provides a possibility for the creation of reliable models that take into account structural, material, and topological properties at different scales. The book addresses four major areas: (i) the basic principles of macroscale, microscale, and nanoscale modeling techniques; (ii) the connection of microscale and/or nanoscale models with macrosimulation software; (iii) optimization development in the framework of multiscale engineering and the solution of identification problems; (iv) the computer science techniques used in this class of models and advice for scientists interested in developing their own models and software for multiscale analysis and optimization.
Therefore, the book presents several approaches to multiscale modelling, such as the bridging and homogenization methods, as well as the general formulation of complex optimization and identification problems in multiscale simulations. It also presents the application of global optimization algorithms based on robust bioinspired algorithms, proposes parallel and multi‐subpopulation approaches in order to speed‐up computations, and discusses several numerical examples of multiscale modeling, optimization, and identification of composite and functionally graded engineering materials.
Multiscale Modelling and Optimisation of Materials and Structures is thereby a valuable source of information for young scientists and students looking to develop their own models, write their own computer programs, and implement them into simulation systems.
Biography
Tadeusz Burczyński: His expertise is in computational sciences, including computational intelligence, computational mechanics, and computational materials science, especially in optimization and multiscale engineering.
Maciej Pietrzyk: His research focuses on numerical modelling including multiscale approach and the application of optimization techniques in materials science.
Wacław Kuś: His scientific interests are related to the applications of parallel and HPC methods in the optimization of multiscale problems in mechanics and biomechanics.
Łukasz Madej: His expertise is in computational materials science and process engineering. The main area of interest is full‐field multiscale modelling of industrial processes and phenomena.
Adam Mrozek: His research focuses on molecular dynamic simulations, optimization of mechanical properties of the 2D materials, and multiscale modelling.
Łukasz Rauch: The main interest of his research is focused on computer science applied in industry including conventional way of modelling as well as application of surrogate models.
1 Introduction to Multiscale Modelling and Optimization
A wide selection of materials exhibits unusual in‐use properties gained by control of phenomena occurring in mesoscale, microscale, and nanoscale during manufacturing. Examples of such materials range from constructional steels (e.g. AHSS – Advanced High Strength Steels for automotive industry [8] and titanium alloys for aerospace industry [10]) through various materials for energy applications [6] to new biocompatible materials for ventricular assist devices [9] or other biomedical applications [11]. Due to potential advances in materials science that could dramatically affect the most innovative technologies, further development in this field is expected. For this to happen, materials science has to be supported by new tools and methodologies, among which numerical modelling plays a crucial role.
On the other hand, to predict the correlation between processing parameters and product properties properly, one needs to investigate macroscopic material behaviour and phenomena occurring at lower dimensional scales, at grain level or even at atomistic levels. Thus, multiscale modelling with the digital materials representation (DMR) concept [7] is a research field that potentially can support the design of new products with unique in‐use properties. The development of new materials modelling techniques that tackle various length scale phenomena is observed in many leading research institutes and universities worldwide. Multiscale analysis of length and temporal scales has already found a wide range of applications in many areas of science. Advantages provided by a combination of numerical approaches: finite element (FEM), crystal plasticity finite element (CPFEM), extended finite element (XFEM), finite volume (FVM), boundary element (BEM), meshfree, multigrid methods, Monte Carlo (MC), cellular automata (CA), molecular dynamics (MD), molecular statics (MS), phase field and level set methods, fast Fourier transformation, etc. are already being successfully applied in practical applications [14].
This book's main feature, which distinguishes it from other publications, is that it is focused on modelling of processing of materials and that it combines the problem of multiscale modelling with the optimization tasks providing a wide range of possibilities for practical industrial applications.
The first part of the book contains a presentation of basic principles of the microscale and nanoscale modelling techniques. The second part supplies information about applications of optimization and identification techniques in multiscale modelling. The book is recapitulated by presenting information on the computer science techniques used in multiscale modelling, and it is focused on computer implementation issues, advising scientists interested in developing their multiscale models.
1.1 Multiscale Modelling
1.1.1 Basic Information on Multiscale Modelling
During the last years, numerical modelling became a widely used tool that successfully supports and comprehends experimental research on various modern materials. Basic principles of this modelling technique, as well as the classification of models, can be found in fundamental works of Allix [1] or Fish [4], and Horstemeyer and Wang [5] which discussed possible scopes of applications of multiscale modelling in the industry. However, within the last several years, various papers on multiscale modelling have been published in the scientific literature concerning both theoretical issues and practical applications. A variety of problems was raised in these papers, and several ambiguities connected with nomenclature and definitions can be found. The problem of naming various scales in multiscale modelling is an example of a lack of consistency in definitions. Commonly, ‘macro’, ‘meso’, ‘micro’, and ‘nano’ scales are mentioned (Figure 1.1).
Nevertheless, this nomenclature can be misleading and often not sufficient. The term ‘macroscale’ is used for different scales, from large structures to single crystals. Others describe the single‐crystal level as ‘microscale’. In many cases, the characteristic entities in the particular scale are important, not the characteristic length. For example the characteristic length of the scale, in which grains are distinguishable, can vary from nanometres to centimetres. Moreover, the same grain‐level scale can be applied as macroscale in connection with an atomistic scale model or as microscale with a macroscopic model of a large structure deformation. Therefore, this book uses the term ‘coarse’ scale for the scale with greater characteristic length and ‘fine’ scale for the scale with smaller characteristic length. It allows using the terms ‘coarser’ and ‘finer’ to describe relations between more than two scales. To keep the concept clear, the fine or coarse scales are usually related to the governing structures in particular cases (e.g. grains, atoms). Despite the length scale problem, there is also an issue with the time scale as many of the phenomena occur in significantly different time regimes. Usually, the temporal scale is unified across the different length scales to provide physically relevant results, which sometimes makes the computational model expensive.
