Reduced-order Homogenization of Heterogeneous Material Systems: from Viscoelasticity to Nonlinear Elasto-plastic Softening Material

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The discovery of efficient and accurate descriptions for the macroscopic constitutive behavior of heterogeneous materials with complex microstructure remains an outstanding challenge in mechanics. On the one hand, great accuracy can be achieved by modeling small domains of a material including all the details in the microstructure, however, at the expense of a large computational cost. On the other hand, efficient descriptions of the macroscopic material behavior can be obtained by empirical constitutive laws, at the expense of a tedious calibration process and limited accuracy. The challenge is in finding an optimal balance between preserving enough small-scale detail and keeping the computational expense low, without the need for empirically calibrated models. Based on the Lippmann-Schwinger integral equation, two novel reduced-order homogenization methods have been developed in this dissertation. An analytical reduced-order micromechanics method is first proposed for linear elastic and viscoelastic heterogeneous material with overlapping geometries. Weighted-mean and additive overlapping conditions are introduced to consider various physical phenomena in the overlapping regions. The corresponding inclusion-wise strain definitions and integral equations under these two overlapping conditions are also derived. Using a Boolean-Poisson model and micromechanics mean-field theory, this analytical homogenization method is applied to a viscoelastic polymer nanocomposite with interphase regions and estimates the properties and thickness of the interphase region based on experimental data for carbon-black filled styrene butadiene rubbers. To consider complex microstructural morphologies and nonlinear history-dependent material behavior, a data-driven reduced-order homogenization method called self-consistent clustering analysis (SCA) is developed. Based on data clustering algorithm in the offline/training stage and self-consistent schemes for solving the Lippmann-Schwinger equation in the online/predicting stage, SCA provides an effective way of developing a microstructural database, which enables an efficient and accurate prediction of nonlinear material properties. Other than generic von Mises elasto-plastic material, it has been applied to 3-Dimensional polycrystal materials with crystal plasticity (CP). Through numerical validations, this data-driven method is believed to open new avenues in homogenization of irreversible processes and parameter-free concurrent multi-scale modeling of heterogeneous material systems. To address the challenges in multiscale modeling of softening materials, a stable three-step homogenization scheme is further presented which removes the material instability issues in the microstructure, and the homogenized stress-strain responses of the representative volume element (RVE) are not sensitive to the RVE size. Combined with SCA, concurrent multiscale simulations with damage are performed. The predicted macroscale strain localization are observed to be sensitive to the combinations of microscale constituents, showing the capability of the microstructural database created by SCA. Finally, the concurrent framework enabled by the three-step scheme and SCA method is applied to a unidirectional (UD) fiber polymer matrix composite, and the predicted macroscale nonlinear anisotropic responses and crack patterns are validated against experiments.

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  • 11/01/2018
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