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Special Issue "Multiscale Methods and Application to Computational Materials Design"

A special issue of Materials (ISSN 1996-1944).

Deadline for manuscript submissions: closed (15 September 2016)

Special Issue Editors

Guest Editor
Prof. Dr. Timon Rabczuk

Faculty of Civil Engineering, Bauhaus Universität Weimar, Weimar, Germany
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Phone: +49-(0)3643-584511
Fax: +49-(0)3643-584514
Interests: structural safety and reliability; dynamic response analysis; damage and fatigue prediction; material models applying multiscale techniques
Guest Editor
Dr.-Ing. Pattabhi Budarapu

Institute for Advanced Studies Lucca, 55100 Lucca, Italy
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Phone: +39-(0)583-4326561
Fax: +39-(0)538-4326565
Interests: multiphysics multiscale methods for fracture; molecular dynamics; photovoltaic modules and extended finite element methods

Special Issue Information

Dear Colleagues,

Defects like cracks and dislocations evolve at nano scales and influence the macroscopic properties such as strength, toughness and ductility of a material. Molecular Dynamics (MD) simulations promise to reveal the fundamental mechanics of material failure by modeling the atom to atom interactions. However, the computational expense of MD simulations limits its application to engineering problems involving macroscopic cracks and shear bands, which occur at larger length and time scales. Therefore, multiscale methods have been developed bridging different time and length scales. This Special Issue aims at providing a forum on modeling of materials in a multi-scale and multi-physics framework. Contributions on models validation through characterization and testing of materials and systems are also welcome.

Topics of interest include:

- Analytical and computational methods for coupled problems

- Multiscale analytical and computational methods

- Interface constitutive laws in multiphysics

- Fracture mechanics models in multiphysics

- Model validation through testing of materials and systems

- Prediction of macroscopic material properties

However, we are not only restricted to above-mentioned topics, but open to articles in the relevant areas.

Prof. Dr.-Ing. Timon Rabczuk
Dr.-Ing. Pattabhi Budarapu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Materials is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1500 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • multiscale
  • multi-physics
  • materials design
  • molecular dynamics
  • computational methods

Published Papers (9 papers)

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Research

Open AccessArticle Effective Properties of Composites with Periodic Random Packing of Ellipsoids
Materials 2017, 10(2), 112; doi:10.3390/ma10020112
Received: 26 October 2016 / Accepted: 3 January 2017 / Published: 26 January 2017
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Abstract
The aim of this paper is to evaluate the effective properties of composite materials with periodic random packing of ellipsoids of different volume fractions and aspect ratios. Therefore, we employ computational homogenization. A very efficient MD-based method is applied to generate the periodic
[...] Read more.
The aim of this paper is to evaluate the effective properties of composite materials with periodic random packing of ellipsoids of different volume fractions and aspect ratios. Therefore, we employ computational homogenization. A very efficient MD-based method is applied to generate the periodic random packing of the ellipsoids. The method is applicable even for extremely high volume fractions up to 60%. The influences of the volume fraction and aspect ratio on the effective properties of the composite materials are studied in several numerical examples. Full article
(This article belongs to the Special Issue Multiscale Methods and Application to Computational Materials Design)
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Open AccessArticle Modelling of Granular Fracture in Polycrystalline Materials Using Ordinary State-Based Peridynamics
Materials 2016, 9(12), 977; doi:10.3390/ma9120977
Received: 1 September 2016 / Revised: 7 November 2016 / Accepted: 22 November 2016 / Published: 2 December 2016
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Abstract
An ordinary state-based peridynamic formulation is developed to analyse cubic polycrystalline materials for the first time in the literature. This new approach has the advantage that no constraint condition is imposed on material constants as opposed to bond-based peridynamic theory. The formulation is
[...] Read more.
An ordinary state-based peridynamic formulation is developed to analyse cubic polycrystalline materials for the first time in the literature. This new approach has the advantage that no constraint condition is imposed on material constants as opposed to bond-based peridynamic theory. The formulation is validated by first considering static analyses and comparing the displacement fields obtained from the finite element method and ordinary state-based peridynamics. Then, dynamic analysis is performed to investigate the effect of grain boundary strength, crystal size, and discretization size on fracture behaviour and fracture morphology. Full article
(This article belongs to the Special Issue Multiscale Methods and Application to Computational Materials Design)
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Open AccessArticle Inclined Fiber Pullout from a Cementitious Matrix: A Numerical Study
Materials 2016, 9(10), 800; doi:10.3390/ma9100800
Received: 30 August 2016 / Revised: 19 September 2016 / Accepted: 20 September 2016 / Published: 26 September 2016
Cited by 1 | PDF Full-text (3999 KB) | HTML Full-text | XML Full-text
Abstract
It is well known that fibers improve the performance of cementitious composites by acting as bridging ligaments in cracks. Such bridging behavior is often studied through fiber pullout tests. The relation between the pullout force vs. slip end displacement is characteristic of the
[...] Read more.
It is well known that fibers improve the performance of cementitious composites by acting as bridging ligaments in cracks. Such bridging behavior is often studied through fiber pullout tests. The relation between the pullout force vs. slip end displacement is characteristic of the fiber-matrix interface. However, such a relation varies significantly with the fiber inclination angle. In the current work, we establish a numerical model to simulate the entire pullout process by explicitly representing the fiber, matrix and the interface for arbitrary fiber orientations. Cohesive elements endorsed with mixed-mode fracture capacities are implemented to represent the bond-slip behavior at the interface. Contact elements with Coulomb’s friction are placed at the interface to simulate frictional contact. The bond-slip behavior is first calibrated through pull-out curves for fibers aligned with the loading direction, then validated against experimental results for steel fibers oriented at 30 and 60 . Parametric studies are then performed to explore the influences of both material properties (fiber yield strength, matrix tensile strength, interfacial bond) and geometric factors (fiber diameter, embedment length and inclination angle) on the overall pullout behavior, in particular on the maximum pullout load. The proposed methodology provides the necessary pull-out curves for a fiber oriented at a given angle for multi-scale models to study fracture in fiber-reinforced cementitious materials. The novelty lies in its capacity to capture the entire pullout process for a fiber with an arbitrary inclination angle. Full article
(This article belongs to the Special Issue Multiscale Methods and Application to Computational Materials Design)
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Open AccessArticle Study on Stress Development in the Phase Transition Layer of Thermal Barrier Coatings
Materials 2016, 9(9), 773; doi:10.3390/ma9090773
Received: 23 May 2016 / Revised: 7 September 2016 / Accepted: 7 September 2016 / Published: 13 September 2016
Cited by 1 | PDF Full-text (8537 KB) | HTML Full-text | XML Full-text
Abstract
Stress development is one of the significant factors leading to the failure of thermal barrier coating (TBC) systems. In this work, stress development in the two phase mixed zone named phase transition layer (PTL), which grows between the thermally grown oxide (TGO) and
[...] Read more.
Stress development is one of the significant factors leading to the failure of thermal barrier coating (TBC) systems. In this work, stress development in the two phase mixed zone named phase transition layer (PTL), which grows between the thermally grown oxide (TGO) and the bond coat (BC), is investigated by using two different homogenization models. A constitutive equation of the PTL based on the Reuss model is proposed to study the stresses in the PTL. The stresses computed with the proposed constitutive equation are compared with those obtained with Voigt model-based equation in detail. The stresses based on the Voigt model are slightly higher than those based on the Reuss model. Finally, a further study is carried out to explore the influence of phase transition proportions on the stress difference caused by homogenization models. Results show that the stress difference becomes more evident with the increase of the PTL thickness ratio in the TGO. Full article
(This article belongs to the Special Issue Multiscale Methods and Application to Computational Materials Design)
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Open AccessArticle Microstructure Design of Tempered Martensite by Atomistically Informed Full-Field Simulation: From Quenching to Fracture
Materials 2016, 9(8), 673; doi:10.3390/ma9080673
Received: 21 June 2016 / Revised: 20 July 2016 / Accepted: 29 July 2016 / Published: 9 August 2016
Cited by 2 | PDF Full-text (12395 KB) | HTML Full-text | XML Full-text
Abstract
Martensitic steels form a material class with a versatile range of properties that can be selected by varying the processing chain. In order to study and design the desired processing with the minimal experimental effort, modeling tools are required. In this work, a
[...] Read more.
Martensitic steels form a material class with a versatile range of properties that can be selected by varying the processing chain. In order to study and design the desired processing with the minimal experimental effort, modeling tools are required. In this work, a full processing cycle from quenching over tempering to mechanical testing is simulated with a single modeling framework that combines the features of the phase-field method and a coupled chemo-mechanical approach. In order to perform the mechanical testing, the mechanical part is extended to the large deformations case and coupled to crystal plasticity and a linear damage model. The quenching process is governed by the austenite-martensite transformation. In the tempering step, carbon segregation to the grain boundaries and the resulting cementite formation occur. During mechanical testing, the obtained material sample undergoes a large deformation that leads to local failure. The initial formation of the damage zones is observed to happen next to the carbides, while the final damage morphology follows the martensite microstructure. This multi-scale approach can be applied to design optimal microstructures dependent on processing and materials composition. Full article
(This article belongs to the Special Issue Multiscale Methods and Application to Computational Materials Design)
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Open AccessArticle Atomistically Informed Extended Gibbs Energy Description for Phase-Field Simulation of Tempering of Martensitic Steel
Materials 2016, 9(8), 669; doi:10.3390/ma9080669
Received: 16 June 2016 / Revised: 1 August 2016 / Accepted: 2 August 2016 / Published: 9 August 2016
Cited by 2 | PDF Full-text (4477 KB) | HTML Full-text | XML Full-text
Abstract
In this study we propose a unified multi-scale chemo-mechanical description of the BCT (Body-Centered Tetragonal) to BCC (Body-Centered Cubic) order-disorder transition in martensitic steel by adding the mechanical degrees of freedom to the standard CALPHAD (CALculation of PHAse Diagrams) type Gibbs energy description.
[...] Read more.
In this study we propose a unified multi-scale chemo-mechanical description of the BCT (Body-Centered Tetragonal) to BCC (Body-Centered Cubic) order-disorder transition in martensitic steel by adding the mechanical degrees of freedom to the standard CALPHAD (CALculation of PHAse Diagrams) type Gibbs energy description. The model takes into account external strain, the effect of carbon composition on the lattice parameter and elastic moduli. The carbon composition effect on the lattice parameters and elastic constants is described by a sublattice model with properties obtained from DFT (Density Functional Theory) calculations; the temperature dependence of the elasticity parameters is estimated from available experimental data. This formalism is crucial for studying the kinetics of martensite tempering in realistic microstructures. The obtained extended Gibbs energy description opens the way to phase-field simulations of tempering of martensitic steel comprising microstructure evolution, carbon diffusion and lattice symmetry change due to the ordering/disordering of carbon atoms under multiaxial load. Full article
(This article belongs to the Special Issue Multiscale Methods and Application to Computational Materials Design)
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Open AccessArticle Micromechanical Modeling of Fiber-Reinforced Composites with Statistically Equivalent Random Fiber Distribution
Materials 2016, 9(8), 624; doi:10.3390/ma9080624
Received: 12 June 2016 / Revised: 9 July 2016 / Accepted: 19 July 2016 / Published: 27 July 2016
Cited by 3 | PDF Full-text (5581 KB) | HTML Full-text | XML Full-text
Abstract
Modeling the random fiber distribution of a fiber-reinforced composite is of great importance for studying the progressive failure behavior of the material on the micro scale. In this paper, we develop a new algorithm for generating random representative volume elements (RVEs) with statistical
[...] Read more.
Modeling the random fiber distribution of a fiber-reinforced composite is of great importance for studying the progressive failure behavior of the material on the micro scale. In this paper, we develop a new algorithm for generating random representative volume elements (RVEs) with statistical equivalent fiber distribution against the actual material microstructure. The realistic statistical data is utilized as inputs of the new method, which is archived through implementation of the probability equations. Extensive statistical analysis is conducted to examine the capability of the proposed method and to compare it with existing methods. It is found that the proposed method presents a good match with experimental results in all aspects including the nearest neighbor distance, nearest neighbor orientation, Ripley’s K function, and the radial distribution function. Finite element analysis is presented to predict the effective elastic properties of a carbon/epoxy composite, to validate the generated random representative volume elements, and to provide insights of the effect of fiber distribution on the elastic properties. The present algorithm is shown to be highly accurate and can be used to generate statistically equivalent RVEs for not only fiber-reinforced composites but also other materials such as foam materials and particle-reinforced composites. Full article
(This article belongs to the Special Issue Multiscale Methods and Application to Computational Materials Design)
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Open AccessFeature PaperArticle A Multiscale Computational Model Combining a Single Crystal Plasticity Constitutive Model with the Generalized Method of Cells (GMC) for Metallic Polycrystals
Materials 2016, 9(5), 335; doi:10.3390/ma9050335
Received: 16 March 2016 / Revised: 22 April 2016 / Accepted: 27 April 2016 / Published: 4 May 2016
Cited by 3 | PDF Full-text (5701 KB) | HTML Full-text | XML Full-text
Abstract
A multiscale computational model is developed for determining the elasto-plastic behavior of polycrystal metals by employing a single crystal plasticity constitutive model that can capture the microstructural scale stress field on a finite element analysis (FEA) framework. The generalized method of cells (GMC)
[...] Read more.
A multiscale computational model is developed for determining the elasto-plastic behavior of polycrystal metals by employing a single crystal plasticity constitutive model that can capture the microstructural scale stress field on a finite element analysis (FEA) framework. The generalized method of cells (GMC) micromechanics model is used for homogenizing the local field quantities. At first, the stand-alone GMC is applied for studying simple material microstructures such as a repeating unit cell (RUC) containing single grain or two grains under uniaxial loading conditions. For verification, the results obtained by the stand-alone GMC are compared to those from an analogous FEA model incorporating the same single crystal plasticity constitutive model. This verification is then extended to samples containing tens to hundreds of grains. The results demonstrate that the GMC homogenization combined with the crystal plasticity constitutive framework is a promising approach for failure analysis of structures as it allows for properly predicting the von Mises stress in the entire RUC, in an average sense, as well as in the local microstructural level, i.e., each individual grain. Two–three orders of saving in computational cost, at the expense of some accuracy in prediction, especially in the prediction of the components of local tensor field quantities and the quantities near the grain boundaries, was obtained with GMC. Finally, the capability of the developed multiscale model linking FEA and GMC to solve real-life-sized structures is demonstrated by successfully analyzing an engine disc component and determining the microstructural scale details of the field quantities. Full article
(This article belongs to the Special Issue Multiscale Methods and Application to Computational Materials Design)
Open AccessArticle The Influence of Crosslink Density on the Failure Behavior in Amorphous Polymers by Molecular Dynamics Simulations
Materials 2016, 9(4), 234; doi:10.3390/ma9040234
Received: 27 December 2015 / Revised: 4 March 2016 / Accepted: 17 March 2016 / Published: 25 March 2016
Cited by 4 | PDF Full-text (12242 KB) | HTML Full-text | XML Full-text
Abstract
The crosslink density plays a key role in the mechanical response of the amorphous polymers in previous experiments. However, the mechanism of the influence is still not clear. In this paper, the influence of crosslink density on the failure behavior under tension and
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The crosslink density plays a key role in the mechanical response of the amorphous polymers in previous experiments. However, the mechanism of the influence is still not clear. In this paper, the influence of crosslink density on the failure behavior under tension and shear in amorphous polymers is systematically studied using molecular dynamics simulations. The present results indicate that the ultimate stresses and the broken ratios (the broken bond number to all polymer chain number ratios) increase, as well as the ultimate strains decrease with increasing crosslink density. The strain concentration is clearer with the increase of crosslink density. In other words, a higher crosslink density leads to a higher strain concentration. Hence, the higher strain concentration further reduces the fracture strain. This study implies that the mechanical properties of amorphous polymers can be dominated for different applications by altering the molecular architecture. Full article
(This article belongs to the Special Issue Multiscale Methods and Application to Computational Materials Design)
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