Cellular and Porous Materials in Structures and Processes

by Altenbach, Holm; Ochsner, Andreas

• ISBN13: 9783709102961
• ISBN10: 3709102960
• Format: Hardcover
• Copyright: 2010-07-15
• Publisher: Springer Verlag

Summary

The book covers the state-of-the-art treatment in modelling and experimental investigation of the mechanical behaviour of cellular and porous materials. Starting from the continuum mechanical modelling, to the numerical simulation, several important questions related to applications such as the fracture and impact behaviour are covered.

Table of Contents

Fracture Mechanics of Foams	p. 1
Fundamentals of Fracture Mechanics	p. 1
Introduction	p. 1
Linear Elastic Fracture Mechanics	p. 3
Crack tip stress and displacement fields in anisotropic materials	p. 12
Experimental Determination of Fracture Toughness of Foam Materials	p. 16
Tear Test for Flexible Cellular Materials	p. 17
Standard Test Methods for Plane-Strain Fracture Toughness and Strain Energy Release Rate of Plastic Materials	p. 18
Fracture Toughness Experimental Results	p. 24
Impact Fracture Toughness	p. 29
Micromechanical Models for Foams Fracture	p. 34
Concluding Remarks	p. 42
Bibliography	p. 43
Finite Element Modeling of Foams	p. 47
Introduction	p. 47
Homogenization and the Unit Cell Method	p. 49
Micro-Mechanical Finite Element Models of Cellular Materials	p. 57
Introduction	p. 57
Open-Cell Foams	p. 63
Closed-Cell Foams	p. 67
Open-Cell Foams with Hollow Struts	p. 72
Micro-Mechanical Models - Methods and Results	p. 73
Elastic Properties	p. 74
Yielding	p. 75
Buckling	p. 80
Densification	p. 91
Fracture	p. 93
Optimization of Foam Density Distribution	p. 96
Summary	p. 98
Bibliography	p. 98
Plasticity of Three-dimensional Foams	p. 107
Fundamentals of Continuum Mechanics	p. 107
Stress Tensor and Decomposition	p. 107
Invariants	p. 109
Constitutive Equations	p. 112
Linear Elastic Behaviour: Generalised Hooke's Law for Isotropic Materials	p. 113
Constitutive Relationships for Pressure Sensitive Materials: Systematic Overview	p. 119
Simple Cubic Cell Models based on Beams and Shells for Open and Closed Cell Materials	p. 129
Relative Density	p. 133
Geometrical Moment of Inertia	p. 135
Young's Modulus	p. 135
Shear Modulus and Poisson's Ratio	p. 136
Yield Stress	p. 140
Procedures to Determine the Influence of the Hydrostatic Stress on the Yield Behaviour	p. 141
Implementation of New Constitutive Equations into Commercial Finite Element Codes	p. 146
One-Dimensional Drucker-Prager Yield Condition	p. 146
Integration of the Constitutive Equations	p. 148
Mathematical Derivation of the Fully Implicit Backward Euler Algorithm	p. 152
Example Problem: Return Mapping for Ideal Plasticity and Linear Hardening	p. 158
Bibliography	p. 164
Thin-walled Structures Made of Foams	p. 167
Introduction	p. 168
Plates as Structural Elements	p. 168
Foams as a Material for Structural Elements	p. 169
Direct Two-dimensional Plate Theory	p. 171
Classical Approaches in the Plate Theory	p. 171
Governing Equations	p. 173
Material-independent Equations	p. 174
Two-dimensional Constitutive Equations	p. 175
Basic Equations in Cartesian Coordinates	p. 176
Stiffness Identification	p. 179
Orthotropic Material Behavior	p. 180
Classical Stiffness Values	p. 181
Non-classical Stiffness Values	p. 183
Special Case - Isotropic Behavior	p. 185
Examples of Effective Stiffness Properties Estimates	p. 186
Homogeneous Plate	p. 186
Classical Sandwich Plate in Reissner's Sense	p. 187
Functionally Graded Materials and Foams	p. 188
On the Plates Made of Nanofoams	p. 193
Symmetric Orthotropic Plate - Static Case	p. 196
Bending Problem - One-dimensional Case	p. 198
Bending Problem - Two-dimensional Case	p. 198
Bending of an Isotropic Plate	p. 199
Bending of an Elastic Plate Made of FGM (Symmetric Case)	p. 200
Dynamics of Plates Made of an Elastic Foam	p. 201
Equations of Motion for a Symmetric Isotropic Plate	p. 201
Free Oscillations and Dispersion curves of a Rectangular Plate	p. 203
Plate Made of a Linear Viscoelastic Material	p. 209
Constitutive Equations	p. 209
Effective Properties	p. 210
Bounds for the Eigen-values	p. 214
Quasi-static Behavior of a Symmetric Orthotropic Plate	p. 215
Examples of Effective Stiffness Relaxation Functions	p. 217
Bending of a Viscoelastic Plate	p. 222
Plate Theory Deduced from the Cosserat Continuum	p. 226
Two-dimensional Governing Equations	p. 226
Reduction of the Three-dimensional Micropolar Equations	p. 228
Summary	p. 232
Bibliography	p. 234
Plasticity of Porous and Powder Metals	p. 243
Introduction	p. 243
Fundamentals of the Theory of Plasticity	p. 245
Rigid Perfectly/Plastic Solids	p. 245
Rigid Plastic Hardening Solids	p. 252
Rigid Viscoplastic Solids	p. 253
Maximum Friction Law and Singular Velocity Fields (Rigid Perfectly/Plastic Material)	p. 254
Maximum Friction Law and Other Models of Pressure-independent Plasticity	p. 261
Plasticity Theory for Porous and Powder Metals Based on the Associated Flow Rule	p. 262
Preliminaries	p. 262
Yield Criteria and the Associated Flow Rule for Porous and Powder Materials	p. 265
Additional Remarks on the Yield Criteria	p. 270
Simple Analytic Example	p. 271
Plasticity Theory for Porous and Powder Metals Based on Non-associated Flow Rules	p. 277
Stress Equations	p. 277
Kinematic Theories	p. 280
The Coaxial Model	p. 281
The Double-shearing Model	p. 282
The Double-slip and Rotation Model	p. 284
Qualitative Behavior of Plastic Solutions for Porous and Powder Metals in the Vicinity of Frictional Interfaces	p. 285
Preliminaries	p. 285
Statement of the Problem	p. 285
Solution for Stresses	p. 289
Solutions for Velocities	p. 290
Frictional Boundary Condition	p. 292
Solution for Pressure-independent Plasticity	p. 299
Singularity in Velocity Fields	p. 300
Applications	p. 302
Bibliography	p. 305
Impact of Cellular Materials	p. 309
Introduction	p. 309
Wave Propagation in a Cellular Rod	p. 311
Rigid Object Strikes on a Cellular Rod of Fixed End	p. 316
Basic Assumptions	p. 316
Shock Wave Analysis	p. 317
Rigid Object Strikes on a Free Cellular Rod	p. 325
Concluding Remarks	p. 333
Bibliography	p. 333
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