stiffening phenomenon for high loadings according to water content. This phenomenon was not taken into account in the proposed model which could explain its limitations. This assumption is confirmed by comparing the evolution of experimental yield stress with the model prediction. [ABSTRACT FROM AUTHOR]