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The mechanical behavior of many applied materials arises from their microstructure. Thus, to aid the design, development and industrialization of new materials, robust computational homogenization methods are indispensable. The present thesis is devoted to investigating and developing FFT-based micromechanics solvers for efficiently computing the (thermo)mechanical response of nonlinear composite materials with complex microstructures.
We investigate deep material networks (DMN). We lay the mathematical foundation of DMNs and present a novel DMN formulation, which is characterized by a reduced number of degrees of freedom. We present a efficient solution technique for nonlinear DMNs to accelerate complex two-scale simulations with minimal computational effort. A new interpolation technique is presented enabling the consideration of fluctuating microstructure characteristics in macroscopic simulations.
Materials of industrial interest often show a complex microstructure which directly influences their macroscopic material behavior. For simulations on the component scale, multi-scale methods may exploit this microstructural information. This work is devoted to a multi-scale approach for brittle materials. Based on a homogenization result for free discontinuity problems, we present FFT-based methods to compute the effective crack energy of heterogeneous materials with complex microstructures.
The aim of this work is to model and experimentally characterize the anisotropic material behavior of SMC composites on the macroscale with consideration of the microstructure. Temperature-dependent thermoelastic behavior and failure behavior are modeled and the corresponding material properties are determined experimentally. Additionally, experimental biaxial damage investigations are performed. A parameter identification merges modeling and experiments and validates the models.
Computational homogenization permits to capture the influence of the microstructure on the cyclic mechanical behavior of polycrystalline metals. In this work we investigate methods to compute Laguerre tessellations as computational cells of polycrystalline microstructures, propose a new method to assign crystallographic orientations to the Laguerre cells and use Bayesian optimization to find suitable parameters for the underlying micromechanical model from macroscopic experiments.
Effective mechanical properties of fiber-reinforced composites strongly depend on the microstructure, including the fibers' orientation. Studying this dependency, we identify the variety of fiber orientation tensors up to fourth-order using irreducible tensors and material symmetry. The case of planar fiber orientation tensors, relevant for sheet molding compound, is presented completely. Consequences for the reconstruction of fiber distributions and mean field homogenization are presented.
This book provides a unified mechanics and materials perspective on polymers: both the mathematics of viscoelasticity theory as well as the physical mechanisms behind polymer deformation processes. Introductory material on fundamental mechanics is included to provide a continuous baseline for readers from all disciplines. Introductory material on the chemical and molecular basis of polymers is also included, which is essential to the understanding of the thermomechanical response. This self-contained text covers the viscoelastic characterization of polymers including constitutive modeling, experimental methods, thermal response, and stress and failure analysis. Example problems are provided within the text as well as at the end of each chapter. New to this edition: · One new chapter on the use of nano-material inclusions for structural polymer applications and applications such as fiber-reinforced polymers and adhesively bonded structures · Brings up-to-date polymer production and sales data and equipment and procedures for evaluating polymer characterization and classification · The work serves as a comprehensive reference for advanced seniors seeking graduate level courses, first and second year graduate students, and practicing engineers