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 …

[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 …

FE: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining

KA Kalina, L Linden, J Brummund, M Kästner - Computational Mechanics, 2023 - Springer
Herein, we present a new data-driven multiscale framework called FE ANN which is based
on two main keystones: the usage of physics-constrained artificial neural networks (ANNs) …

A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua

F Feyel - Computer Methods in applied Mechanics and …, 2003 - Elsevier
A general method called FE2 has been introduced which consists in describing the behavior
of heterogeneous structures using a multiscale finite element model. Instead of trying to …

Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy

VG Kouznetsova, MGD Geers… - Computer methods in …, 2004 - Elsevier
This paper presents the detailed implementation and computational aspects of a novel
second-order computational homogenization procedure, which is suitable for a multi-scale …

[HTML][HTML] 3D stochastic bicontinuous microstructures: Generation, topology and elasticity

C Soyarslan, S Bargmann, M Pradas, J Weissmüller - Acta materialia, 2018 - Elsevier
Motivated by recent experimental investigations of the mechanical behavior of nanoporous
metal we explore an efficient and robust method for generating 3D representative volume …

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 …

Multiscale modeling of concrete: from mesoscale to macroscale

JF Unger, S Eckardt - Archives of computational Methods in Engineering, 2011 - Springer
In this paper, a mesoscale model of concrete is presented, which considers particles, matrix
material and the interfacial transition zone (ITZ) as separate constituents. Particles are …

A review of the FE2 method for composites

K Raju, TE Tay, VBC Tan - Multiscale and Multidisciplinary Modeling …, 2021 - Springer
Composite materials and structures are inherently inhomogeneous and anisotropic across
multiple scales. Multiscale modelling offers opportunities to understand the coupling of …