List of Symbols

Overview of Solid Mechanics and Finite Element Method

Xi

Lagrangian Cartesian Coordinates, i=1,2,3

xi

Eulerian Cartesian Coordinates, i=1,2,3

u

Displacement Field

lij

Lagrange Infinitesimal Strain Tensor

εij,ε

Eulerian Infinitesimal Strain Tensor

t

Stress Vector

σ

Cauchy Stress Tensor

τij

Shear Stress Components

F

Body Force

b

Force per Unit of Mass

ρ

Density of a Body

σmises

Von Mises Effective Stress

εe

Elastic Strain Tensor

ε p

Plastic Strain Tensor

C

Elasticity Tensor

M

Compliance Tensor

λ

Lame Constant

E

Young’s Modulus

ν

Poisson’s Ratio

μ

Shear Modulus

α

Coefficient of Thermal Expansion

δu

Virtual Displacement

δεij

Virtual Strain Components

Stress Evolution during 3D IC Stacking using Open TSVs

pm

Pressure of an Indenter

Y

Uniaxial Compressive Yield Stress of a Sample

a

Contact Area between Indenter and Sample

E*

Reduced Modulus

R

Radius of an Indenter

P

Applied Load by Indenter

d

Penetration Depth in a Sample

Qp

Plastic Potential

I1

First Invariant of Cauchy Stress Tensor

J2

Second Invariant of Cauchy Stress Tensor

J3

Third Invariant of Cauchy Stress Tensor

ε˙p

Plastic Strain Tensor Increment

ε˙pe

Effective Plastic Strain Rate

Fy

Yield Function

σys0

Initial Yield Stress

ETiso

Isotropic Tangent Modulus

Fracture Mechanics and Delamination in Open TSV

ZI

Westergaard Function

KI,KII,KIII

Stress Intensity Factors for mode I, II, and III, respectively

Φ

Airy Stress Function

ε

Bimaterial Constant

G

Energy Release Rate

Gc

Critical Energy Release Rate

Π

Total Potential Energy

U

Total Strain Energy

W

Strain Energy Density

V

Potential of External Force

γ

Fracture Surface Energy

J

J-Integral

Simulation of Intrinsic Stress Build-Up in Thin Metal Films

R

Radius Parameter

Ri

Initial Radius of the Island

Rfr

Frozen-In Radius

hf

Film Thickness

f

Surface Stress

ΔP

Laplace Pressure

γs

Surface Energy

γgb

Grain Boundary Energy

hgb

Grain Boundary Height

vg

Deposition Rate

vgb

Grain Boundary Velocity

μs

Surface Chemical Potential

μgb

Grain Boundary Chemical Potential

Ngb

Number of Atoms Moving from the Surface to Grain Boundary

D

Atom Diffusivity

a

Height of an Atomic Step

Cs

Fractional Coverage of Adatoms

σT

Tensile Stress

σC

Compressive Stress

Ω

Atomic Volume

r

Island Radius at the Coalescence Point

L

Grain Size

ws

Width of the Scallops

hs

Height of the Scallops