New Achievements in Continuum Mechanics and Thermodynamics - A Tribute to Wolfgang H. M?ller

Laudatio

A tale about Wolfgang Müller, the man and the scientist.

Preface

Contents

List of Contributors

1 Magnetorheological Elastomer’s Material Modeling and Parameter Determination by Using the Energy-based Method

1.1 Introduction

1.2 The Energy-based Method for the Inverse Analysis

1.3 Method of Solution and Results

1.4 Conclusion

References

2 On the Size Effects in Indentation Testing of Elastic Functionally-graded Materials

2.1 Introduction

2.2 Small-scale Indentation

2.3 First-order Asymptotic Model for the Indentation Stiffness

2.4 Sample Size Effect in Indentation of a FGM Plate

2.5 Discussion and Conclusion

References

3 The Effect of Mechanical Load-induced Intraosseous Pressure Gradients on Bone Remodeling

3.1 Introduction

3.2 Some Considerations on Bone Physiology

3.3 Modelling

3.3.1 Kinematics

3.3.2 Elastic Mechanical Energy Stored Within the Body

3.3.3 Mechanical Stimulus, Bone Remodeling and Graft Resorption

3.4 Solution Algorithm and Qualitative Results for Tensile Test

3.5 Conclusion and Outlooks

References

4 Mechanical and Thermodynamic Materials Properties Derived by Semi-empirical Atomic Potentials with Special Focus on Ag, Cu, and the Binary Alloy Ag-Cu

4.1 Motivation

4.2 Lattice Kinematics and Energy

4.3 The Embedded Atom Method (EAM)

4.3.1 General Idea of EAM

4.3.2 Restriction to Nearest Neighbor Interactions

4.4 Exploitation of EAM energy expression

4.4.1 Equilibrium Condition and Elastic Constants

4.4.1.1 Pure Metals

4.4.1.2 Binary Alloys

4.4.2 Excess Enthalpy and Phase Diagram

4.4.3 Temperature-dependent Materials Properties

4.4.3.1 Consideration of Lattice Vibrations

4.4.3.2 Kinetic Energy and Heat Capacity

4.5 Summary and Conclusions

References

5 Mechanical Response Change in Fine Grain Concrete Under High Strain and Stress Rates

5.1 Introduction

5.2 Specimen Preparation

5.3 Method of Impact Loading

5.4 Results and Discussion

5.5 Conclusion

References

6 Estimating Fatigue Related Damage in Alloys under Block-type Non-symmetrical Low-cycle Loading

6.1 Introduction

6.2 Defining Relations of Mechanics of Damaged Media

6.2.1 Defining Relations in Plasticity

6.2.2 Evolutionary equations of fatigue damage accumulation

6.2.3 Strength Criterion of the Damaged Material

6.3 Numerical Results

6.4 Conclusion

References

7 On Non-holonomic Boundary Conditions within the Nonlinear Cosserat Continuum

7.1 Introduction

7.2 Constitutive Relations

7.3 Principle of Virtual Work

7.4 Non-holonomic Kinematic Boundary Conditions

7.5 Conclusions

References

8 Nonlinear Localized Waves of Deformation in the Class of Metamaterials as Set as the Mass-in-mass Chain

8.1 Introduction

8.2 Mathematical Model

8.3 Nonlinear Stationary Waves

8.4 Conclusions

References

9 Modelling of a Hydrogen Saturated Layer Within the Micropolar Approach

9.1 Introduction

9.2 Basic Equations of Micropolar Media

9.3 Axially-symmetrical Problem

9.4 Results

9.5 Conclusions and Outlook

References

10 Types of Physical Nonlinearity in the Theory of Constitutive Relations and the Generalized Poynting Effect

10.1 Various Definitions of Tensor Nonlinearity and Their Equivalence

10.2 Establishing experiments to find the material functions B0, B1 and B2

10.3 The Generalized Poynting Effect

References

11 Eigenstresses in a Nonlinearly Elastic Sphere with Distributed Dislocations

11.1 Introduction

11.2 Input Relations

11.3 Spherically Symmetric State

11.4 Transformation of the Boundary Value Problem

11.5 Problem for Semi-linear Material

11.6 Problem for Incompressible Material

11.7 Numerical Results

11.8 Conclusion

References

12 Fundamental Solution for the Generalized Plane Stress of a Nanoplate

12.1 Introduction

12.2 Problem formulation

12.3 Green Functions

12.4 Summary and Conclusions

References

13 Isotropic Linear Viscoelastic Reduced Cosserat Medium: an Acoustic Metamaterial and a First Step to Model Geomedium

13.1 Introduction

13.2 Reduced Linear Isotropic Cosserat Viscoelastic Model

13.2.1 General Equations

13.2.2 Constrained Reduced Cosserat Medium

13.3 Dispersional Relations and Attenuation Factor

13.3.1 General Equations

13.3.2 Detailed Analysis of Shear Waves Dispersion and Dissipation

13.3.2.1 Low Frequencies

13.3.2.2 High Frequencies

13.3.2.3 Attenuation Factor

13.3.2.4 Translational Viscosity (b = 0)

13.3.2.5 Rotational viscosity (n = 0)

13.4 Conclusion

References

14 Numerical Analysis of Free Vibrations of Piezoelectric Cylinders

14.1 Introduction

14.2 Basic Relations

14.3 Spline-collocation Method

14.4 Finite-element Method

14.5 The Results Obtained

14.6 Conclusions

References

15 Qualitative Investigations of Experiments Performed on 3D-FDM-printed Pantographic Structures Made out of PLA

15.1 Introduction

15.2 Materials and Methods

15.3 Results and Discussion

15.3.1 Quasi-static experiments

15.3.2 Cyclic Long-term Experiments

15.4 Conclusion

References

16 Calculation of Stress Intensity Factors for an Arbitrary Oriented Penny-shaped Crack Under Inner Pressure in an Orthotropic Electroelastic Material

16.1 Introduction

16.2 Basic Equations and Statement of the Problem

16.3 Solution Method

16.4 Analysis of the Results of Numerical Investigations

16.5 Conclusion

References

17 On the Quasi-Static Approximation to the Initial Traction Boundary Problem of Linear Elastodynamics

17.1 Introduction

17.2 Preliminaries

17.2.1 Notation

17.2.2 Inequalities

17.3 Exact Initial Boundary Value Problem

17.3.1 Statement of Problem

17.3.2 Conservation Law for Exact Problem

17.4 Quasi-static Approximation

17.4.1 Formulation

17.4.2 Conservation Laws

17.5 Continuous Dependence on Inertia

17.6 Continuous Dependence of Inertia on Prescribed Surface Tractions and Body-force

17.7 Concluding Remarks

References

18 Delamination Buckling in Composite Plates: an Analytical Approach to Predict Delamination Growth

18.1 Introduction

18.2 Model Description

18.3 Energy Formalism

18.3.1 Total potential energy principle

18.3.2 Energy Release Rate

18.4 Results

18.5 Conclusions

References

19 Dynamical Vector Fields on Pantographic Sheet: Experimental Observations

19.1 Introduction

19.2 Setup of the experiment

19.3 Qualitative analysis of the results

19.4 Conclusions and perspectives

References

20 Numerical Solution of the Tri-harmonic KIRCHHOFF Plate Equation Resulting from a Strain Gradient Theory

20.1 Introduction

20.2 The Tri-harmonic Plate Equation

20.2.1 Modified Strain Gradient Theory

20.2.2 KIRCHHOFF Plate assumptions

20.2.3 Variation of the Modified Strain Energy of a KIRCHHOFF Plate

20.2.4 The Governing Tri-harmonic Plate Equation

20.2.5 A NAVIER-Solution with FOURIER-Series

20.3 A C1– continuous Finite Element Approach

20.3.1 The Weak Form of the PDE

20.3.2 Two Dimensional HERMITE Finite Element Formulation

20.3.3 The Element and Global Stiffness Matrix and Realization of the Boundary Condition

20.4 Results

20.4.1 Concerning the Convergence

20.4.2 Results for the Size Effect

20.4.3 Analysis of the C1–continuity

20.5 Conclusions

References

21 Implications of the Lagrange Identity in Thermoelasticity of Dipolar Bodies

21.1 Introduction

21.2 Basic Equations

21.3 Main Result

21.4 Conclusion

References

22 Theory and Computation of Nonlinear Damage Accumulation for Lifetime Prediction

22.1 Introduction

22.2 Modelling of Damage Growth

22.2.1 Creep Damage Evolution

22.2.2 Fatigue Damage Evolution

22.3 Damage Accumulation

22.3.1 Creep and Fatigue Damage Accumulation

22.3.2 Modelling of Nonlinear Damage Accumulation

22.3.3 Discussion of Modelling Approach

22.4 Parameter Identification

22.5 Application to Lifetime Prediction for Adhesive Joints

22.6 Conclusion

References

23 A Non-equilibrium Approach Concerning Thermostatics of Schottky Systems

23.1 Introduction

23.2 Schottky Systems

23.2.1 State Spaces and Processes

23.2.2 The First Law

23.2.3 Entropy Rate and Second Law

23.3 Contact Quantities

23.3.1 Defining Inequalities

23.3.2 Internal Energy and Contact Temperature

23.4 Thermostatic Approach for Schottky Systems

23.5 The Embedding Theorem

23.6 Summary

References

24 On the Temperature Gradient in the Standard Troposphere

24.1 Introduction

24.2 Equations of Balance and Constitutive Relations

24.3 Application to the Troposphere

24.4 Discussion

24.5 Remark on the Lack of Isotropy of Air in a Gravitational Field

References

25 A Brief History of Mechanical Stress and the Method of Experimental Micromechanics with the Raman Microprobe

25.1 Introduction

25.1.1 A bit of History on the Concepts of Stress and Strain

25.1.2 Residual Stress Ghosts from the Industrial World

25.1.3 The Need for a Microscopic and Contactless Probe for Stress

25.2 Working Algorithms for Stress Assessments by Raman Spectroscopy

25.2.1 Step 1: Extracting Crystallographic Information with Polarized Probes

25.2.2 Deconvoluting the Stress Tensor Elements

25.2.3 Deconvoluting the Raman Probe in Space

25.3 Applications of Raman Stress Analysis to Modern Devices

25.3.1 Miniaturized Multilayered Ceramic Condensers

25.3.2 Ceramic Femoral Heads in Artificial Hip Joint

25.4 Conclusion

References

26 Analytical Solutions of 2-dimensional Second Gradient Linear Elasticity for Continua with Cubic-D4 Microstructure

26.1 Introduction

26.2 Outline of the Model

26.3 Some Explicit Computations for the Identification Procedure

26.3.1 Stress and Hyperstress in Terms of the Displacement Field

26.3.2 Partial Differential Equations and Boundary Conditions

26.4 Analytical Solutions of Homogeneous Second Gradient Model

26.4.1 Simple Tension Test

26.4.2 Simple Shear Test

26.4.3 Heavy Sheet

26.4.4 Non-conventional Bending

26.4.5 Trapezoidal Case

26.5 Conclusion

References

27 Gradient Theory of Adhesion and Tabor Parameter

27.1 Introduction

27.2 Method of Dimensionality Reduction Formulation of Johnson-Kendall-Roberts Theory

27.3 Generalization of Method of Dimensionality Reduction for Adhesion with Finite Length Scale

27.4 Conclusion

References

28 Cavity Flow of a Micropolar Fluid - a Parameter Study

28.1 Introduction

28.2 Theory of Micropolar Fluids

28.2.1 Governing Local Balance Equations

28.2.2 Constitutive Laws and Field Equations

28.3 Problem Statement

28.3.1 Dimensionless Equations

28.3.2 Boundary Conditions and Boundary Value Problems

28.3.3 Reference Solution

28.4 Numerical Treatment

28.4.1 Convergence Analysis

28.5 Results and Discussion

28.5.1 Vertical and Horizontal Profiles

28.5.2 Analysis of the Angular Velocity Field

28.6 Conclusion

Appendix:Weak Forms

References

29 Graded Insulation to Improve High Pressure Resistance in Deepwater Flowlines: a Closed Form Analytical Elastic Solution

29.1 Introduction

29.2 Analytical Modelling

29.2.1 Problem Formulation

29.2.2 Method of Solution

29.3 Results and Discussion

29.4 Conclusions

Appendix

References

30 On Brake Pad Shim Characterization: a Homogenization Approach and Finite Element Analysis

30.1 Introduction

30.2 Modeling of Shims

30.2.1 Continuous Mechanical Systems

30.2.2 Constrained Layer Damping Theory

30.3 Experimental Investigations

30.4 Finite Element Approach

30.4.1 Damping

30.4.2 Stiffness - Homogenization Theory

30.4.3 Modeling

30.5 Results and Validation

30.6 Conclusion and Outlook

References

31 Teaching Mechanics: Inequalities in Statically Indeterminate Static Friction Problems

31.1 Introduction

31.2 Aim of the First Example

31.3 First Example

31.4 Aim of the Second Example

31.5 Second Example

31.6 Discussion

References

32 Initial Damage of Composite Materials

32.1 Introduction

32.2 General Statements

32.3 Conclusion

References

33 How the Properties of Pantographic Elementary Lattices Determine the Properties of Pantographic Metamaterials

33.1 Introduction

33.2 Description of Pantographic Units used to form Pantographic Micro-structures

33.3 How the unit Properties Determine the Meso-stiffnesses

33.4 Meso-macro Identification

33.5 Concluding Remarks and Future Challenges

References

34 Metallic Interconnection Technologies for High Power Vertical Cavity Surface Emitting Lasers Modules

34.1 Introduction

34.2 1st Level Interconnection—Mounting GaAs Dies with VCSEL Array onto Ceramic-based Substrate

34.2.1 Application of Metallic Interconnection Technologies

34.2.2 Reliability Testing of Soldered and Silver Sintered 1st Level Interconnects

34.3 2nd Level Interconnection—Mounting DCB onto a Micro Channel Water Cooler by Pressure Assisted Silver Sintering

34.4 Conclusions

References

35 Coupled Thermal and Electrochemical Diffusion in Solid State Battery Systems

35.1 Introduction

35.2 Electrochemo-thermo-mechanical Diffusion

35.2.1 First Law of Thermodynamics

35.2.2 Second Law of Thermodynamics

35.3 Constitutive Relations

35.4 Numerical Examples

35.4.1 Thermal Diffusion

35.4.2 Multifield Chemical Reactions

35.5 Conclusion

References

36 Nonclassical Bending Behavior of Thin Strips of Photochromic Liquid Crystal Elastomers Under Light Illuminations

36.1 Introduction

36.2 TBT Model for Optical-mechanical Bending of Beam Shaped Specimens

36.2.1 Optical-mechanical Constitutive Relations

36.2.2 Timoshenko Beam Model

36.3 Examples of Cantilever Beams and Numerical Results

36.3.1 First Case: no Load

36.3.2 Second Case: a Point Load

36.3.3 Third Case: Uniformly Distributed Load

36.4 Discussion About Shear Correction Factor

36.5 Conclusions

References

37 A Simple Qualitative Model for the Pressure-induced Expansion and Wall-stress Response of Fluid-filled Biological Channels

37.1 Introduction

37.2 Classical Pressure-flow Relations

37.3 Simple Approximations of Radial Deformation

37.3.1 Estimate of Wall Stresses

37.3.2 Determination of the Compliance Constant

37.3.3 Stress Correction Factors

37.3.4 Corrected Material Failure Criteria

37.4 Subsequent Flow Changes

37.5 Closing Remarks

References