Speech and Language (eBook)

Advances in Basic Research and Practice

Norman J. Lass (Herausgeber)

eBook Download: PDF | EPUB

2014 | 1. Auflage
406 Seiten
Elsevier Science (Verlag)
978-1-4832-1992-9 (ISBN)

Infos

Speech and Language: Volume 4, Advances in Basic Research and Practice is a collection of papers that deals with the theories, clinical issues, and pathology of language and speech. Several papers discuss nonlinguistic and linguistic processing in children, phonological development in infants, and the development of speech fluency in children. Other papers examine the four major speech production models, the physiological and acoustical aspects of speech adaptation, spatial-temporal model of velopharyngeal function, and variations in the supraglottal air pressure waveform. One paper notes the relationships of two systems of development as follows: language development is dependent upon cognitive products and cognitive development is dependent upon language development. Such relationship leads to the hypotheses that language and cognitive developments are independent, are interdependent, and are both dependent upon some X abilities. One paper suggests that speech clinicians should have as a goal the achievement of speech that is as normal as possible in all respects, and not just for patients to sound normal. The collection will benefit linguists, ethnologists, psychologists, speech therapists, neurologists, neuropsychologists, neurolinguists, or speech pathologists.

Inhalt

Front Cover 1
Advances in Applied Mechanics 4
Copyright 5
Contents 6
Contributors 8
Preface 10
Chapter One: Mechanics of Material Mutations 11
1. A General View 13
1.1 A Matter of Terminology 13
1.2 Material Elements: Monads or Systems? 13
1.3 Manifold of Microstructural Shapes 16
1.4 Caution 17
1.5 Refined Descriptions of the Material Texture 18
1.6 Comparison Between Microstructural Descriptor Mapsand Displacements over M 20
1.7 Classification of Microstructural Defects 21
1.8 Macroscopic Mutations 21
1.9 Multiple Reference Shapes 23
1.10 Micro-to-Macro Interactions 26
1.11 A Plan for the Next Sections 27
1.12 Advantages 28
1.13 Readership 29
2. Material Morphologies and Deformations 30
2.1 Gross Shapes and Macroscopic Strain Measures 30
2.2 Maps Describing the Inner Morphology 33
2.3 Additional Remarks on Strain Measures 35
2.4 Motions 36
2.5 Further Geometric Notes 37
3. Observers 39
3.1 Isometry-Based Changes in Observers 40
3.1.1 Class 1: Leaving Invariant the Reference Space 40
3.1.2 Class 2: Changing the Reference Space by Isometries 43
3.2 Diffeomorphism-Based Changes in Observers 44
3.2.1 Generalized Class 1 44
3.2.2 Generalized Class 2 45
3.3 Notes on Definitions and Use of Changes in Observers 45
4. The Relative Power in the Case of Bulk Mutations 46
4.1 External Power of Standard and Microstructural Actions 46
4.2 Cauchy's Theorem for Microstructural Contact Actions 50
4.3 The Relative Power: A Definition 52
4.4 Kinetics 54
4.5 Invariance of the Relative Power Under Isometry-Based Changesin Observers 55
4.6 And If We Disregard M During Changes in the Observers? 60
4.7 Perspectives: Low-Dimensional Defects, Strain-Gradient Materials, Covariance of the Second Law 61
5. Balance Equations from the Second Law of Thermodynamics: The Caseof Hardening Plasticity 63
5.1 Multiplicative Decomposition of F 64
5.2 Factorization of Changes in Observers 66
5.3 A Version of the Second Law of Thermodynamics Involvingthe Relative Power 67
5.4 Specific Constitutive Assumptions 67
5.5 The Covariance Principle in a Dissipative Setting 70
5.6 The Covariance Result for Standard Hardening Plasticity 71
5.7 Doyle–Ericksen Formula in Hardening Plasticity 73
5.8 Remarks and Perspectives 74
6. Parameterized Families of Reference Shapes: A Tool for Describing Crack Nucleation 78
6.1 A Remark on Standard Finite-Strain Elasticity 78
6.2 The Current of a Map and the Inner Work of Elastic Simple Bodies 80
6.3 The Griffith Energy 81
6.4 Aspects of a Geometric View Leading to an Extension of the Griffith Energy 83
6.5 Cracks in Terms of Stratified Curvature Varifolds 83
6.6 Generalizing the Griffith Energy 87
6.7 The Contribution of Microstructures 91
7. Notes and Further Perspectives 93
Acknowledgment 96
References 96
Chapter Two: Dynamic Discrete Dislocation Plasticity 103
1. Introduction 105
2. Discrete Dislocation Dynamics 116
2.1 Methods of Dislocation Dynamics 117
3. Dynamic Effects in the Motion of Dislocations 120
3.1 Elastic Fields of a Preexisting, Uniformly Moving Edge Dislocation 121
3.2 Relativistic Effects 123
3.3 Core Instabilities and Kinematic Generation 126
4. Dislocation Dynamics and Causality 128
5. The Dynamic Fields of Dislocations 132
5.1 Governing Equations 132
5.2 The Elastic Fields of an Injected, Nonuniformly Moving Straight Edge Dislocation 135
5.2.1 Solution Procedure 135
5.3 Asymptotic Behavior of the Injection Contributions 140
5.4 The Mobile Contributions 142
5.5 The Uniformly Moving Special Case 142
6. Aspects of the Implementation of the Dynamic Fields of Dislocations 145
6.1 The Integration Limits 148
6.1.1 The Past History Function and the Mobility Law 149
6.2 Numerical Integration Schemes 151
6.3 Integration of the Stress Fields in the Mobile Contributions 152
6.4 Singularities at the Injection Front and Behind the Injection Front 158
6.4.1 Location of the Singularities at the Injection Front 159
7. The Moving Fields of Dislocations 162
7.1 The Injection Contribution Term 163
7.2 The Injected Uniformly Moving Edge Dislocation 167
7.2.1 Dynamic Effects 169
7.3 The Rayleigh Wave Speed 172
7.4 The Injected Nonuniformly Moving Edge Dislocation 178
7.5 The Annihilation of Dislocations 179
8. Methodological Rules 180
8.1 The Integration Scheme 181
8.2 Integration Scheme 183
8.3 Slip Systems 183
8.4 Mobility Laws 186
8.4.1 The Regimes of Motion of a Dislocation 187
8.4.2 Drag-Controlled Regime 189
8.4.3 Thermal Activation Regime 190
8.4.4 Relativistic Regime 191
8.4.5 The Exactitude of the Peach–Koehler Force 192
8.4.6 Inertial Forces 195
8.4.7 Other Considerations 199
8.4.8 The Way Forward 205
8.5 Frank–Read Sources 206
8.5.1 The Source Strength: Strain–Rate Dependence of the Strengthof a Frank–Read Source 207
8.5.2 Activation Times 208
8.6 Source Equilibrium Distance 212
8.6.1 Spatial Distribution of Frank–Read Sources 214
8.7 Homogeneous Nucleation of Dislocations 214
8.7.1 Constitutive Rules for Homogeneous Nucleation in D3P 216
8.8 Virtual Dislocations 216
8.9 The Time Step 219
9. A Sample Simulation 219
10. Conclusions 224
Acknowledgment 228
References 228
Chapter Three: The Hertz-Type and Adhesive Contact Problems for Depth-Sensing Indentation 235
1. Introduction 236
2. The Hertz-Type Contact Problems 242
2.1 Formulations of the Hertz-Type Contact Problems 244
2.1.1 The Hertz Approximation 244
2.1.2 The Hertz-Type Boundary Value Problem 245
2.1.3 The Types of Contact Boundary Conditions 247
2.1.4 The Harmonic Function Formulation of the Frictionless Problem 249
2.1.5 Incompatibility of the Hertz-Type Problem Formulations 250
2.2 Solutions to Frictionless Contact Problems 251
2.2.1 The Classic 3D Hertz Solution 251
2.2.2 Dimensional Analysis of Anisotropic Problems 252
2.2.3 Solutions for Transversely Isotropic Materials 255
2.2.4 Solutions for Prestressed Materials 257
2.2.5 Axisymmetric Frictionless Contact 260
2.3 Galin's Solution for Axisymmetric Contact 261
2.4 Solutions to Nonslipping Contact Problems 266
2.4.1 Historical Preliminaries 266
2.4.2 The Mossakovskii Solution for Nonslipping Contact 267
2.5 Nonslipping Solution for Power-Law-Shaped Indenters 268
2.5.1 The General Solution 268
2.5.2 A Conical Punch 270
2.5.3 A Spherical Punch 271
2.6 Slopes of the Displacement–Force Curves 271
2.6.1 The Frictionless Hertz-Type Contact 271
2.6.2 The Nonslipping Hertz-Type Contact 272
3. Indentation Methods in Materials Science 273
3.1 Historical Overview of Indentation Techniques 273
3.1.1 Hardness Measurements 274
3.1.2 Development of Nanoindentation Techniques 276
3.1.3 Depth-Sensing Indentation 278
3.2 Evaluation of Material Properties by DSI 279
3.2.1 The BASh Formula 279
3.2.2 Development of the BASh Formula 280
3.3 Specific Features of Indentation Problems 281
3.3.1 Practical Applications of Indentation Techniques 281
3.3.2 Advantages and Drawbacks of the Use of Sharp Indenters 283
3.3.3 Effect of Initial Plastic Deformations of the Specimen Surface 284
3.3.4 Surface Effects and Indentation 285
3.3.5 Effect of Lateral Displacements 287
4. Self-similarity of Contact Problems 288
4.1 Classic Dimensional Analysis 289
4.1.1 A Problem for a Sharp Indenter 289
4.1.2 Dimensional Analysis of the Hertz Problem 290
4.1.3 Indentation of a Nonlinear Medium by a Ball 291
4.1.4 Meyer Formula and Its Representations 292
4.1.5 History of the Theorem 293
4.2 Some Homogeneous Constitutive Relations 294
4.2.1 The Theory of Elasticity 294
4.2.2 Theory of Plasticity 294
4.2.3 Hereditarily Elastic (Viscoelastic) and Plastic Materials 297
4.2.4 Creeping Materials 298
4.3 Homogeneity and Parametric Homogeneity 298
4.3.1 Homogeneous Functions 298
4.3.2 Parametric-Homogeneous Functions 299
4.3.3 Fractal PH Surfaces 301
4.4 History of Similarity Analysis of Contact Problems 302
4.4.1 Wedges, Cones, and Pyramids 302
4.4.2 Contact with Isotropic Elastic Media 303
4.4.3 Contact with Viscoelastic and/or Anisotropic Elastic Media 306
4.5 General Similarity Transformations 307
4.5.1 Similarity Transformations of Contact Regions 307
4.5.2 Dilation Similarity Transformations of Hertz-Type Contact 308
4.5.3 Similarity Theorems of Hertz-Type Contact 309
4.6 Rescaling Formulae and Indentation tests 314
4.6.1 General Rescaling Formulae 314
4.6.2 Rescaling Formulae for Hardness and Nanoindentation 315
4.7 Comparison with Some Experimental Data 316
4.7.1 The Power-Law Exponent for Poly(Methyl Methacrylate) 316
4.7.2 Variation of the Loading Time 317
4.7.3 Variation of the Indenter Size and the Load 317
5. Axisymmetric Adhesive Contact Problems 319
5.1 Molecular Adhesion and Its Modeling 319
5.1.1 Basic Terminology 319
5.1.2 Historical Preliminaries 319
5.2 Models of Adhesive Contact 320
5.2.1 Adhesion Between Rigid Spheres 320
5.2.2 Sperling Model of Adhesive Contact 322
5.2.3 The JKR Theory of Adhesive Contact 323
5.2.4 The DMT, Maugis, and Other Theories of Adhesive Contact 326
5.3 The Generalized Frictionless JKR Theory 329
5.3.1 The JKR Theory for an Arbitrary Axisymmetric Indenter 330
5.3.2 The JKR Theory for Axisymmetric Monomial Indenters 332
5.4 General Nonslipping Adhesive Contact 333
5.4.1 The Nonslipping Boussinesq–Kendall Adhesive Contact Problem 333
5.4.2 Energy Approach in the Nonslipping Case 334
5.4.3 Nonslipping JKR Problem for Monomial Indenters 336
5.5 Universal Relations for Non-ideal-Shaped Indenters 337
5.5.1 Frictionless Adhesive Indentation 338
5.5.2 Nonslipping Adhesive Indentation 338
5.5.3 Dimensionless Relations for Adhesive Indentation 339
5.5.4 Adhesive Contact for Nanoindenters of Monomial Shape 341
6. Experimental Evaluation of Work of Adhesion 344
6.1 Customary Techniques 344
6.2 The BG Method 346
6.2.1 The Basic Ideas of the Method 346
6.2.2 The Robustness of the BG Method 347
6.3 Application of the BG Method to Some Experimental Data 349
6.3.1 The Shift of the Coordinate Origin 349
6.3.2 The Experimental Procedure 350
6.3.3 The Results 351
7. Concluding Remarks 353
7.1 The Incompatibility of Adhesive Contact Problems 353
7.2 The Fracture Mechanics Approach to Adhesive Contact 354
7.3 Extension of the JKR Theory to the 3D Case 358
7.4 An Analogy with the Inverse Approach to Impact on a Fluid Surface 359
Acknowledgment 361
References 361
Chapter Four: Multi Field Simulation of Fracture 377
1. Introduction 378
2. Fracture Models 385
2.1. Cohesive Models 386
2.2. Constitutive Equations for Cohesive Models 393
3. Governing Equations 396
4. Numerical Approaches to Fracturing 402
4.1. Review of Numerical Solution Strategies 402
4.2. Smeared and Discrete Crack Approaches 408
4.3. Interface Elements and Embedded Discontinuity Elements 410
4.4. Extended Finite Element Method 415
4.5. Thick Level Set Model for Localization to Fracture Transition 421
4.6. Phase Field Models 425
4.7. Discrete Crack with Adaptive Remeshing 430
4.7.1. 2D Mesh Generation 431
4.7.2. Fracture Nucleation and Propagation 433
4.7.3. Space-Refinement Strategy 438
4.7.4. 3D Problems 445
5. Discretized Governing Equations and Solution Procedure 446
5.1. Time Stepping and Linearization 448
5.2. Finite Elements in Time and Time Adaptivity 452
6. Applications 456
6.1. Validation Procedures 457
6.1.1. Validation of the Projection Method 458
6.1.2. Validation of the TDG Procedure 461
6.2. Thermomechanical Fracture 466
6.3. Hydraulic Fracture: Pumped Well 476
6.4. Hydraulic Fracture: 2D DAM (Benchmark ICOLD) 483
6.5. Hydraulic Fracture: 3D DAM 488
6.6. Fracturing of Drying Concrete 492
6.7. Numerical Simulation of Cracking of a Massive Concrete Beam 498
6.8. Chemical Processes and Their Mechanical Effects 503
7. Discussion and Conclusions 515
Acknowledgments 517
References 517
Index 531

Textauszug

Chapter One

Mechanics of Material Mutations

Paolo Maria Mariano    DICeA, University of Florence, Florence, Italy

Abstract

Mutations in solids are defined here as dissipative reorganizations of the material texture at different spatial scales. We discuss possible views on the description of material mutations with special attention to the interpretations of the idea of multiple reference shapes for mutant bodies. In particular, we analyze the notion of relative power—it allows us to derive standard, microstructural, and configurational actions from a unique source—and the description of crack nucleation in simple and complex materials in terms of a variational selection in a family of bodies differing from one another by the defect pattern, a family parameterized by vector-valued measures. We also show that the balance equations can be derived by imposing structure invariance on the mechanical dissipation inequality.

2000 Mathematics Subject Classification

Primary 05C38

15A15

Secondary 05A15

15A18

Keywords

Continuum mechanics

Defects

Relative power

Covariance

Complex materials

1 A general view

1.1 A matter of terminology

The word “mutation” appearing in the title indicates the occurrence of changes in the material structure of a body, a reorganization of matter with dissipative nature. Implicit is the idea of considering mutations that have a nontrivial influence on the gross behavior of a body under external actions—the adjective “nontrivial” being significant from time to time. I use the word “mutation” here in this sense, relating it to dissipation, although not strictly to irreversible paths in state space1—mentioning dissipation appears necessary because even a standard elastic deformation implies a “reorganization” of the matter (think, for example, of deformation-induced anisotropies).

Mutation implies a relation with some reference configuration or state; in general, a mutation is with respect to a setting that we take as a paragon. Such a setting does not necessarily coincide only with the reference place of a continuum body. In fact, affirming that a mutation is macroscopic or microscopic implies the selection of spatial scales that we consider in representing the characteristic geometric features of a body morphology. Not all these features are entirely described by the assignment of a macroscopic reference place. To clarify this point, it can be useful to recall a few basic issues in continuum mechanics, i.e., the mechanics of tangible bodies, leaving aside corpuscular phenomena adequately treated by using concepts and methods pertaining to quantum theories, or considering just the effects of such phenomena emerging in the long-wavelength approximation.2

1.2 Material elements: monads or systems?

In the first pages of typical basic treatises in continuum mechanics, we read that a body is a set of not further specified material elements (let us say ordered sets of atoms and/or entangled molecules) that we represent just by mapping the body in the three-dimensional Euclidean point space. Then we consider how bodies deform during motions, imposing conditions that select among possible changes of place. Strain tensors indicate just how and how much lines, areas, and volumes are stretched, i.e., the way neighboring material elements move near to or away from each other. They do not provide information on how the matter at a point changes its geometry—if it does it—during a motion. In other words, we consider commonly the material element at a point as an indistinct piece of matter, a black box without further structure. We introduce information on the material texture at the level of constitutive relations—think, for example, of the material symmetries in the case of simple bodies. However, the parameters that the constitutive relations introduce refer to peculiar material features averaged over a piece of matter extended in space, what we call, in homogenization procedures, a representative volume element.3 In other words, in assigning constitutive relations we implicitly specify what we intend for the material element, and this is a matter of modeling in the specific case considered from time to time. This way we include a length scale in the continuum scheme, even when we do not declare it explicitly. This remark is rather clear already in linear elasticity. In fact, when in the linear setting we assign to a point a fourth-rank constitutive tensor, declaring some material symmetry (e.g., cubic), the symmetry at hand is associated with a subclass of rotations, and they are referred to the point considered. A point, however, does not rotate around itself. Hence, in speaking of material symmetries at a point, we are implicitly attributing to it the characteristic features of a piece of matter extended in space, with finite size. For example, in the case of cubic symmetry mentioned above, we imagine that a material point represents at least a cubic crystal, but we do not declare its size, which in this way is an implicit material length scale. We need not declare explicitly the size of the material element in traditional linear elasticity but, nevertheless, such a material length scale does exist. The events occurring above a length-scale considered in a specific continuum model, whatever is its origin, are described by relations among neighboring material elements. The ones below are collapsed at a point. Hence, in thinking of mutations, we can grossly distinguish between rearrangements of matter

• among material elements, and

• inside them.

When we restrict the description of the body morphology to the sole choice of the place occupied by the body (the standard approach), mutations inside material elements appear just in the selection of constitutive equations—material symmetry breaking in linear elasticity is an example—and possible flow rules. However, such mutations can generate interactions which can be hardly described by using only the standard representation of contact actions in terms of the Cauchy or Piola–Kirchhoff stresses. Some examples follow:

• Local couples orient the stick molecules that constitute liquid crystals in nematic order.

• In solid-to-solid phase transition (e.g., austenite to martensite), microactions occur between the different phases.

• Microactions of different types appear in ferroelectrics, produced by neighboring different polarizations and even inside a single crystal by the electric field generated by the local dipole.

• Another example is rather evident when we think of a material constituted by entangled polymers scattered in a soft melt. External actions may produce indirectly local polymer disentanglements or entanglements without altering the connection of the body. Moreover, in principle, every molecule might deform with respect to the surrounding matter, independently of what is placed around it, owing to mechanical, chemical, or electrical effects, the latter occurring when the polymer can suffer polarization. The common limit procedure defining the standard (canonical) traction at a point does not allow us to distinguish between the contributions of the matrix and the polymer. Considering explicitly the local stress fluctuations induced by the polymer would, however, require a refined description of the mechanics of the composite, which could be helpful in specific applications.

• Finally (but the list would not end here), we can think of the actions generated in quasicrystals by atomic flips.

However, beyond these examples, the issue is essentially connected with the standard definition of tractions. At a given point and with respect to an assigned (smooth) surface crossing that point, the traction is a force developing power when multiplied by the velocity of that point, i.e., the local rate at which material elements are crowded and/or sheared. And the velocity vector does not bring with it explicit information on what happens inside the material element at that point, even relatively to the events inside the surrounding elements. When physics suggests we account for the effects of microscopic events, we generally need a representation of the contact actions refined with respect to the standard one. In these cases, the quest does not reduce exclusively to the proposal of an appropriate constitutive relation (often obtained by data-fitting procedures) in the standard setting. We often have to start from the description of the morphology of a body, inserting fields that may bring at a continuum-level information on the microstructure. In this sense, we can call them descriptors of the material morphology (or inner degrees of freedom, even if to me the first expression could be clearer at times). This way, at the level of the geometric description of body morphology, we are considering every material element as a system that can have its own (internal) evolution...

Produkt-Details

• Erscheint lt. Verlag: 28.6.2014
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber ► Gesundheit / Leben / Psychologie ► Krankheiten / Heilverfahren
• Themenwelt: Medizin / Pharmazie ► Medizinische Fachgebiete ► Allgemeinmedizin
• Themenwelt: Sozialwissenschaften ► Ethnologie
• Themenwelt: Sozialwissenschaften ► Politik / Verwaltung
• Themenwelt: Sozialwissenschaften ► Soziologie
• ISBN-10: 1-4832-1992-5 / 1483219925
• ISBN-13: 978-1-4832-1992-9 / 9781483219929