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 …
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 …
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
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) …
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 …
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 …
second-order computational homogenization procedure, which is suitable for a multi-scale …
[HTML][HTML] 3D stochastic bicontinuous microstructures: Generation, topology and elasticity
Motivated by recent experimental investigations of the mechanical behavior of nanoporous
metal we explore an efficient and robust method for generating 3D representative volume …
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
The objective of this contribution is to present a unifying review on strain-driven
computational homogenization at finite strains, thereby elaborating on computational …
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 …
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 …
material and the interfacial transition zone (ITZ) as separate constituents. Particles are …
A review of the FE2 method for composites
Composite materials and structures are inherently inhomogeneous and anisotropic across
multiple scales. Multiscale modelling offers opportunities to understand the coupling of …
multiple scales. Multiscale modelling offers opportunities to understand the coupling of …