Composite Mechanics (Advanced Structured Materials, 184)

✍ Scribed by Andreas Öchsner

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 214
• Category: Library

✦ Synopsis

This book in the advanced structured materials series provides first an introduction to the mircomechanics of fiber-reinforced laminae, which deals with the prediction of the macroscopic mechanical lamina properties based on the mechanical properties of the constituents, i.e., fibers and matrix. Composite materials, especially fiber-reinforced composites, are gaining increasing importance since they can overcome the limits of many structures based on classical metals. Particularly, the combination of a matrix with fibers provides far better properties than the constituents alone. Despite their importance, many engineering degree programs do not treat the mechanical behavior of this class of advanced structured materials in detail, at least on the bachelor’s degree level. Thus, some engineers are not able to thoroughly apply and introduce these modern engineering materials in their design process.

The second part of this book provides a systematic and thorough introduction to the classical laminate theory based on the theory for plane elasticity elements and classical (shear-rigid) plate elements. The focus is on unidirectional lamina which can be described based on orthotropic constitutive equations and their composition to layered laminates. In addition to the elastic behavior, failure is investigated based on the maximum stress, maximum strain, Tsai-Hill, and the Tsai-Wu criteria. The introduced classical laminate theory provides a simplified stress analysis, and a subsequent failure analysis, without the solution of the system of coupled differential equations for the unknown displacements in the three coordinate directions.

The book concludes with a short introduction to a calculation program, the so-called Composite Laminate Analysis Tool (CLAT), which allows the application of the classical laminate based on a sophisticated Python script.

✦ Table of Contents

Preface
Contents
Symbols and Abbreviations
Latin Symbols (Capital Letters)
Latin Symbols (Small Letters)
Greek Symbols (Small Letters)
Mathematical Symbols
Indices, Superscripted
Indices, Subscripted
Abbreviations
1 Introduction
1.1 Composite Materials
1.2 Continuum Mechanical Modeling
References
2 Micromechanics
2.1 Reference Numbers to Characterize Composition
2.2 Prediction of Elastic Properties of Laminae
2.2.1 Mechanics of Materials Approach
2.2.2 Elasticity Solutions with Contiguity after Tsai
2.2.3 Halpin–Tsai Relationships
2.3 Comparison with Experimental Results
2.3.1 Extraction of Experimental Values
2.3.2 Comparison Between Theoretical Predictions and Experimental Results
2.3.3 Optimized Representation of Theoretical Predictions
References
3 Macromechanics of a Lamina
3.1 Introduction
3.2 Kinematics
3.2.1 Plane Elasticity Element
3.2.2 Classical Plate Element
3.2.3 Combined Plane Elasticity and Classical Plate Element
3.3 Constitutive Equation
3.3.1 Isotropic Material: Plane Elasticity Element
3.3.2 Isotropic Material: Classical Plate Element
3.3.3 Isotropic Material: Combined Plane Elasticity and Classical Plate Element
3.3.4 Orthotropic Material: Combined Plane Elasticity and Classical Plate Element
3.4 Equilibrium
3.4.1 Plane Elasticity Element
3.4.2 Classical Plate Element
3.4.3 Combined Plane Elasticity and Classical Plate Element
3.5 Partial Differential Equations
3.5.1 Plane Elasticity Element
3.5.2 Classical Plate Element
3.5.3 Combined Plane Elasticity and Classical Plate Element
3.6 Failure Criteria
3.6.1 Maximum Stress Criterion
3.6.2 Maximum Strain Criterion
3.6.3 Tsai–Hill Criterion
3.6.4 Tsai–Wu Criterion
References
4 Macromechanics of a Laminate
4.1 Introduction
4.2 Generalized Stress–Strain Relationship
4.3 Special Cases of Laminates
4.4 Failure Analysis of Laminates
References
5 Example Problems
5.1 Introduction
5.2 Problem 1: Stresses and Strains in a Symmetric Laminate
5.3 Problem 2: Stresses and Strains in an Asymmetric Laminate
5.4 Problem 3: Failure Criteria
5.5 Problem 4: Ply-By-Ply Failure Loads
5.6 Problem 5: Pole Diagrams of Elastic Properties for Unidirectional Laminae
5.7 Problem 6: Failure Envelopes for Unidirectional Laminae
References
6 Supplementary Problems
6.1 Problems
6.1.1 Supplementary Problem 1: Stresses and Strains in a Symmetric Laminate
6.1.2 Supplementary Problem 2: Stresses and Strains in an Asymmetric Laminate
6.1.3 Supplementary Problem 3: Failure Criteria
6.1.4 Supplementary Problem 4: Ply-by-Ply Failure Loads
6.1.5 Supplementary Problem 5: Pole Diagrams of Elastic Properties for Unidirectional Laminae
6.1.6 Supplementary Problem 6: Failure Envelopes for Unidirectional Laminae
6.2 Short Solutions
6.2.1 Supplementary Problem 1: Stresses and Strains in a Symmetric Laminate
6.2.2 Supplementary Problem 2: Stresses and Strains in an Asymmetric Laminate
6.2.3 Supplementary Problem 3: Failure Criteria
6.2.4 Supplementary Problem 4: Ply-by-Ply Failure Loads
6.2.5 Supplementary Problem 5: Pole Diagrams of Elastic Properties for Unidirectional Laminae
6.2.6 Supplementary Problem 6: Failure Envelopes for Unidirectional Laminae
Reference
7 Composite Laminate Analysis Tool—CLAT
7.1 Introduction
7.2 Analysis Options
Reference
Index