Efficient fast Fourier transform-based solvers for computing the thermomechanical behavior of applied materials
Efficient fast Fourier transform-based solvers for computing the thermomechanical behavior of applied materials

Author: Wicht, Daniel

Publisher: KIT Scientific Publishing

Published: 2022-10-11

Total Pages: 336

ISBN-13: 3731512203

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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.

Deep material networks for efficient scale-bridging in thermomechanical simulations of solids
Deep material networks for efficient scale-bridging in thermomechanical simulations of solids

Author: Gajek, Sebastian

Publisher: KIT Scientific Publishing

Published: 2023-08-25

Total Pages: 326

ISBN-13: 3731512785

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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.

A computational multi-scale approach for brittle materials
A computational multi-scale approach for brittle materials

Author: Ernesti, Felix

Publisher: KIT Scientific Publishing

Published: 2023-04-17

Total Pages: 264

ISBN-13: 3731512858

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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.

Thermomechanical Modeling and Experimental Characterization of Sheet Molding Compound Composites
Thermomechanical Modeling and Experimental Characterization of Sheet Molding Compound Composites

Author: Lang, Juliane

Publisher: KIT Scientific Publishing

Published: 2023-06-28

Total Pages: 250

ISBN-13: 3731512327

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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.

Microstructure modeling and crystal plasticity parameter identification for predicting the cyclic mechanical behavior of polycrystalline metals
Microstructure modeling and crystal plasticity parameter identification for predicting the cyclic mechanical behavior of polycrystalline metals

Author: Kuhn, Jannick

Publisher: KIT Scientific Publishing

Published: 2023-04-04

Total Pages: 224

ISBN-13: 3731512726

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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.

Fiber Orientation Tensors and Mean Field Homogenization: Application to Sheet Molding Compound
Fiber Orientation Tensors and Mean Field Homogenization: Application to Sheet Molding Compound

Author: Bauer, Julian Karl

Publisher: KIT Scientific Publishing

Published: 2023-02-27

Total Pages: 252

ISBN-13: 3731512629

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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.

Computational Frameworks for the Fast Fourier Transform
Computational Frameworks for the Fast Fourier Transform

Author: Charles Van Loan

Publisher: SIAM

Published: 1992-01-01

Total Pages: 286

ISBN-13: 9781611970999

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The most comprehensive treatment of FFTs to date. Van Loan captures the interplay between mathematics and the design of effective numerical algorithms--a critical connection as more advanced machines become available. A stylized Matlab notation, which is familiar to those engaged in high-performance computing, is used. The Fast Fourier Transform (FFT) family of algorithms has revolutionized many areas of scientific computation. The FFT is one of the most widely used algorithms in science and engineering, with applications in almost every discipline. This volume is essential for professionals interested in linear algebra as well as those working with numerical methods. The FFT is also a great vehicle for teaching key aspects of scientific computing.