Stochastic Multiscale Modeling and Analysis of Polymer-Based Materials

This Work focuses on the accurate and efficient modeling of polymer materials. In a first step, the large strain hyperelastic phenomenological constitutive model proposed by V.D. Nguyen et al. for the modeling of highly nonlinear, rate-dependent amorphous glassy polymers at isothermal conditions is enhanced with the introduction of new strain dependent bulk and shear moduli stiffening terms. This addition, allows the correct modeling of the elastic hardening exhibited by some polymer materials, such as semi-crystalline polymers at large strains.
While being able to accurately capture the behavior of highly non-linear polymers, large strain models can become prohibitive for the modeling of composite materials due to their high computational cost. To that end, this Thesis introduces a, possibly damage-enhanced, pressure-dependent based incremental-secant mean-field homogenization (MFH) scheme for two-phase composites. The incremental-secant formulation consists on a fictitious unloading of the material up to a stress-free state, in which a residual stress is attained in its phases. Then the secant method is performed in order to compute the mean stress fields of each phase. One of the main advantages of this method is the natural isotropicity of the secant tensors that allows defining the linear-comparison-composite (LCC). In this Work, we show that this isotropic nature is preserved for a non-associated pressure dependent plastic flow, making possible the direct definition of the LCC. Through several comparisons against full-field simulations and an experimental test, it is shown the ability of this model to capture the behavior of uni directional (UD) composites, while reducing the computational cost of the large strain model by several orders of magnitude. This was used as basis for a surrogate for nonlinear stochastic multiscale analyses of two-phase composites. The homogenized stochastic behavior of the UD composite material is first characterized through full-field simulations on stochastic volume elements (SVE) of the material microstructure. Then, in order to conduct the stochastic nonlinear multiscale simulations, the microscale problem is substituted by a MF-ROM, whose properties are identified by an inverse process from the full-field SVE realizations. Homogenized stress-strain curves are used for the identification process of the nonlinear range. However, a loss of size objectivity is encountered once the strain softening onset is reached. This problem is addressed by introducing a calibration of the energy release rate obtained with a nonlocal MFH micromechanical model, allowing to scale the variability found on each SVE failure characteristics to the macroscale. The obtained random effective properties are then used as input of a data-driven stochastic model to generate the random fields used to feed the stochastic MF-ROM. The MF-ROM is then verified through nonlocal stochastic finite element method (SFEM) simulations against an experimental test and full-field simulations. The introduced innovations allows to conduct stochastic studies on the failure characteristics of material samples without the need for costly experimental campaigns, paving the way for more complete and affordable virtual testing.