Pressure-dependent multiscale stochastic simulations using aMFH model constructed from full-field SVE realizations

Abstract

n order to identify the behaviour of a UD-composite, a large amount of experimental tests are needed due to the non-determinisms inherent to this type of materials. One of these non-determinisms is the disposition of the fibres in the microstructure. This work addresses this problematic by building a pressure-dependent stochastic Mean-Field-Homogenization (MFH) ¿ based model capable of modelling the behaviour of the material up to its failure stage, bringing virtual testing a step closer to have a real engineering application. In order to develop the stochastic MFH model, Stochastic Volume Element (SVE) realisations of a UD composite material microstructure with RTM6 epoxy matrix modelled by a hyperelastic viscoelastic-viscoplastic constitutive model enhanced by a multi-mechanism nonlocal damage model (V.-D. Nguyen et al., ¿A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers¿, in Int. Journal of Solids and Structures, vol. 96, pp. 192-216, 2016) are performed, allowing to fully replicate its complex behaviour. These realizations are then used to obtain their apparent responses, being able to characterise the homogenised stochastic behaviour of the composite and allowing to construct a stochastic MFH model as developed in (L. Wu et al., ¿An inverse micro-mechanical analysis toward the stochastic homogenization of nonlinear random composites¿, in Computer Methods in Applied Mechanics and Engineering, vol. 348, pp. 97-138, 2019). This work completes this model by introducing a pressure-dependency to the MFH model and the ability to account for the failure stage of the material, a phase in which a loss of size objectivity is encountered. In order to recover the size objectivity, the failure damage model parameters of each homogenised SVE model are identified to match the energy release rate of the full field simulations. These identified parameters are then used to generate proper random fields for SFEM. Finally, the built stochastic MFH model is used to perform stochastic analysis of a ply failure taking the geometrical uncertainties of the material microstructure into account