Summary In this article, we propose to discretize the problem of linear elastic homogenization by finite differences on a staggered grid and introduce fast robust solvers. Our method shares some properties with FFT‐based technique Moulinec Suquet, which has received widespread attention recently because its robustness computational speed. These similarities include use FFT resulting performing The discretization, however, offers three crucial improvements. Firstly, solutions obtained our are...

Summary The FFT‐based homogenization method of Moulinec–Suquet has recently emerged as a powerful tool for computing the macroscopic response complex microstructures elastic and inelastic problems. In this work, we generalize to problems discretized by trilinear hexahedral elements on Cartesian grids physically nonlinear elasticity We present an implementation basic scheme that reduces memory requirements factor four conjugate gradient storage necessary nine compared with naive...

Abstract To compute the effective properties of random heterogeneous materials, a number different boundary conditions are used to define apparent on cells finite size. Typically, depending specific condition, numerical methods used. The article at hand provides unified framework for Lippmann–Schwinger solvers in thermal conductivity and Dirichlet (prescribed temperature), Neumann normal heat flux) as well periodic conditions. We focus explicit jump finite‐difference discretization discuss...

We discuss how Dirichlet boundary conditions can be directly imposed for the Moulinec-Suquet discretization on of rectangular domains in iterative schemes based fast Fourier transform (FFT) and computational homogenization problems mechanics. Classically, methods work with periodic conditions. There are applications, however, when (or Neumann) required. For thermal problems, it is straightforward to impose such by using discrete sine (and cosine) transforms instead FFT. This approach, not...

In recent years there was a tremendous progress in robotic systems, and however also increased expectations: A robot should be easy to program reliable task execution. Learning from Demonstration (LfD) offers very promising alternative classical engineering approaches. LfD is natural way for humans interact with robots will an essential part of future service robots. this work we first review heteroscedastic Gaussian processes show how these can used encode task. We then introduce new...

For short fiber reinforced plastic parts the local orientation has a strong influence on mechanical properties. To enable multiscale computations using surrogate models we advocate two-step identification strategy. Firstly, for number of sample orientations an effective model is derived by numerical methods available in literature. Secondly, to cover general state, these are interpolated. In this article develop novel and strategy carry out interpolation. taking into account symmetry...

Summary Building upon the equivalence of basic scheme in work Moulinec and Suquet with gradient descent methods, we investigate effect using celebrated Barzilai‐Borwein step size selection technique this context. We provide an overview recent convergence theory present efficient implementations context computational micromechanics, without globalization. In contrast to polarization schemes fast no lower bound on eigenvalues material tangent is necessary for scheme. demonstrate power proposed...

In this work, we propose a fully coupled multiscale strategy for components made from short fiber reinforced composites, where each Gauss point of the macroscopic finite element model is equipped with deep material network (DMN) which covers different orientation states varying within component. These DMNs need to be identified by linear elastic precomputations on representative volume elements, and serve as high-fidelity surrogates full-field simulations microstructures inelastic...

Abstract In this work, we advocate using Bayesian techniques for inversely identifying material parameters multiscale crystal plasticity models. Multiscale approaches modeling polycrystalline materials may significantly reduce the effort necessary characterizing such models experimentally, in particular when a large number of cycles is considered, as typical fatigue applications. Even appropriate microstructures and microscopic are identified, calibrating individual model to some...

Abstract We extend the FE-DMN method to fully coupled thermomechanical two-scale simulations of composite materials. In particular, every Gauss point macroscopic finite element model is equipped with a deep material network (DMN). Such DMN serves as high-fidelity surrogate for full-field solutions on microscopic scale inelastic, non-isothermal constituents. Building homogenization framework Chatzigeorgiou et al. (Int J Plast 81:18–39, 2016), we DMNs composites by incorporating two-way...

The FFT‐based homogenization method of Moulinec–Suquet has recently attracted attention because its wide range applicability and short computational time. In this article, we deduce an optimal a priori error estimate for the Moulinec–Suquet, which can be interpreted as spectral collocation method. Such methods are well‐known to converge sufficiently smooth coefficients. We extend result rough More precisely, prove convergence fields involved Riemann‐integrable coercive coefficients without...

SUMMARY This work is devoted to investigating the computational power of Quasi‐Newton methods in context fast Fourier transform (FFT)‐based micromechanics. We revisit FFT‐based Newton‐Krylov solvers as well modern approaches such recently introduced Anderson accelerated basic scheme. In this context, we propose two algorithms based on Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) method, one most powerful schemes. To be specific, use BFGS update formula approximate global Hessian or,...

Abstract For fast Fourier transform (FFT)-based computational micromechanics, solvers need to be fast, memory-efficient, and independent of tedious parameter calibration. In this work, we investigate the benefits nonlinear conjugate gradient (CG) methods in context FFT-based micromechanics. Traditionally, CG require dedicated line-search procedures efficient, rendering them not competitive context. We contribute devoid line searches by exploiting similarities between accelerated methods....

We investigate volume-element sampling strategies for the stochastic homogenization of particle-reinforced composites and show, via computational experiments, that an improper treatment particles intersecting boundary cell may affect accuracy computed effective properties. Motivated by recent results on a superior convergence rate systematic error periodized ensembles compared to taking snapshots ensembles, we conduct experiments microstructures with circular, spherical cylindrical...

Abstract We describe an algorithm for generating fiber-filled volume elements use in computational homogenization schemes. The permits to prescribe both a length distribution and fiber-orientation tensor of second order, composites with industrial filler fraction can be generated. Typically, short-fiber composites, data on the fiber-length volume-weighted order is available. consider model where fiber orientation distributions are independent, i.e., uncoupled. discuss closure approximations...

Abstract Imposing nonperiodic boundary conditions for unit cell analyses may be necessary a number of reasons in applications, example, validation purposes and specific computational setups. The work at hand discusses strategy utilizing the powerful technology behind fast Fourier transform (FFT)‐based micromechanics—initially developed with periodic mind—for essential mechanics, as well, case discretization on rotated staggered grid. Introduced by F. Willot into community, grid is presumably...