Foundations of Shape-Memory Materials and Structures
Modeling and Numerics
2016, 350 p.
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Presents the fundamentals of crystalline shape memory materials and structures
Focuses on models for structural analysis and their numerical realization
Self-contained presentation is useful as an introduction to newcomers to the field
Includes many numerical examples that demonstrate the application of the methodologies
This book presents the fundamentals of crystalline shape memory materials and structures made thereof, focusing attention on models useful from the viewpoint of structural analysis and their numerical realization. The book is a self-contained presentation of parts of this intriguing subject and is usful as an introduction to newcomers to the field. It is split in four parts. The first part describes the basic concepts of continuum mechanics and thermodynamics as well as the mathematical notions and computational techniques which are applied in the sequel. Part two is concerned with the mechanical behavior of structural elements within the range of elasticity. Herein the finite element method is presented in detail for structural boundary value problems and its approximation properties are illustrated. After these preliminaries, the shape-memory materials are considered and various theoretical models are developed that take in account the characteristic pseudoelastic hysteretic loops. Part four presents the behavior of various structures (trusses, rods, beams, disks, plates) made of shape-memory materials. The book deals both with the modeling of continuum and structural mechanics problems and the aspects of their computer implementation, and includes many numerical examples that demonstrate the application of the methodologies described. It introduces modern modeling techniques and shows how these techniques can be implemented in computational mechanics of real-world problems. Foundations of Shape-Memory Materials and Structures: Modeling and numerics will be of interest to postgraduate and graduate students of civil, mechanical and materials engineering as well as research engineers and scientists working in this fascinating field.
Part I Fundamental concepts: Introduction.- Elements of continuum mechanics and thermodynamics.- Elements of homogenization theory.- Variational inequalities and complementarity problems.- Finite element discretization.- Solution methods for systems of equations and inequalities.- Part II Elastic structures: Elastic trusses.- Elastic rods.- Elastic beams.- Elastic disks.- Elastic plates.- Part III Shape-memory materials: Continuum theory of crystalline solids.- Martensitic phase transformation.- Analysis of martensitic microstructures.- The shape-memory effect.- One-dimensional model for two-phase material.- One-dimensional model for three-phase material.- The double-well problem of martensitic transformation.- The multi-well problem of martensitic transformation.- Part IV Shape-memory structures: Shape-memory trusses.- Shape-memory rods.- Shape-memory beams.- Shape-memory disks.- Shape-memory plate.