List of Symbols

$u(x,y,z)$	Displacement field
$u x$	Displacement field in the x-direction
$uy$	Displacement field in the y-direction
$uz$	Displacement field in the z-direction
$Dx$	Difference between displacement fields in the x-direction
$α$ , $β$	Congruent skew angles in the xy plane
$γ$ , $ϕ$	Congruent skew angles in the yz plane
$ω$ , $θ$	Congruent skew angles in the xz plane
$ϵii$	Normal strain in the i-direction
$γij$	Engineering shear strain in the ij plane
$F$	External force applied in a solid
$A$	Surface area
$σ$	Stress tensor
$ϵ$	Strain tensor
$σii$	Normal stress in the i-direction
$σij$	Shear stress in the ij plane
$T(ex)$	Traction in the x-direction
$T(ey)$	Traction in the y-direction
$T(ez)$	Traction in the z-direction
$c$	Linear mapping between stress and strain

$E$	Young’s modulus
$ν$	Poisson ratio
$τ$	Shear stress
$G$	Shear modulus
$ΔT$	Temperature variation
$U T$	Total strain energy per unit of area
$UH$	Hydrostatic strain energy per unit of area
$UD$	Distortion strain energy per unit of area
$V$	Sub-space with infinity dimension of continuous with piecewise continuous derivatives
$v$	An element in V space
$ϕ j$	FEM basis function
$V h$	Discrete sub-space of V
$uh$	A sample function in the sub-space $Vh$
$vh$	A second sample function in the sub-space $Vh$
$Ps−1(t)$	Lagrangian polynomial in the BDF method
$σrr$	Normal stress in r direction of a cylindrical coordinate system
$σϕϕ$	Normal stress in $θ$ direction of a cylindrical coordinate system
$σ T$	Thermal stress due to temperature variation
$B(t)$	Bézier polygon
$˙γ$	Strain rate in the low temperature dislocation glide model

$γ0$	Pre-exponential factor
$ΔF$	Activation energy of an obstacle
$σs$	Shear stress in the low temperature dislocation glide model
$T$	Temperature
$T0$	Initial temperature
$k$	Boltzmann constant
$ˆτ$	Shear stress required to trigger dislocations movement
$ϵT$	Thermal strain
$ϵ e$	Elastic strain
$ϵp$	Plastic strain
$σF$	Stress in the film
$Mf$	Biaxial modulus
$s$	Schmid factor
$δ ij$	Dirac delta
$t$	Time
$˙ϵ$	Strain rate tensor
$˙ϵij$	Components of the strain rate tensor
$E 1$	System free energy per unit of area in Hoffman’s model
$E0$	Free surface energy per unit of area ot island’s top in Hoffman’s model
$γsv$	Free surface energy per unit of area of the island’s lateral surface

$γgb$	Energy per unit of area spent in the formation of a grain boundary
$Δ$	Critical distance between two islands in Hoffman’s model
$E2$	Free energy per unit of area after coalescence in Hoffman’s model
$GR$	Strain energy release rate
$Kf$	Stress intensity factor
$R$	Island radius
$Y0$	Height of island coalescence
$Z0$	Maximum displacement of the island surface due to coalescence
$Etotal$	Total energy in Seel’s model
$DR$	Deposition rate