A review of nonlinear FFT-based computational homogenization methods

M Schneider - Acta Mechanica, 2021‏ - Springer
Since their inception, computational homogenization methods based on the fast Fourier
transform (FFT) have grown in popularity, establishing themselves as a powerful tool …

A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

K Matouš, MGD Geers, VG Kouznetsova… - Journal of Computational …, 2017‏ - Elsevier
Since the beginning of the industrial age, material performance and design have been in the
midst of innovation of many disruptive technologies. Today's electronics, space, medical …

A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality

MA Bessa, R Bostanabad, Z Liu, A Hu… - Computer Methods in …, 2017‏ - Elsevier
A new data-driven computational framework is developed to assist in the design and
modeling of new material systems and structures. The proposed framework integrates three …

A recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to random cyclic and non-proportional loading paths

L Wu, NG Kilingar, L Noels - Computer Methods in Applied Mechanics …, 2020‏ - Elsevier
Abstract An artificial Neural Network (NNW) is designed to serve as a surrogate model of
micro-scale simulations in the context of multi-scale analyses in solid mechanics. The …

[HTML][HTML] Multi-scale computational homogenization: Trends and challenges

MGD Geers, VG Kouznetsova… - Journal of computational …, 2010‏ - Elsevier
In the past decades, considerable progress had been made in bridging the mechanics of
materials to other disciplines, eg downscaling to the field of materials science or upscaling to …

Physics-informed Neural Networks (PINN) for computational solid mechanics: Numerical frameworks and applications

H Hu, L Qi, X Chao - Thin-Walled Structures, 2024‏ - Elsevier
For solving the computational solid mechanics problems, despite significant advances have
been achieved through the numerical discretization of partial differential equations (PDEs) …

An approach to micro-macro modeling of heterogeneous materials

V Kouznetsova, WAM Brekelmans… - Computational …, 2001‏ - Springer
A micro-macro strategy suitable for modeling the mechanical response of heterogeneous
materials at large deformations and non-linear history dependent material behaviour is …

Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme

V Kouznetsova, MGD Geers… - … journal for numerical …, 2002‏ - Wiley Online Library
A gradient‐enhanced computational homogenization procedure, that allows for the
modelling of microstructural size effects, is proposed within a general non‐linear framework …

Aspects of computational homogenization at finite deformations: a unifying review from Reuss' to Voigt's bound

S Saeb, P Steinmann, A Javili - Applied …, 2016‏ - asmedigitalcollection.asme.org
The objective of this contribution is to present a unifying review on strain-driven
computational homogenization at finite strains, thereby elaborating on computational …

Homogenization methods and multiscale modeling: nonlinear problems

MGD Geers, VG Kouznetsova… - Encyclopedia of …, 2017‏ - Wiley Online Library
This article focuses on computational multiscale methods for the mechanical response of
nonlinear heterogeneous materials. After a short historical note, a brief overview is given of …