Klaus Hackl

Homogenization is a fairly new, yet deep field of mathematics which is used as a powerful tool for analysis of applied problems which involve multiple scales. Generally, homogenization is utilized as a modeling procedure to describe processes in complex structures. Applications of Homogenization Theory to the Study of Mineralized Tissue functions as an introduction to the theory of homogenization. At the same time, the book explains how to apply the theory to various application problems in biology, physics and engineering. The authors are experts in the field and collaborated to create this book which is a useful research monograph for applied mathematicians, engineers and geophysicists. As for students and instructors, this book is a well-rounded and comprehensive text on the topic of homogenization for graduate level courses or special mathematics classes.Features: Covers applications in both geophysics and biology. Includes recent results not found in classical books on the topic Focuses on evolutionary kinds of problems; there is little overlap with books dealing with variational methods and T-convergence Includes new results where the G-limits have different structures from the initial operators

Homogenization is a fairly new, yet deep field of mathematics which is used as a powerful tool for analysis of applied problems which involve multiple scales. Generally, homogenization is utilized as a modeling procedure to describe processes in complex structures. Applications of Homogenization Theory to the Study of Mineralized Tissue functions as an introduction to the theory of homogenization. At the same time, the book explains how to apply the theory to various application problems in biology, physics and engineering. The authors are experts in the field and collaborated to create this book which is a useful research monograph for applied mathematicians, engineers and geophysicists. As for students and instructors, this book is a well-rounded and comprehensive text on the topic of homogenization for graduate level courses or special mathematics classes.Features: Covers applications in both geophysics and biology. Includes recent results not found in classical books on the topic Focuses on evolutionary kinds of problems; there is little overlap with books dealing with variational methods and T-convergence Includes new results where the G-limits have different structures from the initial operators

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.

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.