Commonly Used Symbols

Appendix A Commonly Used Symbols In an interdisciplinary book such as this, we have found it too demanding to stick to a unique mathematical notation throughout. We have attempted to standardise on commonly used quantities as defined in this appendix but for individual examples we have mainly used the notation of the original authors of the example. Such terms are always defined where they are first used. Symbol

Quantity

Units

D, Dij

Stretching tensor

s

e

Specific internal energy

J kg

F, Fij

Deformation gradient

Dimensionless

J

Jacobian of a matrix

Dimensionless

P

Hydrostatic pressure

Pa

P

(Mean stress)/3

1 1

Pa

R

Rotation matrix

Dimensionless

s

Specific entropy

J kg

T

Temperature

K

t

Time

s

V

Volume

m3

X, Xi

Cartesian coordinates in a reference state

m

x, xi

Cartesian coordinates in the current or deformed state

m

x, y, z

Cartesian coordinates

m

ε, εij

Small strain tensor

Dimensionless

F

Specific dissipation function

J kg

r

Mass density

kg m

1

1

K

s

1

1

3

(Continued)

609

610

APPENDIX A. COMMONLY USED SYMBOLS

Symbol

Quantity

Units

s, sij

Cauchy stress

Pa

J

Specific Helmholtz energy

J kg

1

MATHEMATICAL SYMBOLS ab

Scalar product of vectors a and b

ab

Vector product of vectors a and b

a5b

Diadic product of vectors a and b

A: B

Scalar product of tensors A and B

EAF

Jump in A CHEMICAL SYMBOLS

A; SiO2

The chemical species, A; silica

a; [SiO2]

The concentration (or activity) of A; the concentration (or activity) of SiO2

mol 1, kg

1