Lecture Notes on Composite Materials

by De Borst, Rene; Sadowski, Tomasz

• ISBN13: 9781402087714
• ISBN10: 1402087713
• Format: Hardcover
• Copyright: 2009-01-03
• Publisher: Springer Verlag

Summary

This book presents the latest achievements in the field of composite materials modelling presented by the following authors: (1) Prof. H. Altenbach (Germany), (2) Prof. R. de Borst (The Netherlands), (3) prof. E. Craciun (Romania), (4) Prof. R. Pyrz (Denmark), (5) 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.

Table of Contents

Holm AltenbachAnalysis of Homogeneous and Non-homogeneous Plates1 Classification of Structural Models1.1 Introductional Remarks1.2 Two-dimensional Structures'”Definition, Applications, SomeBasic References1.3 Formulation Principles, Historical Remarks2 Classical Plate Theories2.1 Small Deflections2.2 Large Deflections2.3 Kirchhoff Plate2.4 Mindlin Plate2.5 Von Kármán Plate3 Laminates and Sandwiches4 Direct Approach Based Plate Theory4.1 Motivation4.2 Direct Approach for Plates and Shells4.3 Tensors and Their Symmetry Groups5 Final RemarksReferencesRené de BorstNumerical methods for the modelling of debonding in composites1 Introduction2 Levels of observation3 Three-dimensional framework4 Zero-thickness interface elements5 Solid-like shell formulation6 Meshfree methods7 The partition-of-unity concept8 Delamination in a solid-like shell element9 Discontinuous Galerkin methodsReferencesRyszard PyrzMicromechanics of Composites '”Overall Elastic Properties1 Introduction2 Representative Volume Element3 The Eshelby Equivalent Inclusion Method3.1 Average strain and stress theorems3.2 Relation between averages3.3 The Eshelby solution3.4 Equivalent inclusion method4 The Mori-Tanaka TheoryReferencesTomasz SadowskiNon-symmetric thermal shock in ceramic matrix composite (CMC) materials1. Introduction to ceramic and metal matrix composites2. Thermomechanical properties of CMC's and MMC's2.1 Two-phase CMC with different elastic components2.2 Two-phase CMC's with plastic inclusions and MMC's with elastic inclusions2.2.1 Thermomechanical properties2.2.2 Modelling of the whole stress-strain curve fro MMC2.2.3 Constitutive equations for FGM's in 3-D formulation by self-consistent approach2.2.3 Constitutive equations for FGM's in 3-D formulation by self-consistent approach3. Temperature field under transient thermal loading3.1 FEA approach for heat transfer equation (26)3.2 FD approach for heat transfer equation (26)4. Transient thermal stress state5. Thermal residual stress due to technological cooling process5.1 Analytical models5.2 Numerical models6. Basic fracture mechanics concepts in functionally graded materials (FGM)6.1 Rule of mixture to estimate the fracture toughness in FGMs6.2 Crack-bridging approach to assess the fracture toughness7. Non-symmetric thermal shock in monolithic ceramic and FGM strip7.1 Transient temperature distribution during thermal shock7.2 Thermal and residual stresses7.3 Thermal stress intensity factor7.4 Numerical example8. Two-dimensional thermal shock problem in layered circular plates8.1 Samples preparation and experimental procedure8.2 Theoretical formulation8.2.1 Thermal and mechanical properties of monolithic and FGM material8.2.2 Heat conduction problem in FGM circular plate specimens8.2.3 Determination of the thermal stress8.3 Numerical example9. Concluding remarks10. ReferencesRené de BorstJ. RethoreM.-A. AbellanA precis of two-scale approaches for fracture in porous media1. Introduction2. Balance equations3. Constitutive equations4. Weak form of the balance equations5. Micro-macro coupling6. Discontinuities in a two-phase medium7. Examples: stationary and propagating cracks8. Concluding remarksReferencesEduard Marius CraciunInitial deformations on behaviour of elastic composites1 Influence of homogeneous initial deformations on behaviour of elastic composites2 Representation of the incremental fields3 The opening, sliding and tearing modes4 Asymptotic behavior of the incremental fields4.1 The first mode4.2 The second mode4.3 The third mode5 Griffith's criterion and crack propagation5.1 The first opening modeAcknowledgmentsReferencesEduard Marius CraciunEnergetical crack propagation criteria in pre-stressed elastic composites1. Interaction of two unequal cracks in a pre-stressed fiber reinforced composite1.1 Unequal cracks in a pre-stressed fiber reinforced composite. The first fracture mode1.2 Asymptotic expressions. Griffith - Irwin's method1.3 The study of cracks interaction1.4 Pr