Abbreviations
1
γ
Shear strain
δ ij
Kronecker delta
ε
Total strain tensor
E
p
Plastic strain rate
ρ
Mass density
σ
Total stress tensor
σ
0
First Piola-Kirchhoff stress tensor
e σ
Second Piola-Kirchhoff tensor
φ
Dissipation potential
Φ
Thermodynamic state index
Ψ
Helmholtz-free energy
A
Area
b
Body force per unit mass
B
À1
Cauchy deformation tensor
C
Green deformation tensor
D
Rate of deformation tensor
E
Lagrange strain tensor
E total
Total energy
F
Deformation gradient tensor
F
Force
F
Plasticity yield surface
e
F
Second Piola-Kirchhoff force
g
Gibbs function
h
Enthalpy
1 Most of the time, I tried to use the same character to define a variable. However, due to large
number of characters needed to define variables, some characters were used more than once
to define different variables. In order to clarify the definitions, each variable is defined in each
subsection.
xv
1
γ
Shear strain
δ ij
Kronecker delta
ε
Total strain tensor
E
p
Plastic strain rate
ρ
Mass density
σ
Total stress tensor
σ
0
First Piola-Kirchhoff stress tensor
e σ
Second Piola-Kirchhoff tensor
φ
Dissipation potential
Φ
Thermodynamic state index
Ψ
Helmholtz-free energy
A
Area
b
Body force per unit mass
B
À1
Cauchy deformation tensor
C
Green deformation tensor
D
Rate of deformation tensor
E
Lagrange strain tensor
E total
Total energy
F
Deformation gradient tensor
F
Force
F
Plasticity yield surface
e
F
Second Piola-Kirchhoff force
g
Gibbs function
h
Enthalpy
1 Most of the time, I tried to use the same character to define a variable. However, due to large
number of characters needed to define variables, some characters were used more than once
to define different variables. In order to clarify the definitions, each variable is defined in each
subsection.
xv