Preface	6
	Contents	8
	Micro and Nanoscale Modeling	10
	On the Variational Analysis of Vibrations of Prestressed Six-Parameter Shells	11
	1 Introduction	11
	2 Dynamics and Statics of Micropolar Plates and Shells	13
	3 Linearized Boundary-Value Problems	17
	4 Eigen-Vibrations of Prestressed Micropolar Shells	20
	5 Rayleigh Principle	20
	6 Conclusions	24
	References	24
	Multi-objective Topology Optimization Design of Micro-structures	28
	1 Introduction	28
	2 Multi-objective Problem Formulation	29
	2.1 Preliminaries in the Multi-scale Modeling	30
	2.2 The Homogenized Conductivity Tensor	31
	2.3 The Homogenized Elasticity Tensor	34
	3 Topological Derivative	37
	4 Numerical Results	42
	4.1 Example 1. Bulk Modulus and Horizontal Conductivity Maximization	45
	4.2 Example 2. Bulk Modulus and Orthogonal Conductivity Maximization	46
	4.3 Example 3. Poisson's Ratio and Horizontal Conductivity Maximization	47
	4.4 Example 4. Poisson's Ratio Minimization and Horizontal Conductivity Maximization	48
	4.5 Example 5. Poisson Ratio Minimization and Orthogonal Conductivity Maximization	49
	4.6 Example 6. Shear Modulus and Horizontal Conductivity Maximization	51
	5 Concluding Remarks	52
	References	52
	3 Sensitivity Analysis of Micro Models for Solidification of Pure Metals	55
	Abstract	55
	1 Introduction	55
	2 Governing Equations	57
	3 Nucleation and Nuclei Growth	60
	4 Sensitivity Analysis	65
	5 Final Remarks	69
	Acknowledgments	69
	References	69
	Biological Tissues	71
	Variational Constituive Models for Soft Biological Tissues	72
	1 Background	72
	2 Variational Framework	73
	3 A Set of Variational Inelastic Models	76
	3.1 A Viscoelastic Model for Isotropic Soft Materials	77
	3.2 A Viscoelastic Model for Fiber-Reinforced Soft Materials	79
	3.3 A Viscoplastic Model for Isotropic Soft Materials Undergoing Permanent Deformations	82
	3.4 Material Models	84
	3.5 Tangent Moduli	86
	4 Numerical Examples	87
	4.1 Isotropic Viscoelastic Case	88
	4.2 Viscoelastic Fiber-Reinforced Case	88
	4.3 Elasto-Vicoplastic Model	90
	5 Concluding Remarks	92
	References	92
	5 Sensitivity Analysis of Temperature Field and Parameter Identification in Burned and Healthy Skin Tissue	94
	Abstract	94
	1 Introduction	95
	2 Governing Equations	96
	3 Sensitivity Analysis	97
	4 Boundary Element Method	99
	5 Inverse Problem	107
	6 Shape Sensitivity Analysis	108
	7 Results of Computations	109
	8 Conclusions	116
	Acknowledgements	116
	References	116
	Application of the hp-FEM for Hyperelastic Problems with Isotropic Damage	118
	1 Introduction	118
	2 Hyperelasticity	120
	2.1 Compressible Neo-Hookean Material	120
	2.2 Nearly-Incompressible Mooney-Rivlin Material	121
	2.3 Principle of Virtual Power (PVP)	123
	2.4 Linearization of the Weak Form	124
	2.5 High-Order Shape Functions	127
	2.6 Local Finite Element Discretization	128
	2.7 Local Pressure Projection	128
	2.8 Discretization of the Equilibrium Equation	132
	2.9 Discretization of the Linearized Equilibrium Equation	133
	2.10 Global Newton-Raphson Equation	134
	3 Hyperelastic Damage	135
	3.1 Mullins Effect in Hyperelastic Materials	135
	3.2 Damage Variable and Thermodynamic Aspects	136
	3.3 Damage Criterion	138
	3.4 Damage Evolution Law	139
	3.5 Constitutive Relations	140
	3.6 Damage Algorithm	141
	4 Convergence Tests	143
	4.1 Test 1---Nearly-Incompressible Mooney-Rivlin Material	144
	4.2 Test 2---Damaged Neo-Hookean Material	149
	4.3 Test 3---Damaged Nearly-Incompressible Mooney-Rivlin Material	150
	5 Conclusion	153
	References	154
	Mechanical Characterization of the Human Aorta: Experiments, Modeling and Simulation	156
	1 Introduction	157
	2 Materials and Methods	161
	2.1 Experimental Procedure	161
	2.2 Constitutive Modeling	170
	2.3 Material Characterization via the Tensile Test	172
	2.4 Analysis of the Pressurization Test	174
	3 Results	175
	3.1 Ascending Aorta	175
	3.2 Aortic Arch	178
	3.3 Descending Aorta	186
	4 Discussion	191
	4.1 Ascending Aorta	191
	4.2 Aortic Arch	195
	4.3 Descending Aorta	199
	5 Conclusions	200
	6 Conflicts of Interest	202
	References	203
	Porous and Multiphase Materials	208
	8 Optimization of Functionally Graded Materials Considering Dynamical Analysis	209
	Abstract	209
	1 Introduction	210
	2 Functionally Graded Materials	211
	3 Topology Optimization Method for FGM Design	214
	3.1 Basics of the Topology Optimization Method	214
	3.2 Topology Optimization of FGMs	218
	4 Topology Optimization of Dynamically Loaded Structures	220
	4.1 Dynamic Finite Element Analysis	220
	4.2 Topology Optimized Structures Under Impact Loads	224
	4.3 Equivalent Static Loads	226
	4.4 The Optimization Process with ESLs	226
	5 TOM-Based Design of FGMs Under Impact Loads	228
	5.1 Heuristic Approach	228
	5.2 Optimized Approach	233
	6 Conclusions of the Chapter	240
	Acknowledgments	240
	References	240
	Complex Variable Semianalytical Method for Sensitivity Evaluation in Nonlinear Path Dependent Problems: Applications to Periodic Truss Materials	242
	1 Introduction	242
	2 Nonlinear Truss Finite Element Formulation	244
	2.1 Virtual Work	246
	2.2 Internal Force Vector	247
	2.3 Tangent Stiffness Matrix	248
	2.4 Geometric Nonlinearity	249
	2.5 Material Nonlinearity: A Coupled Elastoplastic Model for Ductile Damage	250
	2.6 Tangent Modulus	255
	3 Sensitivity Analysis	255
	3.1 Sensitivity Analysis for Path Independent Problems	256
	3.2 Sensitivity Analysis for Path Dependent Problems	260
	4 Periodic Truss Material	264
	4.1 Sensitivity Analysis of Periodic Truss Materials	264
	4.2 Bulk Modulus Sensitivity Expression	267
	4.3 Numerical Evaluation of the Bulk Modulus Sensitivity	268
	5 Conclusion	270
	References	271
	10 Laser Beam Drilling of Cellular Metals: Numerical Simulation	274
	Abstract	274
	1 Introduction	275
	2 Fundamentals of Laser Technology	276
	2.1 Laser Beam Drilling Technology	276
	2.2 Laser Beam Behavior	276
	2.3 Homogenization and RVE	281
	3 Program Code	283
	3.1 Flow Chart of the Program Code	283
	3.2 Finite Volume Method	284
	4 Results	286
	4.1 Sintered and Soldered Cells	288
	4.2 Thermal Conductivity Influence	289
	4.3 Considerations About the Results	293
	5 Gradient of Temperature and Velocity of Drilling	294
	6 Total Heat and Expected Heat	295
	7 Drilling Width	296
	8 Conclusions	298
	References	299
	11 Metallic Foam Density Distribution Optimization Using Genetic Algorithms and Voronoi Tessellation	301
	Abstract	301
	1 Introduction	302
	2 Modeling of Open-Cell Foam Structures	303
	3 Optimization	305
	3.1 Density Modification of Foam	305
	3.2 Genetic Algorithms	306
	3.2.1 Selection	307
	3.2.2 Crossover	307
	3.2.3 Mutation	308
	3.3 Fitness Function Evaluation	308
	3.4 Algorithm	310
	4 Applications	311
	4.1 Example 1	311
	4.2 Example 2	314
	4.3 Example 3	316
	5 Conclusions	317
	Acknowledgments	318
	References	318
	Polymers	320
	12 Modeling Material Behavior of Polymers	321
	Abstract	321
	1 Introduction	321
	1.1 Micromolecular Background to Viscous and Solid Behavior	322
	1.2 Types of Polymers and Their Tensile and Compressive Behavior	323
	1.3 Experimental Considerations	327
	1.4 Polymer Material Testing at the University of Waterloo	328
	2 Constitutive Modeling	332
	2.1 Micro- and Macro-Scale Modeling	332
	2.2 Viscoelastic Modeling	333
	2.3 Viscoplastic Modeling	335
	3 Parameter Estimation for Linear Modeling	336
	4 Nonlinear Modeling	339
	4.1 Methods for ‘Nonlinearization’ of the Model Parameters	340
	5 Extending the Material Parameters to Longer Times Frames	343
	5.1 Using Short Term Testing for Predictions at Longer Time Frames	343
	5.2 Viscoelastic (NVE) and Viscoplastic (NVP) Long Term Responses	344
	6 Modeling the Response Under Varying Stress	346
	6.1 Modified Superposition Principle (MSP)	346
	7 Conclusion	349
	References	350
	Material Model Based on Response Surfaces of NURBS Applied to Isotropic and Orthotropic Materials	353
	1 Introduction	354
	2 Nonuniform Rational B-Spline Curves and Surfaces	355
	2.1 Tensor Product Surfaces	355
	2.2 Definition of B--Spline Basis Functions	356
	2.3 Definition of B--Spline Curves	356
	2.4 Definition of B--Spline Surfaces	357
	2.5 Definition of NURBS Surfaces	359
	2.6 Derivatives of a NURBS Surface	359
	3 Data Fitting	361
	4 Material Model Based on NURBS for Principal Directions (NURBS--Material)	362
	5 Application of NURBS--Material in Membrane Finite Element Modeling	366
	5.1 Comparison with Elastoplastic Material Model	366
	5.2 Comparison with an Orthotropic Material Model	370
	6 Conclusions	372
	References	373
	14 Characterization of Constitutive Parameters for Hyperelastic Models Considering the Baker-Ericksen Inequalities	374
	Abstract	374
	1 Introduction	374
	2 Constitutive Parameters Optimization Technique	376
	3 Imposing the Inequalities to the Models	380
	4 Experimental Data	383
	5 Results	384
	6 Conclusions	390
	References	391