Multiscale Materials Modeling Research Articles

A Multiscale Materials Modeling Method With Seamless Zooming Capability Based on Surfacelets1

In multiscale materials modeling, it is desirable that different levels of details can be specified in different regions of interest without the separation of scales so that the geometric and physical properties of materials can be designed and characterized. Existing materials modeling approaches focus more on the representation of the distributions of material compositions captured from images. In this paper, a multiscale materials modeling method is proposed to support interactive specification and visualization of material microstructures at multiple levels of details, where designer's intent at multiple scales is captured. This method provides a feature-based modeling approach based on a recently developed surfacelet basis. It has the capability to support seamless zoom-in and zoom-out. The modeling, operation, and elucidation of materials are realized in both the surfacelet space and the image space.

Multiscale modelling of graphene platelets-based nanocomposite materials

This work presents a multiscale framework for the elasto-plastic response of platelets-like inclusions reinforced nanocomposite materials. The solution of the heterogeneous material problem is solved by a kinematic integral equation. An imperfect interface is introduced between the particles and the matrix through a linear spring model LSM, leading to a modified Eshelby’s tensor. The interfacial contribution, related to the strain concentration tensor within each material phase and inside the average strain field, is described by a modified Mori–Tanaka scheme. The non-linear response is established in the framework of the J2 flow rule. An expression of the algorithmic tangent operator for each phase is obtained and used as an uniform modulus for homogenisation purpose. Numerical results are conducted on graphene platelets GPL-reinforced polymer PA6 composite for several design parameters such as GPL volume fraction, aspect ratio and the interfacial compliance. These results clearly highlight the impact of the aspect ratio as well as the volume fraction by a softening in the overall response when imperfection is considered at the interface. Finally, a multiscale simulation is performed on a three bending specimen showing the capability of the developed constitutive equations to be implemented in a finite element FE code.

A Review of Multiscale Computational Methods in Polymeric Materials.

Polymeric materials display distinguished characteristics which stem from the interplay of phenomena at various length and time scales. Further development of polymer systems critically relies on a comprehensive understanding of the fundamentals of their hierarchical structure and behaviors. As such, the inherent multiscale nature of polymer systems is only reflected by a multiscale analysis which accounts for all important mechanisms. Since multiscale modelling is a rapidly growing multidisciplinary field, the emerging possibilities and challenges can be of a truly diverse nature. The present review attempts to provide a rather comprehensive overview of the recent developments in the field of multiscale modelling and simulation of polymeric materials. In order to understand the characteristics of the building blocks of multiscale methods, first a brief review of some significant computational methods at individual length and time scales is provided. These methods cover quantum mechanical scale, atomistic domain (Monte Carlo and molecular dynamics), mesoscopic scale (Brownian dynamics, dissipative particle dynamics, and lattice Boltzmann method), and finally macroscopic realm (finite element and volume methods). Afterwards, different prescriptions to envelope these methods in a multiscale strategy are discussed in details. Sequential, concurrent, and adaptive resolution schemes are presented along with the latest updates and ongoing challenges in research. In sequential methods, various systematic coarse-graining and backmapping approaches are addressed. For the concurrent strategy, we aimed to introduce the fundamentals and significant methods including the handshaking concept, energy-based, and force-based coupling approaches. Although such methods are very popular in metals and carbon nanomaterials, their use in polymeric materials is still limited. We have illustrated their applications in polymer science by several examples hoping for raising attention towards the existing possibilities. The relatively new adaptive resolution schemes are then covered including their advantages and shortcomings. Finally, some novel ideas in order to extend the reaches of atomistic techniques are reviewed. We conclude the review by outlining the existing challenges and possibilities for future research.

A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

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, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.

Vision for Data and Informatics in the Future Materials Innovation Ecosystem

The high cost and time typically expended in the successful deployment of new materials into high-performance commercial products is attributable to multiple factors. The most significant of these include the heavy reliance on experiments, the persisting disconnect between multiscale experiments and multiscale models, the lack of a broadly accessible data and knowledge infrastructure that can support the implementation of a holistic systems approach, and the lack of a suitable framework for facilitating and enhancing the critically needed cross-disciplinary collaborations. The emerging discipline of materials data science and informatics (MDSI) promises to address these key technology gaps. The potential benefits to the materials innovation enterprise that could accrue from an aggressive adoption of the novel concepts and toolsets offered by MDSI are examined. A specific vision is expounded for the role of MDSI in bridging the large gap that exists between the multiscale materials experiments and the multiscale materials models.

Environmental degradation of composites for marine structures: new materials and new applications.

This paper describes the influence of seawater ageing on composites used in a range of marine structures, from boats to tidal turbines. Accounting for environmental degradation is an essential element in the multi-scale modelling of composite materials but it requires reliable test data input. The traditional approach to account for ageing effects, based on testing samples after immersion for different periods, is evolving towards coupled studies involving strong interactions between water diffusion and mechanical loading. These can provide a more realistic estimation of long-term behaviour but still require some form of acceleration if useful data, for 20 year lifetimes or more, are to be obtained in a reasonable time. In order to validate extrapolations from short to long times, it is essential to understand the degradation mechanisms, so both physico-chemical and mechanical test data are required. Examples of results from some current studies on more environmentally friendly materials including bio-sourced composites will be described first. Then a case study for renewable marine energy applications will be discussed. In both cases, studies were performed first on coupons at the material level, then during structural testing and analysis of large components, in order to evaluate their long-term behaviour. This article is part of the themed issue 'Multiscale modelling of the structural integrity of composite materials'.

Micromechanical Characteristics of Hardly Deformable Mg Alloys

Mechanical characterization of individual microstructural phases of hardly deformable magnesium alloys is of crucial importance for the development of multi-scale material models. The magnesium alloys are used for preparation of fine tubes with diameter of a few millimeters and tens of millimeters wall thickness. It is hard to control an ordinary drawing process for the preparation of such tubes. However, the tubes can be prepared with a laser dieless drawing process that is, in contrary to conventional drawing, able to draw low formability materials and it is able to produce variable cross-sections of the tube or a wire with high precision. The magnesium alloy tubes are used in various fields as micro-electro-mechanical systems, medicine, electrical, biological and chemical fields. In this paper, preliminary microstructural studies and local mechanical characterization of pure Mg, MgCa0.8 and AZ31 magnesium alloys used for tube extrusion, is provided. The material microstructure is studied by means of scanning electron, atomic force microscopes and nanoindentation. Elastic properties and volume fractions of mechanically distinct phases that are not accessible by standard testing methods are provided in the paper.

Can a continuous mineral foam explain the stiffening of aged bone tissue? A micromechanical approach to mineral fusion in musculoskeletal tissues

Recent experimental data revealed a stiffening of aged cortical bone tissue, which could not be explained by common multiscale elastic material models. We explain this data by incorporating the role of mineral fusion via a new hierarchical modeling approach exploiting the asymptotic (periodic) homogenization (AH) technique for three-dimensional linear elastic composites. We quantify for the first time the stiffening that is obtained by considering a fused mineral structure in a softer matrix in comparison with a composite having non-fused cubic mineral inclusions. We integrate the AH approach in the Eshelby-based hierarchical mineralized turkey leg tendon model (Tiburtius et al 2014 Biomech. Model. Mechanobiol. 13 1003–23), which can be considered as a base for musculoskeletal mineralized tissue modeling. We model the finest scale compartments, i.e. the extrafibrillar space and the mineralized collagen fibril, by replacing the self-consistent scheme with our AH approach. This way, we perform a parametric analysis at increasing mineral volume fraction, by varying the amount of mineral that is fusing in the axial and transverse tissue directions in both compartments. Our effective stiffness results are in good agreement with those reported for aged human radius and support the argument that the axial stiffening in aged bone tissue is caused by the formation of a continuous mineral foam. Moreover, the proposed theoretical and computational approach supports the design of biomimetic materials which require an overall composite stiffening without increasing the amount of the reinforcing material.

Magnetic hysteresis at the domain scale of a multi-scale material model for magneto-elastic behaviour

This paper proposes a multi-scale energy-based material model for poly-crystalline materials. Describing the behaviour of poly-crystalline materials at three spatial scales of dominating physical mechanisms allows accounting for the heterogeneity and multi-axiality of the material behaviour. The three spatial scales are the poly-crystalline, grain and domain scale. Together with appropriate scale transitions rules and models for local magnetic behaviour at each scale, the model is able to describe the magneto-elastic behaviour (magnetostriction and hysteresis) at the macroscale, although the data input is merely based on a set of physical constants. Introducing a new energy density function that describes the demagnetisation field, the anhysteretic multi-scale energy-based material model is extended to the hysteretic case. The hysteresis behaviour is included at the domain scale according to the micro-magnetic domain theory while preserving a valid description for the magneto-elastic coupling. The model is verified using existing measurement data for different mechanical stress levels.

Self-consistent clustering analysis: An efficient multi-scale scheme for inelastic heterogeneous materials

The discovery of efficient and accurate descriptions for the macroscopic behavior of materials with complex microstructure is an outstanding challenge in mechanics of materials. A mechanistic, data-driven, two-scale approach is developed for predicting the behavior of general heterogeneous materials under irreversible processes such as inelastic deformation. The proposed approach includes two major innovations: (1) the use of a data compression algorithm, k-means clustering, during the offline stage of the method to homogenize the local features of the material microstructure into a group of clusters; and (2) a new method called self-consistent clustering analysis used in the online stage that is valid for any local plasticity laws of each material phase without the need for additional calibration. A particularly important feature of the proposed approach is that the offline stage only uses the linear elastic properties of each material phase, making it efficient. This work is believed to open new avenues in parameter-free multi-scale modeling of complex materials, and perhaps in other fields that require homogenization of irreversible processes.

A multiscale micromechanical approach to model the deteriorating impact of alkali-silica reaction on concrete

The alkali-silica reaction (ASR) in concrete is one of the most harmful deterioration processes, which leads to expansion and cracking of the material. To understand the evolution of ASR in concrete and its deteriorating impact on the material, a multiscale material model, from aggregate to concrete level, is proposed. The concrete, which at macro scale is considered a homogeneous material, is micromechanically modelled by a matrix-cracks system, in which each phase is uniform and behaves elastically. The damage criterion, associated to the cracks, is formulated on the basis of linear fracture mechanics theory. The model, which is analytically solved, is based on a limited numbers of input parameters, to be determined via micro and macro experimental investigations. The model is able to predict the non-linear behaviour of concrete subject to uniaxial loading in good agreement with code formulations, which are usually input for numerical analyses of structures. For the case of ASR-affected material, the model overestimates the degradation rate of mechanical properties as a function of the expansion. On the contrary, the relationship between stiffness and strength deterioration is correctly approximated. Various model modifications are explored suggesting that the assumption of elastic behaviour of each phase should be reconsidered.

A nonlinear manifold-based reduced order model for multiscale analysis of heterogeneous hyperelastic materials

A new manifold-based reduced order model for nonlinear problems in multiscale modeling of heterogeneous hyperelastic materials is presented. The model relies on a global geometric framework for nonlinear dimensionality reduction (Isomap), and the macroscopic loading parameters are linked to the reduced space using a Neural Network. The proposed model provides both homogenization and localization of the multiscale solution in the context of computational homogenization. To construct the manifold, we perform a number of large three-dimensional simulations of a statistically representative unit cell using a parallel finite strain finite element solver. The manifold-based reduced order model is verified using common principles from the machine-learning community. Both homogenization and localization of the multiscale solution are demonstrated on a large three-dimensional example and the local microscopic fields as well as the homogenized macroscopic potential are obtained with acceptable engineering accuracy.

Three-Dimensional Continuum Dislocation Dynamics Simulations of Dislocation Structure Evolution in Bending of a Micro-Beam

ABSTRACTA persistent challenge in multi-scale modeling of materials is the prediction of plastic materials behavior based on the evolution of the dislocation state. An important step towards a dislocation based continuum description was recently achieved with the so called continuum dislocation dynamics (CDD). CDD captures the kinematics of moving curved dislocations in flux-type evolution equations for dislocation density variables, coupled to the stress field via average dislocation velocity-laws based on the Peach-Koehler force. The lowest order closure of CDD employs three internal variables per slip system, namely the total dislocation density, the classical dislocation density tensor and a so called curvature density.In the current work we present a three-dimensional implementation of the lowest order CDD theory as a materials sub-routine for Abaqus®in conjunction with the crystal plasticity framework DAMASK. We simulate bending of a micro-beam and qualitatively compare the plastic shear and the dislocation distribution on a given slip system to results from the literature. The CDD simulations reproduce a zone of reduced plastic shear close to the surfaces and dislocation pile-ups towards the center of the beam, which have been similarly observed in discrete dislocation simulations.

Multiscale approach for modeling electron spectra induced by photons from solids

Physical and chemical phenomena reflected in electron spectra excited by photons from solids take place on very wide scales of space, time, and excitation energy, covering sometimes differences of many orders of magnitude. Therefore, the use of multiscale approaches seems to be promising when extracting information on electronic structure or chemical composition from such electron spectra. Following a summary of phenomena reflected in electron spectra induced from solids by photons and different type of models available for their interpretation, the challenges of characterization of advanced materials and the need for multiscale materials analysis and modeling will be discussed. Copyright © 2015 John Wiley & Sons, Ltd.

Review of the synergies between computational modeling and experimental characterization of materials across length scales

With the increasing interplay between experimental and computational approaches at multiple length scales, new research directions are emerging in materials science and computational mechanics. Such cooperative interactions find many applications in the development, characterization and design of complex material systems. This manuscript provides a broad and comprehensive overview of recent trends in which predictive modeling capabilities are developed in conjunction with experiments and advanced characterization to gain a greater insight into structure–property relationships and study various physical phenomena and mechanisms. The focus of this review is on the intersections of multiscale materials experiments and modeling relevant to the materials mechanics community. After a general discussion on the perspective from various communities, the article focuses on the latest experimental and theoretical opportunities. Emphasis is given to the role of experiments in multiscale models, including insights into how computations can be used as discovery tools for materials engineering, rather than to “simply” support experimental work. This is illustrated by examples from several application areas on structural materials. This manuscript ends with a discussion on some problems and open scientific questions that are being explored in order to advance this relatively new field of research.

Fiber-matrix interphase in applied short glass fiber composites determined by a nano-scratch method

Abstract The fiber-matrix interphase in composites is defined as the intersection region between fibers and the matrix material. It shows altered matrix material properties. In dependency of the matrix material or the fiber coating, this phase is created by interdiffusion processes at the macromolecular scale driven by thermodynamic forces. Especially for FE simulations of composites and the validation of multi-scale material modeling approaches, the information about the existing interphase becomes important. Thus, the present study analyses the interphase in applied short glass fiber reinforced thermoplastics. For the identification of the interphase thickness, the nano-scratch method provides admissible results. This methodology is improved and adapted to the use in short fiber composite specimens. Thereby, the measured range of interphase thickness represents the inhomogeneity of the interphase. To assure that the measured interphase is not mainly constituted by the sizing of the glass fiber, incineration tests are performed additionally. The comparison of the interphase and the sizing thickness shows a significant thicker interphase.

Localized microstructural characterization of a dissimilar metal electron beam weld joint from an aerospace component

Hydrogen induced cold cracking (HICC) and hydrogen embrittlement (HE) are influenced by the microstructural evolution, residual plastic strain (i.e. local misorientation), recrystallization of grains and the resultant grain boundary characteristic distribution (GBCD) brought about by welding processes. HICC and HE are known to cause failures in aerospace components and it is vitally important to quantify the microstructural evolution, degree of residual plastic strain and determine the GBCD across dissimilar weld joints in order to assess the susceptibility of the weld joint to these phenomena. In this investigation a full a microstructural characterization study was carried out at various locations within and around a dissimilar weld joint of pulse-plated nickel (PP-Ni) and Inconel 718 (IN718), taken from an aerospace component. Areas examined included the base metals, weld fusion zone and heat affected zones on both sides of the weld joint, formed via electron beam welding. Scanning electron microscopy (SEM) in combination with electron backscatter diffraction (EBSD) was employed to measure the residual plastic strain, grain structure, grain size distribution, crystal orientation distribution, grain boundary misorientation distribution and GBCD of the dissimilar metal weld joint. Finally a metallurgical examination was carried out using SEM on the IN718 HAZ in order to investigate the secondary phase precipitation arising from the welding process. The results shows large variety of GBCD, crystallographic orientation distribution, local plastic strain distribution and grain size, shape and structure distribution across dissimilar weld joint. And these localized microstructural characterized data sets need to be carefully transferred using data-driven approach in order to develop predictive multiscale material modelling for hydrogen induced cracking and hydrogen embrittlement.

Multi-scale defect interactions in high-rate failure of brittle materials, Part II: Application to design of protection materials

Micromechanics based damage models, such as the model presented in Part I of this 2 part series (Tonge and Ramesh, 2015), have the potential to suggest promising directions for materials design. However, to reach their full potential these models must demonstrate that they capture the relevant physical processes. In this work, we apply the multiscale material model described in Tonge and Ramesh (2015) to ballistic impacts on the advanced ceramic boron carbide and suggest possible directions for improving the performance of boron carbide under impact conditions. We simulate both dynamic uniaxial compression and simplified ballistic loading geometries to demonstrate that the material model captures the relevant physics in these problems and to interrogate the sensitivity of the simulation results to some of the model input parameters. Under dynamic compression, we show that the simulated peak strength is sensitive to the maximum crack growth velocity and the flaw distribution, while the stress collapse portion of the test is partially influenced by the granular flow behavior of the fully damaged material. From simulations of simplified ballistic impact, we suggest that the total amount of granular flow (a possible performance metric) can be reduced by either a larger granular flow slope (more angular fragments) or a larger granular flow timescale (larger fragments). We then discuss the implications for materials design.

Multiscale characterization and modeling of granular materials through a computational mechanics avatar: a case study with experiment

Through a first-generation computational mechanics avatar that directly links advanced X-ray computed tomographic experimental techniques to a discrete computational model, we present a case study where we made the first attempt to characterize and model the grain-scale response inside the shear band of a real specimen of Caicos ooids subjected to triaxial compression. The avatar has enabled, for the first time, the transition from faithful representation of grain morphologies in X-ray tomograms of granular media to a morphologically accurate discrete computational model. Grain-scale information is extracted and upscaled into a continuum finite element model through a hierarchical multiscale scheme, and the onset and evolution of a persistent shear band is modeled, showing excellent quantitative agreement with experiment in terms of both grain-scale and continuum responses in the post-bifurcation regime. More importantly, consistency in results across characterization, discrete analysis and continuum response from multiscale calculations are found, achieving the first and long sought-after quantitative breakthrough in grain-scale analysis of real granular materials.

12th Russia/CIS/Baltic/Japan Symposium on Ferroelectricity and 9th International Conference on Functional Materials and Nanotechnologies (RCBJSF-2014-FM&NT)

The joint International Symposium RCBJSF–2014–FM&NT successfully has united two international events – 12th Russia/CIS/Baltic/Japan Symposium on Ferroelectricity (RCBJSF-12) and 9th International Conference Functional Materials and Nanotechnologies (FM&NT-2014). The RCBJSF symposium is a continuation of series of meetings on ferroelectricity, the first of which took place in Novosibirsk (USSR) in 1976. FM&NT conferences started in 2006 and have been organized by Institute of Solid State Physics, University of Latvia in Riga. In 2012 the International program committee decided to transform this conference into a traveling Baltic State conference and the FM&NT-2013 was organized by the Institute of Physics, University of Tartu, Estonia. In 2014 the joint international symposium RCBJSF–2014–FM&NT was organized by the Institute of Solid State Physics, University of Latvia and was part of Riga – 2014, the European Capital of Culture event. The purpose of the joint Symposium was to bring together scientists, students and high-level experts in solid state physics, materials science, engineering and related disciplines. The number of the registered participants from 26 countries was over 350. During the Symposium 128 high quality scientific talks (5 plenary, 42 invited, 81 oral) and over 215 posters were presented. All presentations were divided into 4 parallel sessions according to 4 main topics of the Symposium: Ferroelectricity, including ferroelectrics and multiferroics, pyroelectrics, piezoelectrics and actuators, integrated ferroelectrics, relaxors, phase transitions and critical phenomena. Multifunctional Materials, including theory, multiscale and multiphenomenal material modeling and simulation, advanced inorganic, organic and hybrid materials. Nanotechnologies, including progressive methods, technologies and design for production, investigation of nano- particles, composites, structures, thin films and coatings. Energy, including perspective materials and technologies for renewable and hydrogen energy, fuel cells, photovoltaics, LEDs, OLEDs. Based on these reports, 48 papers are included in this volume of IOP Conference Series: Materials Science and Engineering. Additional information about RCBJSF–2014–FM&NT is available at the homepage http://www.fmnt.lu.lv. The Organizing Committee would like to thank all the speakers, contributors, session chairs, referees and other involved staff for their efforts in making the RCBJSF–2014–FM&NT successful. Sincerely, organizers of the event Andris Sternberg Liga Grinberga Anatolijs Sarakovskis Martins Rutkis