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 …

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 …

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 …

A numerical two-scale homogenization scheme: the FE2-method

J Schröder - Plasticity and beyond: microstructures, crystal-plasticity …, 2014 - Springer
A wide class of micro-heterogeneous materials is designed to satisfy the advanced
challenges of modern materials occurring in a variety of technical applications. The effective …

FE2 computational homogenization for the thermo-mechanical analysis of heterogeneous solids

I Özdemir, WAM Brekelmans, MGD Geers - Computer Methods in Applied …, 2008 - Elsevier
This paper presents a two-scale thermo-mechanical analysis framework for heterogeneous
solids based on a computational homogenization technique. The evolution of the …

A direct fe2 method for concurrent multilevel modeling of piezoelectric materials and structures

H Li, L Chen, G Zhi, L Meng, H Lian, Z Liu, T Yu… - Computer Methods in …, 2024 - Elsevier
Multiscale piezoelectric materials and structures have shown their promising potential of
applications in sensor, energy harvester, actuator and so on. However, the large complexity …

Novel boundary conditions for strain localization analyses in microstructural volume elements

EWC Coenen, VG Kouznetsova… - International Journal for …, 2012 - Wiley Online Library
Multi‐scale modeling frequently relies on microstructural representative volume elements
(RVEs) on which macroscopic deformation is imposed through kinematical boundary …

Mechanical characterization of structured sheet materials

C Schumacher, S Marschner, M Gross… - ACM Transactions on …, 2018 - dl.acm.org
We propose a comprehensive approach to characterizing the mechanical properties of
structured sheet materials, ie, planar rod networks whose mechanics and aesthetics are …