This monograph provides a concise overview of the main theoretical and numerical tools to solve homogenization problems in solids with finite elements. Starting from simple cases (linear thermal case) the problems are progressively complexified to finish with nonlinear problems. The book is not an overview of current research in that field, but a course book, and summarizes established knowledge in this area such that students or researchers who would like to start working on this subject will acquire the basics without any preliminary knowledge about homogenization. More specifically, the book is written with the objective of practical implementation of the methodologies in simple programs such as Matlab. The presentation is kept at a level where no deep mathematics are required.​

The latest state of simulation techniques to model plasticity and fracture in crystalline materials on the nano- and microscale is presented. Discrete dislocation mechanics and the neighbouring fields molecular dynamics and crystal plasticity are central parts. The physical phenomena, the theoretical basics, their mathematical description and the simulation techniques are introduced and important problems from the formation of dislocation structures to fatigue and fracture from the nano- to microscale as well as it’s impact on the macro behaviour are considered.

The book presents the latest findings in experimental plasticity, crystal plasticity, phase transitions, advanced mathematical modeling of finite plasticity and multi-scale modeling. The associated algorithmic treatment is mainly based on finite element formulations for standard (local approach) as well as for non-standard (non-local approach) continua and for pure macroscopic as well as for directly coupled two-scale boundary value problems. Applications in the area of material design/processing are covered, ranging from grain boundary effects in polycrystals and phase transitions to deep-drawing of multiphase steels by directly taking into account random microstructures.

Written by the leading experts in computational materials science, this handy reference concisely reviews the most important aspects of plasticity modeling: constitutive laws, phase transformations, texture methods, continuum approaches and damage mechanisms. As a result, it provides the knowledge needed to avoid failures in critical systems udner mechanical load. With its various application examples to micro- and macrostructure mechanics, this is an invaluable resource for mechanical engineers as well as for researchers wanting to improve on this method and extend its outreach.

In this, its second corrected printing, Zohdi and Wriggers’ illuminating text presents a comprehensive introduction to the subject. The authors include in their scope basic homogenization theory, microstructural optimization and multifield analysis of heterogeneous materials. This volume is ideal for researchers and engineers, and can be used in a first-year course for graduate students with an interest in the computational micromechanical analysis of new materials.

The book contains state-of the-art reviews in the area of effective properties of heterogeneous materials - the classical field at interface of materials science and solid mechanics. The primary focus is on thermo-mechanical properties, materials science applications, as well as computational aspects and new opportunities provided by rapidly increasing computer powers. The reviews are at the level that is appropriate for a substantial community of researchers working in this field, both at universities and in the industry, and to graduate students. The book can be used as supplementary reading to graduate level courses.

A classroom-tested textbook providing a fundamental understandingof basic kinetic processes in materials This textbook, reflecting the hands-on teaching experience of itsthree authors, evolved from Massachusetts Institute of Technology'sfirst-year graduate curriculum in the Department of MaterialsScience and Engineering. It discusses key topics collectivelyrepresenting the basic kinetic processes that cause changes in thesize, shape, composition, and atomistic structure of materials.Readers gain a deeper understanding of these kinetic processes andof the properties and applications of materials. Topics are introduced in a logical order, enabling students todevelop a solid foundation before advancing to more sophisticatedtopics. Kinetics of Materials begins with diffusion, offering adescription of the elementary manner in which atoms and moleculesmove around in solids and liquids. Next, the more complex motion ofdislocations and interfaces is addressed. Finally, still morecomplex kinetic phenomena, such as morphological evolution andphase transformations, are treated. Throughout the textbook, readers are instilled with an appreciationof the subject's analytic foundations and, in many cases, theapproximations commonly used in the field. The authors offer manyextensive derivations of important results to help illuminate theirorigins. While the principal focus is on kinetic phenomena incrystalline materials, select phenomena in noncrystalline materialsare also discussed. In many cases, the principles involved apply toall materials. Exercises with accompanying solutions are provided throughoutKinetics of Materials, enabling readers to put their newfoundknowledge into practice. In addition, bibliographies are offeredwith each chapter, helping readers to investigate specializedtopics in greater detail. Several appendices presenting importantbackground material are also included. With its unique range of topics, progressive structure, andextensive exercises, this classroom-tested textbook provides anenriching learning experience for first-year graduate students.