Lim Auxetic Materials and Structures

2015
ISBN: 978-981-287-275-3
Verlag: Springer Singapore
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 591 Seiten, eBook

Reihe: Engineering Materials

This book lays down the foundation on the mechanics and design of auxetic solids and structures, solids that possess negative Poisson's ratio. It will benefit two groups of readers: (a) industry practitioners, such as product and structural designers, who need to control mechanical stress distributions using auxetic materials, and (b) academic researchers and students who intend to produce unique mechanical and other physical properties of structures using auxetic materials.

Dr. T.C. Lim earned his PhD in the area of material mechanics in 2001, and thereafter pioneered auxetic solids research in Asia. In addition to being Asia's leading researcher in the area of auxetic solids, Dr. Lim is also a pioneer and one of the world leaders in the area of semi-auxetics. Dr. Lim has been serving as a scientific committee member in auxetic conferences and workshops since 2009. In addition, he has been serving as a journal reviewer for auxetic-related papers since 2004.

Zielgruppe

Research

Autoren/Hrsg.

Lim, Teik-Cheng

Inhaltsverzeichnis

1;Preface;7
2;Contents;8
3;About the Author;14
4;1 Introduction;15
4.1;Abstract;15
4.2;1.1 Definition of Poisson's Ratio;15
4.3;1.2 History of Poisson's Ratio;16
4.4;1.3 Definition of Auxetic Materials;17
4.5;1.4 History of Negative Poisson's Ratio;19
4.6;1.5 Naturally Occurring Auxetic Materials;20
4.7;1.6 Auxetic Foams;21
4.8;1.7 Auxetic Yarns and Textiles;46
4.9;1.8 Auxetic Liquid Crystalline Polymers;51
4.10;1.9 Other Topics;52
4.11;References;54
5;2 Micromechanical Models for Auxetic Materials;58
5.1;Abstract;58
5.2;2.1 Introduction;58
5.3;2.2 Re-entrant Open-Cell Microstructure;58
5.4;2.3 Nodule Fibril Microstructure---Hinging, Flexure and Stretching Modes of Fibrils;61
5.5;2.4 Generalized 3D Tethered-Nodule Model;71
5.6;2.5 Rotating Squares and Rectangles Models;75
5.7;2.6 Rotating Triangles Models;85
5.8;2.7 Tetrahedral Framework Structure;89
5.9;2.8 Hard Cyclic Hexamers Model;92
5.10;2.9 Missing Rib Models;94
5.11;2.10 Chiral and Anti-chiral Lattice Models;101
5.12;2.11 Interlocking Hexagons Model;110
5.13;2.12 Egg Rack Structure;116
5.14;References;116
6;3 Elasticity of Auxetic Solids;119
6.1;Abstract;119
6.2;3.1 Constitutive Relationships;119
6.3;3.2 Bounds in Poisson's Ratio for Isotropic Solids;125
6.4;3.3 Constitutive Relationships for Isotropic Solids;129
6.5;3.4 Moduli Relations;132
6.6;3.5 Density-Modulus Relation in Auxetic Foams;134
6.7;3.6 Large Elastic Deformation of Auxetic Solids;137
6.8;3.7 Anisotropic Auxetic Solids;140
6.9;3.8 Elastoplasticity of Auxetic Solids;154
6.10;3.9 Viscoelasticity of Auxetic Solids;156
6.11;References;156
7;4 Stress Concentration, Fracture and Damage in Auxetic Materials;158
7.1;Abstract;158
7.2;4.1 Introduction;158
7.3;4.2 Stress Concentration in Auxetic Solids with Cavities;159
7.4;4.3 Stress Concentration in Auxetic Solids with Rigid Inclusions;160
7.5;4.4 Stress Concentration in Auxetic Plates;162
7.6;4.5 Stress Concentration in Auxetic Rods;163
7.7;4.6 Fracture Characteristics of Auxetic Solids;167
7.8;4.7 Stress and Displacement Fields Around Notches in Auxetic Solids;169
7.9;4.8 Mode I Dimensionless Displacement Fields;172
7.10;4.9 Mode II Dimensionless Displacement Fields;173
7.11;4.10 Mode III Dimensionless Displacement Field;176
7.12;4.11 Damage in Auxetic Solids;177
7.13;4.12 Fatigue in Auxetic Materials;178
7.14;References;179
8;5 Contact and Indentation Mechanics of Auxetic Materials;181
8.1;Abstract;181
8.2;5.1 Introduction;181
8.3;5.2 Line Contact on Auxetic Materials;181
8.4;5.3 Point Contact on Auxetic Materials;190
8.5;5.4 Effect of Indenter Shape on Auxetic Materials;195
8.6;5.5 Contact Between Auxetic Spheres;201
8.7;5.6 Contact Deformation in Auxetic Composites;205
8.8;5.7 Indentation of Auxetic Foams;207
8.9;References;209
9;6 Auxetic Beams;210
9.1;Abstract;210
9.2;6.1 Stretching of Auxetic Bars;210
9.3;6.2 Cantilever Bending of Auxetic Beams with Circular Cross Sections;212
9.4;6.3 Cantilever Bending of Auxetic Beams with Rectangular Cross Sections;214
9.5;6.4 Cantilever Bending of Auxetic Beams with Narrow Rectangular Cross Sections;215
9.6;6.5 Cantilever Bending of Auxetic Beams with Wide Rectangular Cross Sections;215
9.7;6.6 Cantilever Bending of Auxetic Beams with Regular Rectangular Cross Sections;216
9.8;6.7 Uniformly Loaded Auxetic Beams with Narrow Rectangular Cross Sections;219
9.9;6.8 Torsion of Auxetic Rods;220
9.10;6.9 Remarks on Auxetic Rods with Circular Cross Sections;222
9.11;References;224
10;7 Auxetic Solids in Polar and Spherical Coordinates;225
10.1;Abstract;225
10.2;7.1 Introduction;225
10.3;7.2 Thick-Walled Auxetic Cylinders;226
10.4;7.3 Rotating Thin Auxetic Disks;229
10.5;7.4 Rotating Thick Auxetic Disks;232
10.6;7.5 Thick-Walled Auxetic Spheres;234
10.7;References;238
11;8 Thin Auxetic Plates and Shells;239
11.1;Abstract;239
11.2;8.1 Introduction;240
11.3;8.2 Flexural Rigidity of Auxetic Plates;240
11.4;8.3 Circular Auxetic Plates;249
11.5;8.4 Rectangular Auxetic Plates;267
11.6;8.5 Auxetic Plates on Auxetic Foundation;283
11.7;8.6 In-Plane Compression of Constrained Auxetic Plate;291
11.8;8.7 Spherical Auxetic Shells;293
11.9;A.0. Appendix A;298
11.10;A.0. Appendix B;299
11.11;References;299
12;9 Thermal Stresses in Auxetic Solids;301
12.1;Abstract;301
12.2;9.1 Introduction;301
12.3;9.2 General Thermoelasticity of Auxetic Solids;302
12.4;9.3 Thermoelasticity of 3D Auxetics with Complete Geometrical Constraints;306
12.5;9.4 Thermoelasticity of Plates with Temperature Variation Along Thickness;306
12.6;9.5 Thermoelasticity of Beams with Temperature Variation Along the Beam Thickness;308
12.7;9.6 Dimensionless Thermal Stresses for Auxetic Plates and Shells;310
12.8;9.7 Thermal Stresses for Auxetic Plates and Shells;316
12.9;9.8 Summary on Thermal Stresses in Auxetic Plates and Shells;324
12.10;9.9 Thermal Conductivity in Multi--re-entrant Honeycomb Structures;326
12.11;References;328
13;10 Elastic Stability of Auxetic Solids;329
13.1;Abstract;329
13.2;10.1 Introduction;329
13.3;10.2 Buckling of Auxetic Columns;330
13.4;10.3 Buckling of Rectangular Auxetic Plates;332
13.5;10.4 Buckling of Circular Auxetic Plates;336
13.6;10.5 Buckling of Cylindrical Auxetic Shells;340
13.7;10.6 Buckling of Spherical Auxetic Shells;344
13.8;10.7 Recent Advances on Instability in Relation to Auxetic Materials and Structures;346
13.9;References;352
14;11 Vibration of Auxetic Solids;353
14.1;Abstract;353
14.2;11.1 Introduction;353
14.3;11.2 Vibration of Circular Auxetic Plates;354
14.4;11.3 Vibration of Rectangular Auxetic Plates;358
14.5;11.4 Vibration of Cylindrical Auxetic Shells;366
14.6;11.5 Vibration of Spherical Auxetic Shells;369
14.7;11.6 Advanced Topics on Vibration and Acoustics of Auxetic Solids and Structures;370
14.8;References;372
15;12 Wave Propagation in Auxetic Solids;374
15.1;Abstract;374
15.2;12.1 Introduction;374
15.3;12.2 Longitudinal Waves in Prismatic Auxetic Bars;376
15.4;12.3 Plane Waves of Dilatation in Auxetic Solids;377
15.5;12.4 Plane Waves of Distortion in Auxetic Solids;378
15.6;12.5 Rayleigh Waves in Auxetic Solids;380
15.7;12.6 Non-dimensionalization of Wave Velocities;381
15.8;12.7 Advanced Topics on Wave Motion in Auxetic Solids;387
15.9;References;389
16;13 Wave Transmission and Reflection Involving Auxetic Solids;391
16.1;Abstract;391
16.2;13.1 Introduction;391
16.3;13.2 Analysis;393
16.4;13.3 Longitudinal Wave (1D Stress State or 3D Strain State);395
16.5;13.4 Longitudinal Wave (Width-Constrained Plates);396
16.6;13.5 Plane Waves of Dilatation (1D Strain State or 3D Stress State);396
16.7;13.6 Torsional Waves;397
16.8;13.7 Rayleigh Waves;398
16.9;13.8 Non-dimensionalization of Transmitted and Reflected Stresses;398
16.10;13.9 Dimensionless Transmitted Stress in Longitudinal Waves (1D Stress State);400
16.11;13.10 Dimensionless Transmitted Stress in Longitudinal Waves (Constrained-Width Plates);401
16.12;13.11 Dimensionless Transmitted Stress in Plane Waves of Dilatation;403
16.13;13.12 Dimensionless Transmitted Stress in Torsional Waves;405
16.14;13.13 Dimensionless Transmitted Stress in Rayleigh Waves;407
16.15;13.14 Summary on Stress Wave Transmission Involving Auxetic Solids;409
16.16;References;410
17;14 Longitudinal Waves in Auxetic Solids;411
17.1;Abstract;411
17.2;14.1 Introduction;411
17.3;14.2 Review of Elementary Analysis;413
17.4;14.3 Density Correction;414
17.5;14.4 Lateral Inertia;415
17.6;14.5 Density Correction and Lateral Inertia;417
17.7;14.6 Analogy with Plane Waves of Dilatation;422
17.8;14.7 Lateral Inertia in Auxetic Love Rods;425
17.9;14.8 Lateral Inertia and Density Correction in Auxetic Love Rods;428
17.10;References;431
18;15 Shear Deformation in Auxetic Solids;432
18.1;Abstract;432
18.2;15.1 Introduction;432
18.3;15.2 Laterally-Loaded Thick Auxetic Beams;433
18.4;15.3 Shear Correction Factors for Isotropic Plates Within 22121 2264 v 2264 0.5;441
18.5;15.4 Laterally-Loaded Thick Circular Auxetic Plates;445
18.6;15.5 Laterally-Loaded Thick Polygonal Auxetic Plates;449
18.7;15.6 Laterally-Loaded Thick Rectangular Auxetic Plates;452
18.8;15.7 Buckling of Thick Auxetic Columns;458
18.9;15.8 Buckling of Thick Auxetic Plates;464
18.10;15.9 Vibration of Thick Auxetic Plates;472
18.11;References;477
19;16 Simple Semi-auxetic Solids;479
19.1;Abstract;479
19.2;16.1 Introduction;479
19.3;16.2 Elastic Properties of a Directional Semi-auxetic Solid;480
19.4;16.3 Kinematical Studies on Rotation-Based Semi-auxetics;486
19.5;16.4 Analysis of Semi-auxetic Yarns;493
19.6;16.5 Processing of Semi-auxetic Yarns;502
19.7;16.6 Functionally-Graded Semi-auxetic Beams;507
19.8;16.7 Semi-auxetic Rods;512
19.9;16.8 Semi-auxetic Sandwich Plates;519
19.10;16.9 Mixed Auxeticity of Semi-auxetic Sandwich Structures;525
19.11;References;535
20;17 Semi-auxetic Laminates and Auxetic Composites;537
20.1;Abstract;537
20.2;17.1 Introduction;537
20.3;17.2 Semi-auxetic Unidirectional Fiber Composites;538
20.4;17.3 Out-of-Plane Modulus of Semi-auxetic Laminates;540
20.5;17.4 In-plane Modulus of Semi-auxetic Laminates;548
20.6;17.5 Further Counter-Intuitive Modulus from Semi-auxetic Laminates;554
20.7;17.6 Comparison Between In-Plane and Out-of-Plane Modulus of Semi-auxetic Laminates;561
20.8;17.7 Semi-auxetic and Alternating Positive and Negative Thermal Expansion Laminates;562
20.9;17.8 Auxetic Composites;573
20.10;References;583
21;Index;585

Introduction.- Micromechanical Models for Auxetic Materials.- Elasticity of Auxetic Solids.- Stress Concentration, Fracture and Damage in Auxetic Materials.- Contact and Indentation Mechanics of Auxetic Materials.- Auxetic Beams.- Auxetic Solids in Polar and Spherical Coordinates.- Thin Auxetic Plates and Shells.- Thermal Stresses in Auxetic Solids.- Elastic Stability of Auxetic Solids.- Vibration of Auxetic Solids.- Wave Propagation in Auxetic Solids.- Wave Transmission and Reflection involving Auxetic Solids.- Longitudinal Waves in Auxetic Solids.- Shear Deformation in Auxetic Solids.- Simple Semi-auxetic Solids.- Semi-auxetic Laminates and Auxetic Composites.

Über Autor(innen)

Dr. T.C. Lim earned his PhD in the area of material mechanics in 2001, and thereafter pioneered auxetic solids research in Asia. In addition to being Asia’s leading researcher in the area of auxetic solids, Dr. Lim is also a pioneer and one of the world leaders in the area of semi-auxetics. Dr. Lim has been serving as a scientific committee member in auxetic conferences and workshops since 2009. In addition, he has been serving as a journal reviewer for auxetic-related papers since 2004.