Search results for: multiscale-modeling-of-heterogeneous-structures

Multiscale Modeling of Heterogeneous Structures

Author : Jurica Sorić
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This book provides an overview of multiscale approaches and homogenization procedures as well as damage evaluation and crack initiation, and addresses recent advances in the analysis and discretization of heterogeneous materials. It also highlights the state of the art in this research area with respect to different computational methods, software development and applications to engineering structures. The first part focuses on defects in composite materials including their numerical and experimental investigations; elastic as well as elastoplastic constitutive models are considered, where the modeling has been performed at macro- and micro levels. The second part is devoted to novel computational schemes applied on different scales and discusses the validation of numerical results. The third part discusses gradient enhanced modeling, in particular quasi-brittle and ductile damage, using the gradient enhanced approach. The final part addresses thermoplasticity, solid-liquid mixtures and ferroelectric models. The contents are based on the international workshop “Multiscale Modeling of Heterogeneous Structures” (MUMO 2016), held in Dubrovnik, Croatia in September 2016.

Multiscale Modeling of Heterogeneous Structures

Author : Jurica Sorić
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This book provides an overview of multiscale approaches and homogenization procedures as well as damage evaluation and crack initiation, and addresses recent advances in the analysis and discretization of heterogeneous materials. It also highlights the state of the art in this research area with respect to different computational methods, software development and applications to engineering structures. The first part focuses on defects in composite materials including their numerical and experimental investigations; elastic as well as elastoplastic constitutive models are considered, where the modeling has been performed at macro- and micro levels. The second part is devoted to novel computational schemes applied on different scales and discusses the validation of numerical results. The third part discusses gradient enhanced modeling, in particular quasi-brittle and ductile damage, using the gradient enhanced approach. The final part addresses thermoplasticity, solid-liquid mixtures and ferroelectric models. The contents are based on the international workshop “Multiscale Modeling of Heterogeneous Structures” (MUMO 2016), held in Dubrovnik, Croatia in September 2016.

Multiscale Modeling of Heterogeneous Catalysis in Porous Metal Foam Structures Using Particle based Simulation Methods

Author : Sebastian J. Mühlbauer
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Multiscale Formulation for Heterogeneous Materials

Author : Shafigh Mehraeen
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Multiscale Modeling and Uncertainty Quantification of Materials and Structures

Author : Manolis Papadrakakis
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This book contains the proceedings of the IUTAM Symposium on Multiscale Modeling and Uncertainty Quantification of Materials and Structures that was held at Santorini, Greece, September 9 – 11, 2013. It consists of 20 chapters which are divided in five thematic topics: Damage and fracture, homogenization, inverse problems–identification, multiscale stochastic mechanics and stochastic dynamics. Over the last few years, the intense research activity at micro scale and nano scale reflected the need to account for disparate levels of uncertainty from various sources and across scales. As even over-refined deterministic approaches are not able to account for this issue, an efficient blending of stochastic and multiscale methodologies is required to provide a rational framework for the analysis and design of materials and structures. The purpose of this IUTAM Symposium was to promote achievements in uncertainty quantification combined with multiscale modeling and to encourage research and development in this growing field with the aim of improving the safety and reliability of engineered materials and structures. Special emphasis was placed on multiscale material modeling and simulation as well as on the multiscale analysis and uncertainty quantification of fracture mechanics of heterogeneous media. The homogenization of two-phase random media was also thoroughly examined in several presentations. Various topics of multiscale stochastic mechanics, such as identification of material models, scale coupling, modeling of random microstructures, analysis of CNT-reinforced composites and stochastic finite elements, have been analyzed and discussed. A large number of papers were finally devoted to innovative methods in stochastic dynamics.

Multiscale Modeling and Simulation of Composite Materials and Structures

Author : Young W. Kwon
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This book presents the state-of-the-art in multiscale modeling and simulation techniques for composite materials and structures. It focuses on the structural and functional properties of engineering composites and the sustainable high performance of components and structures. The multiscale techniques can be also applied to nanocomposites which are important application areas in nanotechnology. There are few books available on this topic.

Multiscale Structural Topology Optimization

Author : Liang Xia
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Multiscale Structural Topology Optimization discusses the development of a multiscale design framework for topology optimization of multiscale nonlinear structures. With the intention to alleviate the heavy computational burden of the design framework, the authors present a POD-based adaptive surrogate model for the RVE solutions at the microscopic scale and make a step further towards the design of multiscale elastoviscoplastic structures. Various optimization methods for structural size, shape, and topology designs have been developed and widely employed in engineering applications. Topology optimization has been recognized as one of the most effective tools for least weight and performance design, especially in aeronautics and aerospace engineering. This book focuses on the simultaneous design of both macroscopic structure and microscopic materials. In this model, the material microstructures are optimized in response to the macroscopic solution, which results in the nonlinearity of the equilibrium problem of the interface of the two scales. The authors include a reduce database model from a set of numerical experiments in the space of effective strain. Presents the first attempts towards topology optimization design of nonlinear highly heterogeneous structures Helps with simultaneous design of the topologies of both macroscopic structure and microscopic materials Helps with development of computer codes for the designs of nonlinear structures and of materials with extreme constitutive properties Focuses on the simultaneous design of both macroscopic structure and microscopic materials Includes a reduce database model from a set of numerical experiments in the space of effective strain

Materials with Internal Structure

Author : Patrizia Trovalusci
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The book presents a series of concise papers by researchers specialized in various fields of continuum and computational mechanics and of material science. The focus is on principles and strategies for multiscale modeling and simulation of complex heterogeneous materials, with periodic or random microstructure, subjected to various types of mechanical, thermal, chemical loadings and environmental effects. A wide overview of complex behavior of materials (plasticity, damage, fracture, growth, etc.) is provided. Among various approaches, attention is given to advanced non-classical continua modeling which, provided by constitutive characterization for the internal and external actions (in particular boundary conditions), is a very powerful frame for the gross mechanical description of complex material behaviors, able to circumvent the restrictions of classical coarse–graining multiscale approaches.

Multi scale Modeling and Design of Heterogeneous Nano microstructure for Improved Mechanical Properties

Author : Mehdi Hamid Vishkasougheh
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The effect of grain boundary back stress field, slip transfer across grain boundaries and grain boundary sliding is analyzed for gradient microstructures under loading conditions like tensile and compression. One of the objectives is to address the existing trade-off between the strength and ductility for metallic materials. A multiscale crystal plasticity based framework is developed and gradient microstructures based on electron back scatter diffraction microscopy results are designed and implemented to the framework. The gradient microstructures are manufactured with severe plastic deformation techniques like high pressure torsion and shot pinning for pure Cu and Mg AZ31. The modeling and experimental mechanical performance of these samples are analyzed. The microstructures are designed by controlling the spatial grain size distribution in the range of a few hundreds of nanometers to tens of micrometers. Several layers with various thicknesses and grain sizes are combined to design these structures. A control voronoi tessellation method is applied for this purpose.The effect of different mechanisms like stress/strain gradient, slip transfer across grain boundaries, back stress field of grain boundaries and grain boundary sliding is studied for different metallic materials like IF (Interstitial Free) steel, Cu, Mg AZ31, and silver with gradient and bi-modal microstructures.The multiscale modeling span is further developed by coupling the stress/strain gradient formulation along with dislocation density evaluation relations to finite element solver as a user materials model to analyze the compression and buckling behavior of 3D printed micropillars as an application for this multiscale modeling framework. The main objective of this part of research is to add the grain size effect, strain rate sensitivity, statistically stored dislocation density effect, and geometrical necessary dislocation density to a continuum mechanics modeling environment. The generic tailor made crystal plasticity based user material model is written in Fortran environment. A parametric study is added to explain the effect of geometrical imperfection/eccentricity along with dislocation density content, grain size and strain rate sensitivity besides the predicted force vs. displacement results are compared with experimental results. The void size, porosity percentage and grain size effect of these AM micropillars are also analyzed and compared with experiments.

IUTAM Symposium on Multiscale Modelling of Fatigue Damage and Fracture in Smart Materials

Author : Meinhard Kuna
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Today, multi-functional materials such as piezoelectric/ferroelectric ceramics, magneto-strictive and shape memory alloys are gaining increasing applications as sensors, actuators or smart composite materials systems for emerging high tech areas. The stable performance and reliability of these smart components under complex service loads is of paramount practical importance. However, most multi-functional materials suffer from various mechanical and/or electro-magnetical degra-dation mechanisms as fatigue, damage and fracture. Therefore, this exciting topic has become a challenge to intensive international research, provoking the interdisciplinary approach between solid mechanics, materials science and physics. This book summarizes the outcome of the above mentioned IUTAM-symposium, assembling contributions by leading scientists in this area. Particularly, the following topics have been addressed: (1) Development of computational methods for coupled electromechanical field analysis, especially extended, adaptive and multi-level finite elements. (2) Constitutive modeling of non-linear smart material behavior with coupled electric, magnetic, thermal and mechanical fields, primarily based on micro-mechanical models. (3) Investigations of fracture and fatigue in piezoelectric and ferroelectric ceramics by means of process zone modeling, phase field simulation and configurational mechanics. (4) Reliability and durability of sensors and actuators under in service loading by alternating mechanical, electrical and thermal fields. (5) Experimental methods to measure fracture strength and to investigate fatigue crack growth in ferroelectric materials under electromechanical loading. (6) New ferroelectric materials, compounds and composites with enhanced strain capabilities.

Multiscale Modeling in Solid Mechanics

Author : Ugo Galvanetto
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This unique volume presents the state of the art in the field of multiscale modeling in solid mechanics, with particular emphasis on computational approaches. For the first time, contributions from both leading experts in the field and younger promising researchers are combined to give a comprehensive description of the recently proposed techniques and the engineering problems tackled using these techniques. The book begins with a detailed introduction to the theories on which different multiscale approaches are based, with regards to linear Homogenisation as well as various nonlinear approaches. It then presents advanced applications of multiscale approaches applied to nonlinear mechanical problems. Finally, the novel topic of materials with self-similar structure is discussed. Sample Chapter(s). Chapter 1: Computational Homogenisation for Non-Linear Heterogeneous Solids (808 KB). Contents: Computational Homogenisation for Non-Linear Heterogeneous Solids (V G Kouznetsova et al.); Two-Scale Asymptotic Homogenisation-Based Finite Element Analysis of Composite Materials (Q-Z Xiao & B L Karihaloo); Multi-Scale Boundary Element Modelling of Material Degradation and Fracture (G K Sfantos & M H Aliabadi); Non-Uniform Transformation Field Analysis: A Reduced Model for Multiscale Non-Linear Problems in Solid Mechanics (J-C Michel & P Suquet); Multiscale Approach for the Thermomechanical Analysis of Hierarchical Structures (M J Lefik et al.); Recent Advances in Masonry Modelling: Micro-Modelling and Homogenisation (P B Louren o); Mechanics of Materials with Self-Similar Hierarchical Microstructure (R C Picu & M A Soare). Readership: Researchers and academics in the field of heterogeneous materials and mechanical engineering; professionals in aeronautical engineering and materials science.

Micromechanical Analysis and Multi Scale Modeling Using the Voronoi Cell Finite Element Method

Author : Somnath Ghosh
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As multi-phase metal/alloy systems and polymer, ceramic, or metal matrix composite materials are increasingly being used in industry, the science and technology for these heterogeneous materials has advanced rapidly. By extending analytical and numerical models, engineers can analyze failure characteristics of the materials before they are integrated into the design process. Micromechanical Analysis and Multi-Scale Modeling Using the Voronoi Cell Finite Element Method addresses the key problem of multi-scale failure and deformation of materials that have complex microstructures. The book presents a comprehensive computational mechanics and materials science–based framework for multi-scale analysis. The focus is on micromechanical analysis using the Voronoi cell finite element method (VCFEM) developed by the author and his research group for the efficient and accurate modeling of materials with non-uniform heterogeneous microstructures. While the topics covered in the book encompass the macroscopic scale of structural components and the microscopic scale of constituent heterogeneities like inclusions or voids, the general framework may be extended to other scales as well. The book presents the major components of the multi-scale analysis framework in three parts. Dealing with multi-scale image analysis and characterization, the first part of the book covers 2D and 3D image-based microstructure generation and tessellation into Voronoi cells. The second part develops VCFEM for micromechanical stress and failure analysis, as well as thermal analysis, of extended microstructural regions. It examines a range of problems solved by VCFEM, from heat transfer and stress-strain analysis of elastic, elastic-plastic, and viscoplastic material microstructures to microstructural damage models including interfacial debonding and ductile failure. Establishing the multi-scale framework for heterogeneous materials with and without damage, the third part of the book discusses adaptive concurrent multi-scale analysis incorporating bottom-up and top-down modeling. Including numerical examples and a CD-ROM with VCFEM source codes and input/output files, this book is a valuable reference for researchers, engineers, and professionals involved with predicting the performance and failure of materials in structure-materials interactions.

Toward Multi scale Modeling and Simulation of Conduction in Heterogeneous Materials

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This report summarizes a project in which the authors sought to develop and deploy: (i) experimental techniques to elucidate the complex, multiscale nature of thermal transport in particle-based materials; and (ii) modeling approaches to address current challenges in predicting performace variability of materials (e.g., identifying and characterizing physical- chemical processes and their couplings across multiple length and time scales, modeling infor- mation transfer between scales, and statically and dynamically resolving material structure and its evolution during manufacturing and device performance). Experimentally, several capabilities were sucessfully advanced. As discussed in Chapter 2 a flash diffusivity capabil- ity for measuring homogeneous thermal conductivity of pyrotechnic powders (and beyond) was advanced; leading to enhanced characterization of pyrotechnic materials and properties impacting component development. Chapter 4 describes sucess for the first time, although preliminary, in resolving thermal fields at speeds and spatial scales relevant to energetic components. Chapter 7 summarizes the first ever (as far as the authors know) application of TDTR to actual pyrotechnic materials. This is the first attempt to actually characterize these materials at the interfacial scale. On the modeling side, new capabilities in image processing of experimental microstructures and direct numerical simulation on complicated structures were advanced (see Chapters 3 and 5). In addition, modeling work described in Chapter 8 led to improved prediction of interface thermal conductance from first principles calculations. Toward the second point, for a model system of packed particles, significant headway was made in implementing numerical algorithms and collecting data to justify the approach in terms of highlighting the phenomena at play and pointing the way forward in de- veloping and informing the kind of modeling approach oringinally envisioned (see Chapter 6). In both cases much more remains to be accomplished.

Computational Technology Reviews 2010

Author : B. H. V. Topping
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With contributions by well-known experts in the various branches of computational mechanics, this valuable collaboration reviews the historic and ongoing research in computational technology. Topics include, but are not limited to, radial basis functions, multiscale modeling strategies for heterogeneous materials, computational models for wooden structures, and composite and adaptive structures.

Heterogeneous Nanocomposite Adhesive Experimental Testing and Computational Multiscale Modeling

Author : Kevin Schreader
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This study is focused on a multiscale adhesive used for the investigation of bone bonding applications. Additionally hydroxyapatite nanoparticles were added to the adhesive to create a composite in attempts to enhance both the mechanical and biological properties. One of the main objectives was creating an adhesive system that is tailored to the biological environment in which it must operate. A solid adhesive layer as found in most engineering applications would be counterproductive to the bone healing process and thus an alternative solution was sought. A preliminary cell culture demonstrated that a polyurethane based adhesive tested was nontoxic to cells, and had the unique chemistry that would allow it to be processed into a foam. This porous structure is advantageous in a fracture healing scenario since the interconnecting pores aid in cell migration and ingrowth. This heterogeneous nanocomposite foam that is able to provide optimum conditions for the biological environment also presents additional issues that are of interest from a fundamental viewpoint. The material is composed of multiscale features with hydroxyapatite particles at the nano-scale level, and pores at the micro-scale level. This porosity and spatial heterogeneity introduces new challenges and opportunities for characterization and modeling. The experimental testing of this composite adhesive with unique characteristics then also provides support for the development of open issues in multiscale heterogeneous adhesive models.

Multiscale Modeling of Cementitious Materials

Author : Katie Elizabeth Bryan
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Cementitious material is modeled at multiple length scales to provide an understanding of its structure-property relations at the mesoscale. The ultimate research goal is to improve the predictability of multiscale, heterogeneous Ultra-High Performance Concrete (UHPC) using mesoscale Finite Element Analysis (FEA). The structural scale Finite Element (FE) simulation of an ASTM C1609 four-point bending test on a UHPC beam is calibrated to match the experimental data. A hierarchical process is employed to apply the resulting displacement of the calibrated structural scale simulation as boundary conditions for the FE simulations of three separate mesoscale RVE cubes, in descending order, to determine the behavior of each mesostructure. By investigating the stress and strain behaviors at each mesoscale, a multiscale model is established, giving insight to the structure-property relations to enable the design of UHPC materials with far more accuracy than using a single length scale model.

Multiscale Analysis of Deformation and Failure of Materials

Author : Jinghong Fan
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Presenting cutting-edge research and development within multiscale modeling techniques and frameworks, Multiscale Analysis of Deformation and Failure of Materials systematically describes the background, principles and methods within this exciting new & interdisciplinary field. The author’s approach emphasizes the principles and methods of atomistic simulation and its transition to the nano and sub-micron scale of a continuum, which is technically important for nanotechnology and biotechnology. He also pays close attention to multiscale analysis across the micro/meso/macroscopy of a continuum, which has a broad scope of applications encompassing different disciplines and practices, and is an essential extension of mesomechanics. Of equal interest to engineers, scientists, academics and students, Multiscale Analysis of Deformation and Failure of Materials is a multidisciplinary text relevant to those working in the areas of materials science, solid and computational mechanics, bioengineering and biomaterials, and aerospace, automotive, civil, and environmental engineering. Provides a deep understanding of multiscale analysis and its implementation Shows in detail how multiscale models can be developed from practical problems and how to use the multiscale methods and software to carry out simulations Discusses two interlinked categories of multiscale analysis; analysis spanning from the atomistic to the micro-continuum scales, and analysis across the micro/meso/macro scale of continuum.

Multiscale Modeling Using Goal oriented Adaptivity and Numerical Homogenization

Author : Chetan Kumar Jhurani
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Modeling of engineering objects with complex heterogeneous material structure at nanoscale level has emerged as an important research problem. In this research, we are interested in multiscale modeling and analysis of mechanical properties of the polymer structures created in the Step and Flash Imprint Lithography (SFIL) process. SFIL is a novel imprint lithography process designed to transfer circuit patterns for fabricating microchips in low-pressure and room-temperature environments. Since the smallest features in SFIL are only a few molecules across, approximating them as a continuum is not completely accurate. Previous research in this subject has dealt with coupling discrete models with continuum hyperelasticity models. The modeling of the post-polymerization step in SFIL involves computing solutions of large nonlinear energy minimization problems with fast spatial variation in material properties. An equilibrium configuration is found by minimizing the energy of this heterogeneous polymeric lattice. Numerical solution of such a molecular statics base model, which is assumed to describe the microstructure completely, is computationally very expensive. This is due to the problem size -- on the order of millions of degrees of freedom (DOFs). Rapid variation in material properties, ill-conditioning, nonlinearity, and non-convexity make this problem even more challenging to solve. We devise a method for efficient approximation of the solution. Combining numerical homogenization, adaptive finite element meshes, and goaloriented error estimation, we develop a black-box method for efficient solution of problems with multiple spatial scales. The purpose of this homogenization method is to reduce the number of DOFs, find locally optimal effective material properties, and do goal-oriented mesh refinement. In addition, it smoothes the energy landscape. Traditionally, a finite element mesh is designed after obtaining material properties in different regions. The mesh has to resolve material discontinuities and rapid variations. In our approach, however, we generate a sequence of coarse meshes (possibly 1-irregular), and homogenize material properties on each coarse mesh element using a locally posed constrained convex quadratic optimization problem. This upscaling is done using Moore-Penrose pseudoinverse of the linearized fine-scale element stiffness matrices, and a material independent interpolation operator. This requires solution of a continuous-time Lyapunov equation on each element. Using the adjoint solution, we compute local error estimates in the quantity of interest. The error estimates also drive the automatic mesh adaptivity algorithm. The results show that this method uses orders of magnitude fewer degrees of freedom to give fast and approximate solutions of the original fine-scale problem. Critical to the computational speed of local homogenization is computing Moore-Penrose pseudoinverse of rank-deficient matrices without using Singular Value Decomposition. To this end, we use four algorithms, each having different desirable features. The algorithms are based on Tikhonov regularization, sparse QR factorization, a priori knowledge of the null-space of the matrix, and iterative methods based on proper splittings of matrices. These algorithms can exploit sparsity and thus are fast. Although the homogenization method is designed with a specific molecular statics problem in mind, it is a general method applicable for problems with a given fine mesh that sufficiently resolves the fine-scale material properties. We verify the method using a conductivity problem in 2-D, with chessboard like thermal conductivity pattern, which has a known homogenized conductivity. We analyze other aspects of the homogenization method, for example the choice of norm in which we measure local error, optimum coarse mesh element size for homogenizing SFIL lattices, and the effect of the method chosen for computing the pseudoinverse.

Dislocation based Multi scale Modeling for Size dependent Plasticity of Heterogeneous Materials

Author : Hao Lyu
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First, this framework is applied to study the size effect and deformation mechanisms of dual phase steel. Here, only the strain gradient theory is employed to predict the response of dual phase steel under constant strain rate tensile test. The predicted mechanical behavior and texture evolution are in good agreement with experimental works.

Multiscale Modeling of Complex Materials

Author : Tomasz Sadowski
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The papers in this volume deal with materials science, theoretical mechanics and experimental and computational techniques at multiple scales, providing a sound base and a framework for many applications which are hitherto treated in a phenomenological sense. The basic principles are formulated of multiscale modeling strategies towards modern complex multiphase materials subjected to various types of mechanical, thermal loadings and environmental effects. The focus is on problems where mechanics is highly coupled with other concurrent physical phenomena. Attention is also focused on the historical origins of multiscale modeling and foundations of continuum mechanics currently adopted to model non-classical continua with substructure, for which internal length scales play a crucial role.