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2012 | Buch

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Continuum Damage Mechanics

A Continuum Mechanics Approach to the Analysis of Damage and Fracture

verfasst von: Sumio Murakami

Verlag: Springer Netherlands

Buchreihe : Solid Mechanics and Its Applications

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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Über dieses Buch

Recent developments in engineering and technology have brought about serious and enlarged demands for reliability, safety and economy in wide range of fields such as aeronautics, nuclear engineering, civil and structural engineering, automotive and production industry. This, in turn, has caused more interest in continuum damage mechanics and its engineering applications.

This book aims to give a concise overview of the current state of damage mechanics, and then to show the fascinating possibility of this promising branch of mechanics, and to provide researchers, engineers and graduate students with an intelligible and self-contained textbook.

The book consists of two parts and an appendix. Part I is concerned with the foundation of continuum damage mechanics. Basic concepts of material damage and the mechanical representation of damage state of various kinds are described in Chapters 1 and 2. In Chapters 3-5, irreversible thermodynamics, thermodynamic constitutive theory and its application to the modeling of the constitutive and the evolution equations of damaged materials are descried as a systematic basis for the subsequent development throughout the book.

Part II describes the application of the fundamental theories developed in Part I to typical damage and fracture problems encountered in various fields of the current engineering. Important engineering aspects of elastic-plastic or ductile damage, their damage mechanics modeling and their further refinement are first discussed in Chapter 6. Chapters 7 and 8 are concerned with the modeling of fatigue, creep, creep-fatigue and their engineering application. Damage mechanics modeling of complicated crack closure behavior in elastic-brittle and composite materials are discussed in Chapters 9 and 10. In Chapter 11, applicability of the local approach to fracture by means of damage mechanics and finite element method, and the ensuing mathematical and numerical problems are briefly discussed.

A proper understanding of the subject matter requires knowledge of tensor algebra and tensor calculus. At the end of this book, therefore, the foundations of tensor analysis are presented in the Appendix, especially for readers with insufficient mathematical background, but with keen interest in this exciting field of mechanics.

Inhaltsverzeichnis

Frontmatter

Foundations of Continuum Damage Mechanics

Frontmatter

Chapter 1. Material Damage and Continuum Damage Mechanics

Abstract

Continuum damage mechanics is a mechanical theory for analyzing damage and fracture processes in materials from a continuum mechanics point of view. The present chapter starts with the notion of material damage and that of continuum damage mechanics. Section 1.1 is concerned with the definition of damage, its mechanical aspects observed in different scales, the physical mechanisms of damage development, and its examples encountered in the engineering problems of strength and fracture. In Section 1.2, furthermore, fundamental notion of continuum damage mechanics and of the mechanical procedures of its formulation and applications will be discussed.

Sumio Murakami

Chapter 2. Mechanical Representation of Damage and Damage Variables

Abstract

The procedure of the continuum damage mechanics is to represent first the damage state of a material in terms of properly defined damage variables, and then to describe the mechanical behavior of the damaged material and the further development of the damage by the use of these damage variables. In Section 2.1, methods of the mechanical modeling of material damage are described in the case of uniaxial state of stress. Then Section 2.2 is concerned with extensive discussion of the three-dimensional modeling of material damage and the resulting damage variables, because this is one of the most important problems to secure the reliability of the continuum damage mechanics. The mechanical behavior of a damaged material is usually described by using the notion of the effective stress, together with the hypothesis of mechanical equivalence between the damaged and the undamaged material.

Sumio Murakami

Chapter 3. Thermodynamics of Damaged Material

Abstract

In the preceding chapter, we discussed the mechanical modeling of the damaged state of materials by means of internal variables, and called them damage variables. The present chapter is concerned with the thermodynamic constitutive theory with internal variables, which furnishes a consistent basis to formulate the mechanical behavior of damaged materials. In Section 3.1, the fundamental principles and the basic laws of the non-equilibrium continuum thermodynamics are presented as the foundations for the succeeding discussions. In Section 3.2, the notion and the procedure of the thermodynamic constitutive theory with internal variables will be described in detail. It is shown that the inelastic constitutive equations and the evolution equations for internal variables are formulated as a set of generalized normality rule defined by a dissipation potential function and a common multiplier.

Sumio Murakami

Chapter 4. Inelastic Constitutive Equation and Damage Evolution Equation of Material with Isotropic Damage

Abstract

The thermodynamic constitutive theory described in the preceding chapter is applied to inelastic materials with isotropic damage. In Section 4.1, one-dimensional elastic-plastic and elastic-viscoplastic constitutive equations of damaged materials will be described as the basis for the succeeding sections. The application of the constitutive theory of Chapter 3 to the three-dimensional case will be discussed in Section 4.2. The strain energy release rate due to damage development and the stress criterion for elastic-plastic damage growth will be considered in Section 4.3, while Section 4.4 is concerned with the inelastic damage theories based on the hypothesis of mechanical equivalence.

Sumio Murakami

Chapter 5. Inelastic Constitutive Equation and Damage Evolution Equation of Material with Anisotropic Damage

Abstract

The development of microvoids in materials usually depends on the direction of the applied stress, and hence the material damage is essentially anisotropic. In this chapter we consider the damage mechanics theories of the constitutive and the evolution equations of materials with anisotropic damage.

Sumio Murakami

Application of Continuum Damage Mechanics

Frontmatter

Chapter 6. Elastic-Plastic Damage

Abstract

The preceding chapters were concerned with the notion and the fundamental theories of continuum damage mechanics (CDM). Hereafter we will discuss the application of CDM to damage and fracture phenomena encountered in wide range of engineering problems. The present chapter starts with the modeling of elastic-plastic damage and its application. In Section 6.1, we summarized the constitutive and the evolution equations of elastic-plastic isotropic damage of materials developed in Chapter 4, and discuss their application to the problems of ductile damage, brittle damage and quasi-brittle damage. Section 6.2, on the other hand, is concerned with the detailed discussion of ductile damage process, i.e., the discussion of physical and mechanical aspects of ductile damage, their mechanical modeling and its analysis.

Sumio Murakami

Chapter 7. Fatigue Damage

Abstract

Fatigue damage in polycrystalline metals is caused by the microcrack formation in accumulated slip bands due to repeated loading. These slip bands develop in favorably oriented grains located on the material surface as a result of irreversible dislocation glide process.

Sumio Murakami

Chapter 8. Creep Damage and Creep-Fatigue Damage

Abstract

A time-dependent deformation occurring in a material subject to load for a prolonged period of time is called creep. In a narrower sense, creep means a time-dependent deformation caused by a constant stress or a constant load. Materials undergoing creep for long time are often accompanied by time dependent internal deterioration. This deterioration is called creep damage. When metals and alloys are subject to a variable load at elevated temperature, the materials are deteriorated by combined damage of creep and fatigue. This damage is called creep-fatigue damage. Creep damage and creep-fatigue damage, therefore, give essential failure modes of high temperature components.

Sumio Murakami

Chapter 9. Elastic-Brittle Damage

Abstract

Besides ductile materials considered hitherto, a variety of brittle materials, like concrete, rocks and ceramics, are widely employed in engineering practice. Their mechanical behavior can not be described by the elastic-plastic damage theory or by the viscoplastic damage theory discussed already. The present chapter is concerned with the damage and the deformation behavior of elastic-brittle materials, and the related continuum damage mechanics theory to describe them. In Section 9.1, to begin with, the microscopic mechanisms of damage and the ensuing mechanical behavior of microcracks in concrete will be discussed. Application of the simplest theory of isotropic damage to the damage process of concrete with unilateral crack effect is descried in Section 9.2.

Sumio Murakami

Chapter 10. Continuum Damage Mechanics of Composite Materials

Abstract

Damage and fracture of composite materials occur in various level of scale, and are much more complicated than those of uniform materials (Sadowski 2005, 2006). Continuum damage mechanics, however, furnishes effective means of damage and fracture analysis also for composite materials. The present chapter is concerned with the application of continuum damage mechanics theory to the damage analysis of composites mainly of polymer-, metal-, and ceramic-matrix. In Section 10.1, to begin with, we discuss the elastic-plastic damage analysis of fiber-reinforced plastic laminates by using three scalar damage variables. In Section 10.2, on the other hand, the elastic brittle damage theory of ceramics matrix composites is elucidated by the use of a fourth-order damage variable and by taking account of unilateral effects of cracks. Finally, a local damage theory of metal matrix composite will be described in Section 10.3.

Sumio Murakami

Chapter 11. Local Approach to Damage and Fracture Analysis

Abstract

Continuum damage mechanics facilitates not only the modeling of crack initiation due to damage development but also the analysis of the damage and fracture process up to the final fracture. The local approach to fracture by means of continuum damage mechanics and finite element method has developed as a systematic engineering method to analyze the whole process of damage and fracture. At the end of this book, we consider the notion, applicability and the fundamental issues of this approach. Section 11.1 is concerned with its procedure, applicability and the related numerical problems. In Section 11.2, the material instability and the resulting loss of uniqueness will be discussed as the major causes of the mesh-sensitivity in time-independent (rate-independent) strain-softening materials.

Sumio Murakami

Chapter 12. Foundations of Tensor Analysis – Tensor Algebra and Tensor Calculus

Abstract

Continuum mechanics has been formulated mainly in the mathematical framework of tensor algebra and tensor calculus. The accurate understanding and the proper application of continuum damage mechanics, therefore, necessitate sound foundation of this mathematical subject. The present chapter is the presentation of the foundation of tensor analysis in some detail for the convenience of readers not familiar enough with this important subject. The present chapter is the presentation of the foundation of tensor analysis in some detail for the convenience of readers not familiar enough with this important subject.

Sumio Murakami

Backmatter

Titel: Continuum Damage Mechanics
verfasst von: Sumio Murakami
Verlag: Springer Netherlands
Electronic ISBN: 978-94-007-2666-6
Print ISBN: 978-94-007-2665-9
DOI: https://doi.org/10.1007/978-94-007-2666-6

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