WHY MATERIALS MATTER? - THEORY
Franz-Josef Ulm
First Edition February 2016
Contents
1 The Mechanics-of-Materials Science and Engineering Para- digm 1 1.1 Scales of Observation 1 1.2 Mechanics of Materials Science and Engineering 2
I Elasticity-Principles of Reversibility
4
2 Elasticity 5 2.1 Thermodynamics: First and Second Law 5 2.2 Elasticity Tensor : 6 2.3 Experimental Determination of Isotropic Elasticity Properties 9 2.3.1 Mechanical (Static) Testing : 9 2.3.2 Dynamic Testing: Acoustic Measurements 11 2.3.3 Elasticity Properties from Contact Indentation Exper- iments 15 2.4 Elasticity of Composite Materials 19 2.4.1 Displacement Approach: Strain Localization 20 2.4.2 Stress Approach: Stress Localization 21 2.4.3Voigt-Reuss Bounds 22
3 Thermo-Elasticity 3.1 Thermodynamics 3.2 Linear Thermo-Elastic Behavior: Thermal Expansion 3.3 Thermal Eigenstresses : 3.4 An Instructive Exercise: Thermal Mismatch in Composite Ma- terials 3.5 Thermo-Elasticity of Composite Materials
24 24 25 27
28 30
2
3.5.1 Hill Lemma 3.5.2 Displacement Approach: Eigenstress 3.5.3 Stress Approach: Eigenstrain
31 31 33
4 Poro-Elasticity 36 4.1 Porosity 36 4.2 Displacement Approach: Biot-Coussy Theory of Porous Media 37 4.3 Adding the Fluid to the System: Undrained Properties 43 4.4 An Instructive Exercise: Consolidation of a Soil Layer 44
5 Eigenstresses in Structural Mechanics 47 5.1 Beam Section Equations : 47 5.2 Eigen-Forces and Eigen-Moments 48 5.3 Applications 50 5.3.1 Bi-Material Strip: Bending due to Thermal Mismatch . 50 5.3.2 Eigenstresses in Pavements due to Temperature Gradient 53
A The First Appendix
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