A finite strain incremental-secant homogenization model for elasto-plastic composites

Abstract

This paper presents a finite strain extension of the incremental-secant mean-field homogenization (MFH) formulation for two-phase elasto-plastic composites. The formulation of the local finite strain elasto-plastic constitutive equations of each phase is based on a multiplicative decomposition of the deformation gradient as suggested by Simo in (Computer Methods in Applied Mechanics and Engineering, 99(1):61-112, 1992.). The latter has proposed algorithms which preserve the classical return mapping schemes of the infinitesimal theory by using principal Kirchhoff stresses and logarithmic eigenvalues of the left elastic Cauchy-Green strain. Relying on this property, we show that, by considering a quadratic logarithmic free energy and J2-flow theory at the local level, infinitesimal strain incremental-secant MFH is readily extended to finite strains. The proposed formulation and corresponding numerical algorithms are then presented. Finally, the predictions are illustrated with several numerical simulations which are verified against full-field finite element simulations of composite cells, demonstrating that the micro-mechanically based approach is able to predict the influence of the micro-structure and of its evolution on the macroscopic properties in a very cost-effective manner.

Micromechanical modelling of mechanochemical processes in heterogeneous materials

“…There are multiple ways of modelling particle-reinforced heterogeneous materials via micromechanical full-field (FF) and mean-field (MF) approaches. For a recent review of the FF homogenisation techniques, the reader is referred to [23], while a recent overview of the MF techniques can be found in [24][25][26]. FF homogenisation techniques have an advantage over the MF techniques in terms of accuracy; however, they require the FF solution of the underlying PDEs.…”

“…Furthermore, this scheme has also been applied to obtain the effective properties of the composite electrodes [40,41], again, in the elastic regime. The Mori-Tanaka scheme has originally been proposed for linear elasticity [35,36], later extended to non-elastic behaviour using an incremental formulation [42] and, finally, has also been formulated for finite deformations [24,25]. However, up to now, the Mori-Tanaka approach has not been applied to heterogeneous materials, where mechanochemical transformation takes place and involves propagating reaction fronts, in both smallstrain and nonlinear finite-strain settings.…”

Micro-mechanics and data-driven based reduced order models for multi-scale analyses of woven composites

“…In the future work, the presented models will be enhanced by adding damage variables in the matrix [40] and fibres [34,47]. The MFH formula developed in the finite strain regime [48] can also be considered.…”

Adaptive Affine Homogenization Method for Visco-hyperelastic Composites with Interfacial Damage

“…Alternatively, the incremental secant method was developed which combines the advantages of secant modulus and tangent modulus methods [27][28][29][30]. The method showed acceptable predictability for materials with elasto-plasticity or elasto-viscoplasticity, but its extension to viscoelastic-viscoplastic composites has not been proposed yet.…”