Synopses & Reviews
This book presents the latest achievements in the field of composite materials modelling presented by the following authors: - Prof. H. Altenbach (Germany) - Prof. R. de Borst (The Netherlands) - Prof. E. Craciun (Romania) - Prof. R. Pyrz (Denmark) - Prof. T.Sadowski (Poland) The text gives a modern, up-to-date account of recent developments in the modelling of composite materials. Multiscale concepts, which are the new paradigm in (computational) mechanics, are at the heart of this text, and are treated in detail in the first three chapters of the book. Other relevant developments are covered in the later chapters of the book, beginning with the most relevant issue of coupling stress analysis and diffusion phenomena that arise from hygral and/or thermal loading, which are of crucial importance of the short and long-term resistance of composite materials. The volume facilitates understanding of the basic principles of damage growth and fracture processes in various composite materials, including ceramics, polymers, metal-matrix composites and porous materials.
This text explores new developments in the modeling of composite materials. It fully covers multiscale concepts and other developments such as coupling stress analysis and diffusion phenomena that arise from hygral and/or thermal loading.
Table of Contents
Holm Altenbach Analysis of Homogeneous and Non-homogeneous Plates 1 Classification of Structural Models 1.1 Introductional Remarks 1.2 Two-dimensional Structures--Definition, Applications, Some Basic References 1.3 Formulation Principles, Historical Remarks 2 Classical Plate Theories 2.1 Small Deflections 2.2 Large Deflections 2.3 Kirchhoff Plate 2.4 Mindlin Plate 2.5 Von Kármán Plate 3 Laminates and Sandwiches 4 Direct Approach Based Plate Theory 4.1 Motivation 4.2 Direct Approach for Plates and Shells 4.3 Tensors and Their Symmetry Groups 5 Final Remarks References René de Borst Numerical methods for the modelling of debonding in composites 1 Introduction 2 Levels of observation 3 Three-dimensional framework 4 Zero-thickness interface elements 5 Solid-like shell formulation 6 Meshfree methods 7 The partition-of-unity concept 8 Delamination in a solid-like shell element 9 Discontinuous Galerkin methods References Ryszard Pyrz Micromechanics of Composites --Overall Elastic Properties 1 Introduction 2 Representative Volume Element 3 The Eshelby Equivalent Inclusion Method 3.1 Average strain and stress theorems 3.2 Relation between averages 3.3 The Eshelby solution 3.4 Equivalent inclusion method 4 The Mori-Tanaka Theory References Tomasz Sadowski Non-symmetric thermal shock in ceramic matrix composite (CMC) materials 1. Introduction to ceramic and metal matrix composites 2. Thermomechanical properties of CMC's and MMC's 2.1 Two-phase CMC with different elastic components 2.2 Two-phase CMC's with plastic inclusions and MMC's with elastic inclusions 2.2.1 Thermomechanical properties 2.2.2 Modelling of the whole stress-strain curve fro MMC 2.2.3 Constitutive equations for FGM's in 3-D formulation by self-consistent approach 2.2.3 Constitutive equations for FGM's in 3-D formulation by self-consistent approach 3. Temperature field under transient thermal loading 3.1 FEA approach for heat transfer equation (26) 3.2 FD approach for heat transfer equation (26) 4. Transient thermal stress state 5. Thermal residual stress due to technological cooling process 5.1 Analytical models 5.2 Numerical models 6. Basic fracture mechanics concepts in functionally graded materials (FGM) 6.1 Rule of mixture to estimate the fracture toughness in FGMs 6.2 Crack-bridging approach to assess the fracture toughness 7. Non-symmetric thermal shock in monolithic ceramic and FGM strip 7.1 Transient temperature distribution during thermal shock 7.2 Thermal and residual stresses 7.3 Thermal stress intensity factor 7.4 Numerical example 8. Two-dimensional thermal shock problem in layered circular plates 8.1 Samples preparation and experimental procedure 8.2 Theoretical formulation 8.2.1 Thermal and mechanical properties of monolithic and FGM material 8.2.2 Heat conduction problem in FGM circular plate specimens 8.2.3 Determination of the thermal stress 8.3 Numerical example 9. Concluding remarks 10. References René de Borst J. Rethore M.-A. Abellan A precis of two-scale approaches for fracture in porous media 1. Introduction 2. Balance equations 3. Constitutive equations 4. Weak form of the balance equations 5. Micro-macro coupling 6. Discontinuities in a two-phase medium 7. Examples: stationary and propagating cracks 8. Concluding remarks References Eduard Marius Craciun Initial deformations on behaviour of elastic composites 1 Influence of homogeneous initial deformations on behaviour of elastic composites 2 Representation of the incremental fields 3 The opening, sliding and tearing modes 4 Asymptotic behavior of the incremental fields 4.1 The first mode 4.2 The second mode 4.3 The third mode 5 Griffith's criterion and crack propagation 5.1 The first opening mode Acknowledgments References Eduard Marius Craciun Energetical crack propagation criteria in pre-stressed elastic composites 1. Interaction of two unequal cracks in a pre-stressed fiber reinforced composite 1.1 Unequal cracks in a pre-stressed fiber reinforced composite. The first fracture mode 1.2 Asymptotic expressions. Griffith - Irwin's method 1.3 The study of cracks interaction 1.4 Pre-stressed elastic composite with two unequal crack. Second fracture mode 2. Sih's generalized fracture criterion for pre-stressed orthotropic and isotropic materiale 2.1 Sih's generalized fracture criterion for pre-stressed orthotropic 2.2 Crack propagation for orthotropic materials 2.3 Sih's material parameter Sc versus Griffith's specific surface energy 2.4 Pre-stressed isotropic material 2.5 Sih's energetical criterion in the second fracture mode 3. Inclined crack in pre-stressed elastic composite 3.1 Guz's representation theorem for incremental fields 3.2 Sih's energetically criterion in a mixed fracture mode 3.3 Crack propagation for unpre-stressed orthotropic materials 3.4 Resonance phenomenon for an inclined crack 3.5 Remarks Acknowledgments References