Generalized models and non-classical approaches in complex materials 1 /
This book is the first of 2 special volumes dedicated to the memory of Gérard Maugin. Including 40 papers that reflect his vast field of scientific activity, the contributions discuss non-standard methods (generalized model) to demonstrate the wide range of subjects that were covered by this excepti...
| Other Authors: | Altenbach, Holm, 1956-, Pouget, Joël,, Rousseau, Martine,, Collet, Bernard, 1950-, Michelitsch, Thomas,, SpringerLink (Online service) |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham, Switzerland :
Springer,
2018.
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| Physical Description: |
1 online resource (xlii, 760 pages). |
| Series: |
Advanced structured materials ;
89. |
| Subjects: |
| Summary: |
This book is the first of 2 special volumes dedicated to the memory of Gérard Maugin. Including 40 papers that reflect his vast field of scientific activity, the contributions discuss non-standard methods (generalized model) to demonstrate the wide range of subjects that were covered by this exceptional scientific leader. The topics range from micromechanical basics to engineering applications, focusing on new models and applications of well-known models to new problems. They include micro-macro aspects, computational endeavors, options for identifying constitutive equations, and old problems with incorrect or non-satisfying solutions based on the classical continua assumptions. |
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| Item Description: |
Includes bibliographical references. Intro; Foreword; Preface; Contents; List of Contributors; 1 Effective Coefficients and Local Fields of Periodic Fibrous Piezocomposites with 622 Hexagonal Constituents; Abstract; 1.1 Introduction; 1.2 A Boundary Value Problem of the Linear Piezoelectricity Theory; 1.3 Homogenization, Local Problems and Effective Coefficients; 1.3.1 Explicit Form of the Homogenized Problem, Effective Coefficients and Local Problems; 1.3.2 Local Fields; 1.4 Application to a Binary Fibrous Piezocomposite with Perfect Contact Conditions at the Interfaces. 1.5 Local Problems for Fibrous Composites with Constituents of 622 Hexagonal Class1.5.1 Local Problems L23 and L1; 1.5.2 Effective Coefficients Related with the Local Problems L23 and L1; 1.5.3 Local Problems L13 and L2 and Related Effective Coefficients; 1.5.4 On the Computation of the Local Fields from the Solutions of the Local Problem L13; 1.6 Numerical Examples; 1.6.1 Square Array Distribution; 1.6.2 Rectangular Array Distribution; 1.6.3 Spatial Distribution of Local Fields; 1.7 Concluding Remarks; References; 2 High-Frequency Spectra of SH Guided Waves in Continuously Layered Plates. Abstract2.1 Introduction; 2.2 Statement of the Problem and Main Equations; 2.3 The Propagator Matrix and Its Adiabatic Approximation; 2.4 Boundary Problems and Their General Solutions; 2.4.1 Spectral Regions Without Division Points; 2.4.1.1 The Range s max{{u015D}(y)}(I2 in Fig. 2.2); 2.4.2 Spectral Regions with one Division Point; 2.4.2.1 The Case ŝ' (a)> 0 (the Range II in Fig. 2.2); 2.4.2.2 The Case ŝ' (a) 0, ŝ' (b) <0. 2.4.3.2 The Case ŝ' (a) 0 (the Range III in Fig. 2.2)2.4.4 Extension for an Arbitrary Number of Division Points; 2.4.4.1 An Odd Number of Division Points N = 2n{u2212}1 (n > 1); 2.4.4.2 An Even Number of Division Points N = 2n (n > 1); 2.5 The Low-Slowness Approximation and the Cut-Off Frequencies; 2.6 Example of Inhomogeneity Admitting an Explicit Analysis; 2.6.1 The Region 0 < s {u2264} ŝ0; 2.6.1.1 The Cut-Off Frequencies of the Spectrum; 2.6.1.2 Spectrum just Under the Level sl = ŝ0; 2.6.2 The Region ŝ0 < s {u2264} ŝm; 2.6.2.1 Spectrum just Over the Level sl = ŝ0. 2.6.2.2 Spectrum Under the Asymptote s = ŝm2.7 Levels Related to Extreme Points on the Slowness Profile; 2.7.1 An Absolute Minimum of the Function ŝ(y); 2.7.1.1 Spectral Features just Under the Level s = ŝ1; 2.7.1.2 Spectrum Features just Over the Level s = ŝ1; 2.7.2 The Level Related to an Inflection Point; 2.7.3 Asymptote Related to Maximum at the Profile ŝ(y); 2.8 Conclusions; References; 3 Nonlinear Schrödinger and Gross -- Pitaevskii Equations in the Bohmian or Quantum Fluid Dynamics (QFD) Representation; Abstract; 3.1 Introduction; 3.2 Polar Representation of the Wave Function. This book is the first of 2 special volumes dedicated to the memory of Gérard Maugin. Including 40 papers that reflect his vast field of scientific activity, the contributions discuss non-standard methods (generalized model) to demonstrate the wide range of subjects that were covered by this exceptional scientific leader. The topics range from micromechanical basics to engineering applications, focusing on new models and applications of well-known models to new problems. They include micro-macro aspects, computational endeavors, options for identifying constitutive equations, and old problems with incorrect or non-satisfying solutions based on the classical continua assumptions. |
| Physical Description: |
1 online resource (xlii, 760 pages). |
| Bibliography: |
Includes bibliographical references. |
| ISBN: |
9783319724409 3319724401 |
| ISSN: |
1869-8433 ; |