Journal ArticleDOI
An efficient solution scheme for small-strain crystal-elasto-viscoplasticity in a dual framework
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TLDR
The primal and dual formulation of the unit cell problem of computational homogenization and state of the art FFT-based algorithms for its solution are revisited and performance and convergence behavior of the different solvers are investigated.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2020-01-01. It has received 30 citations till now. The article focuses on the topics: Homogenization (chemistry) & Viscoplasticity.read more
Citations
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Journal ArticleDOI
A review of nonlinear FFT-based computational homogenization methods
TL;DR: A condensed overview of results scattered throughout the literature is provided and guides the reader to the current state of the art in nonlinear computational homogenization methods using the fast Fourier transform.
Journal ArticleDOI
On the micromechanics of deep material networks
TL;DR: It is established that deep material networks inherit thermodynamical consistency and stress-strain monotonicity from their phases and is clarified theoretically by showing that, to first order in the strain rate, the effective inelastic behavior of composite materials is determined by linear elastic localization.
Journal ArticleDOI
On Quasi‐Newton methods in fast Fourier transform‐based micromechanics
TL;DR: This work proposes two algorithms based on the Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) method, one of the most powerful Quasi‐Newton schemes, which are compared with the convergence characteristics and runtime of the proposed techniques for complex microstructures with nonlinear material behavior and finite as well as infinite material contrast.
Journal ArticleDOI
An FE–DMN method for the multiscale analysis of short fiber reinforced plastic components
TL;DR: In this article, a fully coupled multiscale strategy for components made from short fiber reinforced composites is proposed, where each Gauss point of the macroscopic finite element model is equipped with a deep material network (DMN) which covers the different fiber orientation states varying within the component.
Journal ArticleDOI
Fast methods for computing centroidal Laguerre tessellations for prescribed volume fractions with applications to microstructure generation of polycrystalline materials
TL;DR: It is shown that modern gradient-based optimization algorithms devoid of backtracking like the Malitsky–Mishchenko method and the Barzilai–Borwein scheme easily overcome the described difficulty, leading to a significant speed-up compared to more traditional solvers.
References
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Convex Optimization
Stephen Boyd,Lieven Vandenberghe +1 more
TL;DR: In this article, the focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them, and a comprehensive introduction to the subject is given. But the focus of this book is not on the optimization problem itself, but on the problem of finding the appropriate technique to solve it.
Journal ArticleDOI
The Design and Implementation of FFTW3
Matteo Frigo,Steven G. Johnson +1 more
TL;DR: It is shown that such an approach can yield an implementation of the discrete Fourier transform that is competitive with hand-optimized libraries, and the software structure that makes the current FFTW3 version flexible and adaptive is described.
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Mechanics of Solid Materials
TL;DR: In this article, the physical mechanisms of deformation and fracture are discussed, including linear elasticity, thermo-elasticity, and viscoelastic properties of real solids.
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Introductory Lectures on Convex Optimization: A Basic Course
TL;DR: A polynomial-time interior-point method for linear optimization was proposed in this paper, where the complexity bound was not only in its complexity, but also in the theoretical pre- diction of its high efficiency was supported by excellent computational results.
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Single Crystal Elastic Constants and Calculated Aggregate Properties. A Handbook
Gene Simmons,Herbert F. Wang +1 more
TL;DR: In this paper, the authors present data on the elastic properties of single crystals collected from the literature through mid-1970 and the elastic property of isotropic aggregates which are calculated according to the schemes of Voigt and Reuss for all materials, and Hashin and Shtrikman for materials with cubic symmetry.
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