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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