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Über dieses Buch

This book offers an essential introduction to the linear and non-linear behavior of solid materials, and to the concepts of deformation, displacement and stress, within the context of continuum mechanics and thermodynamics. To illustrate the fundamental principles, the book starts with an overview of solid mechanics, experimental methods, classes of material behaviors, and the thermodynamic modeling framework. It then explores linear elastic behavior, thermoelasticity, plasticity, viscoplasticity, fracture mechanics and damage behavior. The last part of the book is devoted to conventional and magnetic shape memory alloys, which may be used as actuators or sensors in adaptive structures. Given its range of coverage, the book will be especially valuable for students of engineering courses in Mechanics. Further, it includes a wealth of examples and exercises, making it accessible to the widest possible audience.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction: Elementary Concepts

Abstract
In reference to its desired use, the materials’ properties are described. A particular attention is paid to the description of experimental methods for the material characterization. A short list of possible behavior models is given.
Christian Lexcellent

Chapter 2. Thermodynamics Framework for Modeling Solid Materials

Abstract
This chapter is aimed at defining a constitutive framework for modeling solid materials. The purpose of continuum mechanic of deformable bodies is to deliver databases of solid behavior investigation. At first, the concepts of « vectorial displacement » strain and stress are introduced. In the framework of thermodynamic of irreversible process, the modeling scheme is explicited.
Christian Lexcellent

Chapter 3. Linear Elastic Behavior, Thermoelasticity

Abstract
This chapter is devoted to linear elasticity and thermoelasticity in the «small strains» hypothesis. At first, the isotropic behavior is studied and the planar linear elasticity is introduced (Airy function). In the second part, the anisotropic elastic behavior is investigated for composite materials.
Christian Lexcellent

Chapter 4. Yield Elasticity Criteria

Abstract
The establishment of behavior laws requires the definition of an elasticity domain, at least in the stress space for which there is no plastic or viscoplastic flow. In a general case, this domain must be convex. One introduces the independence from the hydrostatic pressure (Von Mises or Tresca criterium). The asymmetry between tension and compression is integrated and also the material anisotropy.
Christian Lexcellent

Chapter 5. Multiaxial PlasticityMultiaxial plasticity

Abstract
The formulation of the elastic-plastic behavior of a deformable continuous medium is considered under the assumption of «small perturbations». As plasticity is defined as a «time-independent» behavior, the constitutive law is incremental. A distinction is made between materials with «work hardening» or without (perfect plasticity). A particular attention is paid to the normal strain rate vector of the elasticity domain. Proportional and non-proportional loadings are investigated via an exercise on thin tubes under tension-torsion.
Christian Lexcellent

Chapter 6. Viscoelasticity

Abstract
«Soft solids» such as polymers, organic matrix composites, and bitumen have dissipative phenomena associated with elasticity also known as «viscosity». The viscoelastic characteristics of a body are the dependence of its response on the strain rate and a long recovery time of the initial state after the removal of mechanical loading. Different models can be constructed from the rheological description: springs and dampers in series or in parallel.
Christian Lexcellent

Chapter 7. Viscoplasticity

Abstract
The viscoplasticity is defined as a «time-dependent» behavior. The creep mechanisms (and by duality relaxation) are the first manifestations of material viscoplasticity. The general form of the viscoplastic-unified constitutive model comes from Chaboche in 2008. A comparison between «plasticity» and «viscoplasticity» ended the chapter.
Christian Lexcellent

Chapter 8. The Shape-Memory Alloys

Abstract
One focuses on «shape memory alloys» (SMAs), where a phase transformation (martensite) can be induced by stress and (or) temperature variations. A process of martensite variants reorientation can also take place. The SMAs functional properties such as pseudoelasticity, one-way shape memory effect, recovery stress, double-shape memory effect (training) are described. In the framework of thermodynamics of irreversible process applied to the generalized standard materials, a macroscopic model with internal variables is built. At last, a design of SMAs elements is done.
Christian Lexcellent

Chapter 9. Behavior of Magnetic Shape Memory Alloys

Abstract
The main advantage of magnetic shape memory alloys (MSMAs) over conventional shape memory alloys (SMAs) lies in the possibility for their actuation not only by stress or temperature but also by a magnetic field. This chapter is mainly devoted to the modeling of the thermo-magneto-mechanical behavior of single crystals under compressive loading (considering their fragility) and also under a magnetic field.
Christian Lexcellent

Chapter 10. Mechanical Elements ofFracture Fracture and DamageDamage

Abstract
The purpose of the fracture mechanics is to study and predict the initiation and propagation of macroscopic cracks in solids. The damage manifests itself by micro-cracks which have surface discontinuities and cavities such as volume is continuities. Apparently, between damage and fracture, it is a question of scale! The « linear fracture mechanic » assumption, that is to say brittle fracture, is considered. For the resolution of damage, a so-called internal variable « mechanical damage variable » is introduced.
Christian Lexcellent

Backmatter

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