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Computational Modeling of Complex Materials Across the Scales

Guest Editors: 

  • Julien Yvonnet (Université Gustave Eiffel, Paris, France)
  • Paul Steinmann (University of Erlangen-Nuremberg, Erlangen, Germany)
  • Marc Geers (Eindhoven University of Technology, Eindhoven, Netherlands)
  • Andrew McBride (University of Glasgow, Scotland, UK)

In recent years, a revolution has occurred in the field of material engineering. The breakthrough is the possibility to design, predict the properties of, and even manufacture materials – not only with the help of experiments, but also with advanced computational modeling techniques. Until recently, determining mechanical properties of a material, such as its stiffness or strength, was only accessible through mechanical testing. In that context, the selection or manufacturing of new materials with enhanced properties was a time-consuming trial-and-error process, requiring significant experience and intuition about elementary phenomena and the influence of constituents. 

Today, due to the conjunction of several advances in physical/mechanical modeling, computational capabilities, numerical/mathematical methods, and the development of new manufacturing processes like 3D printing, it is possible to accurately predict the properties of a large range of man-made materials like polymer/ceramic/metallic composites, concrete, or nanostructured materials – and manufacture them with controlled microstructures. While analytical micromechanical models have successfully helped to predict effective properties of heterogeneous materials for idealized microstructures, computational methods, computer capacities and the development of computational multiscale methods permit one to go beyond these restrictive assumptions and to consider realistic or architectured microstructures, with complex behaviors like elastoplasticity, damage, microcracking, or phase changes. Another new possibility offered by computational multiscale material modeling is to account for several space or time scales, or several models, e.g. atomistic and continuum. 

While these developments are quite mature in the research community, their transition into engineering practice has only begun its first faltering steps. One reason is that many difficulties still persist in reaching solutions for industrial problems. Examples include predicting damage from microcracking, prediction of fatigue, and taking into account the complexity of microstructures with all their uncertainties in realistic materials. Another factor is that simulations related to complex material microstructures still involve extensive computational resources in terms of memory and CPU time, and cannot yet be efficiently incorporated in codes.

In this special issue, we invite experts from different disciplines working on open issues for scale-bridging in computational modeling of complex materials. Open problems are, among many others: the modeling and design of materials with emergent behavior (i.e. effective behaviors which are not observed for individual constituents), the reduction of computational costs in multiscale modeling for use in industrial applications, the use of realistic 3D experimental images (e.g. microtomography images), the prediction of damage of complex heterogeneous materials as in 3D printed structures, and the integration of stochastic phenomena.

  1. This study presents a method for constructing a surrogate localization model for a periodic microstructure, or equivalently, a unit cell, to efficiently perform micro-macro coupled analyses of hyperelastic com...

    Authors: Ryo Hatano, Seishiro Matsubara, Shuji Moriguchi, Kenjiro Terada and Julien Yvonnet
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2020 7:39
  2. We present a variational framework for the computational homogenization of chemo-mechanical processes of soft porous materials. The multiscale variational framework is based on a minimization principle with de...

    Authors: Elten Polukhov and Marc-André Keip
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2020 7:35
  3. Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the pr...

    Authors: Ondřej Rokoš, Jan Zeman, Martin Doškář and Petr Krysl
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2020 7:19

    The Correction to this article has been published in Advanced Modeling and Simulation in Engineering Sciences 2020 7:25

  4. In this paper, we propose a general framework for projection-based model order reduction assisted by deep neural networks. The proposed methodology, called ROM-net, consists in using deep learning techniques to a...

    Authors: Thomas Daniel, Fabien Casenave, Nissrine Akkari and David Ryckelynck
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2020 7:16
  5. In this article, we present a computationally efficient homogenization technique for linear coupled diffusion–mechanics problems. It considers a linear chemo-mechanical material model at the fine scale, and re...

    Authors: Abdullah Waseem, Thomas Heuzé, Laurent Stainier, Marc G. D. Geers and Varvara G. Kouznetsova
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2020 7:14
  6. An enriched homogenized model is developed based on a proposed homogenization strategy, to describe the wave propagation behaviour through periodic layered composites. The intrinsic parameters characterising t...

    Authors: Swee Hong Tan and Leong Hien Poh
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2020 7:4