Multiscale stochastic simulations using a MFH model constructed from full-field SVE realizations

Nowadays experimental testing of composite materials represents a big challenge for companies, as a large number of tests are necessary to fully characterize a material.
Virtual testing represents one of the bests options for reducing dramatically these costs in the near future. In order to make virtual testing become a real alternative for industry when characterizing the performance of a material, it is important not only to have a good representation of its deterministic behavior, but to take into account all the stochastic non-determinisms that can be present in it: for example geometry variations in the microstructure due to the disposition of the fibers.
In this paper, an inverse Mean-Field Homogenization (MFH) model of a UD composite material used in industry is built from the homogenized stochastic behavior obtained by performing full- field simulations of Stochastic Volume Element (SVE).
As a first step, a micro-mechanical model of reinforced polymer failure with length scale effects is used to simulate the results obtained in tensile tests at constant speed rate of the epoxy used for the construction of the UD material. To this purpose, the complex polymer behavior is represented by a hyperelastic viscoelastic-viscoplastic constitutive model enhanced by a multi-mechanism nonlocal damage model (1). This law is composed of three components: hardening, saturation and failure laws. The characterization of the numerical parameters of the epoxy are obtained by simulating the experimental tensile test and matching the experimental energy release rate (Gc) of the material.
Once the micro-mechanical model of the epoxy is characterized, multiple full-field simulations of composite Stochastic Volume Element (SVE) realizations are performed to characterize the homogenized stochastic behavior of the composite, information that will be used to build the MFH model as developed in. After finalizing the tuning of the MFH model, efficient macro scale simulations taking into account geometrical variabilities of the microstructure will be possible, bringing the industry closer to a possible future virtual testing of composite materials.