Hygrothermoelasticity

1 Classical diffusion theories.- 1.1 Introduction.- 1.2 Thermal diffusion: heat conduction.- 1.2.1 Law of heat conduction.- 1.2.2 Temperature field.- 1.3 Moisture diffusion.- 1.3.1 Moisture concentration field.- 1.3.2 Non-steady state moisture distribution.- 1.3.3 Time dependence.- 1.3.4 Temperature variation.- 1.3.5 Effect of relative humidity.- 1.3.6 Non-Fickian behavior.- 1.3.7 Dependency on concentration history.- 1.3.8 Influence of internal stress.- 1.3.9 Experimental results.- 1.4 Appendix: Anisotropic character of diffusion coefficient in fiber reinforced composite.- References.- 2 Coupled diffusion of temperature and moisture.- 2.1 Introduction.- 2.2 Dufour and Soret effects.- 2.3 Linear dependence of moisture and temperature in two-phase system.- 2.3.1 Vapor diffusion.- 2.3.2 Heat diffusion.- 2.3.3 Coupled diffusion.- 2.4 Solution by normal coordinates.- 2.4.1 One-dimensional.- 2.4.2 Three-dimensional.- 2.4.3 Time dependent external conditions.- 2.5 Evaluation of coupling constants.- 2.5.1 Change in moisture content.- 2.5.2 Change in heat content.- 2.5.3 Numerical results on coupling constants.- 2.6 Temperature and moisture diffusion in T300/5208 graphite/epoxy system.- 2.6.1 Determination of coupling coefficients.- 2.6.2 Transient temperature and moisture distribution in slab.- 2.7 Appendix A: Additional models of moisture and temperature coupling.- 2.7.1 Direct determination of moisture mass.- 2.7.2 Interaction of moisture energy.- 2.7.3 Phase transformation of liquid and vapor.- 2.8 Appendix B: Diffusion parameters for simultaneous moisture and temperature boundary conditions.- References.- 3 Analytical solutions of transient hygrothermal stresses in elastic bodies.- 3.1 Introduction.- 3.2 One-dimensional stress and strain expressions.- 3.2.1 Small deformation theory.- 3.2.2 Internal stresses.- 3.2.3 Material properties.- 3.3 Symmetric through thickness diffusion.- 3.3.1 Surface moisture boundary condition.- 3.3.2 Surface temperature boundary condition.- 3.4 Anti-symmetric through thickness diffusion.- 3.4.1 Sudden moisture change.- 3.4.2 Sudden temperature change.- 3.5 Spherical cavity in infinite solid.- 3.5.1 Problem statement and solution form.- 3.5.2 Discussion of special cases.- 3.5.3 Displacement and stress expressions.- 3.5.4 Coupled and uncoupled solutions.- 3.6 Appendix A: Elastic properties of T300/5208 graphite/epoxy laminate.- 3.7 Appendix B: General solution for coupled diffusion problems.- 3.7.1 Moisture and temperature distribution.- 3.7.2 Hygrothermal stresses.- References.- 4 Time dependent finite element formulation of hygrothermal elasticity problems.- 4.1 Introduction.- 4.2 Finite element applied to coupled diffusion equations.- 4.2.1 Discretization of temperature and moisture field.- 4.2.2 Variational calculus.- 4.2.3 Matrix decomposition.- 4.3 Laplace transformation and eigenvalue formulation.- 4.3.1 Surface moisture boundary condition.- 4.3.2 Surface temperature boundary conditions.- 4.3.3 Comparison with exact solution.- 4.4 Finite element hygrothermal stress formulation.- 4.4.1 Stress and strain relation.- 4.4.2 Strain and displacement expressions.- 4.5 Sudden localized heating of semi-infinite solid.- 4.5.1 Moisture and temperature distribution.- 4.5.2 Hygrothermal stresses.- 4.6 Concentration of diffusion and stresses around a circular cavity.- 4.6.1 Finite element grid pattern.- 4.6.2 Change of surface moisture.- 4.6.3 Change of surface temperature.- 4.6.4 Radial, circumferential and transverse normal stresses.- 4.7 Redistribution of hygrothermal stresses around an elliptical opening.- 4.7.1 Grid pattern for region with elliptical hole.- 4.7.2 Moisture boundary condition.- 4.7.3 Temperature boundary condition.- 4.7.4 Transient hygrothermal stresses.- 4.8 Appendix A: Variational procedure.- 4.9 Appendix B: Derivation of ?TI and ?CI.- 4.10 Appendix C: Modal decomposition.- References.- 5 Coupled theory of heat, moisture and deformation.- 5.1 Introduction.- 5.2 General information.- 5.2.1 Irreversible thermodynamics.- 5.2.2 Coupled linear elastic deformation.- 5.3 Plane hygrothermoelasticity.- 5.3.1 Plane stress.- 5.3.2 Plane strain.- 5.4 Method of hygrothermoelastic potential.- 5.5 Physical constants in deformation coupled theory.- 5.5.1 Moisture boundary conditions.- 5.5.2 Temperature boundary conditions.- 5.6 Uncoupled theories.- References.- 6 Complex variable formulation of hygrothermoelasticity problems.- 6.1 Introduction.- 6.2 Stress function.- 6.3 Complex formulation.- 6.4 Conformai transformation.- 6.4.1 Mapping function.- 6.4.2 Curvilinear coordinates.- 6.5 Circular region subjected to diffusion and deformation.- 6.5.1 Coupled solution.- 6.5.2 Displacement potential.- 6.5.3 Uniform compression.- 6.5.4 Suddenly applied compression.- 6.6 Remote extension of region with cavity.- 6.6.1 Superposition scheme.- 6.6.2 Circular cavity in infinite domain.- References.- 7 Numerical analysis of coupled diffusion and deformation problems.- 7.1 Introduction.- 7.2 Basic formulation.- 7.3 Smooth slab subjected to sudden moisture change.- 7.4 Smooth slab subjected to sudden temperature change.- 7.5 Diffusion and stress boundary conditions applied to body with circular cavity.- 7.5.1 Sudden moisture rise on cavity.- 7.5.2 Sudden temperature rise on cavity.- 7.6 Hygrothermal stresses around narrow elliptical cavity.- 7.6.1 Sudden moisture change on elliptical cavity.- 7.6.2 Sudden temperature change in elliptical cavity.- 7.6.3 Coupled thermal stresses around ellipse.- References.- 8 The strain energy density function.- 8.1 Introduction.- 8.2 Energy per unit volume.- 8.2.1 Isothermal and constant moisture.- 8.2.2 Non-isothermal and moisture change.- 8.3 Energy density decay near a crack.- 8.3.1 Moisture rise on crack.- 8.3.2 Temperature rise on crack.- 8.3.3 Coupled thermoelasticity.- 8.4 Failure criterion.- 8.4.1 Stationary values.- 8.4.2 Failure interpretation.- 8.4.3 Irreversibility.- References.- Author index.