Nomenclature
List of definition
$\underset{=}{S}$/S	Second Piola-Kirchoff stress tensor	Papp	Applied pressure
$\underset{=}{C}$/C	Right Cauchy-Green strain tensor	a, b, w	Dimension parameters
w	Internal potential energy	D	Degree of intimate contact
$\underset{=}{F}$/F	Deformation gradient tensor	η	Matrix viscosity
I1, I2, I3… In	Invariants	k1, k2	Geometric ratios
Aelong1, Aelong2	Parameter A related to elongation mode in warp, weft direction	A0, An, An+1	Parameter A at initial state, before, after nth time increment
Aχ1, Aχ2	Parameter A related to bending mode in warp, weft direction	Ashear, Acomp	Parameter A related to in-plane shearing mode, and compression mode
T	Temperature	${\mathrm{W}}_{\mathrm{ext}},{\mathrm{W}}_{\mathrm{int}},{\mathrm{W}}_{\mathrm{acc}}$	External, internal and inertial work
Ei	Young’s modulus of spring element i	$\mathsf{\delta }u$	Virtual displacement vector
${\eta }_i$	Viscosity of dashpot i	u, $\ddot{u}$	Displacement and acceleration vectors
τi	Relaxation time	$F_{\mathrm{ext}}, F_{\mathrm{int}}$	Exterior and interior load vectors
γi	Relative weight	Superscript α	Index related to bending, membrane, or pinching deformation
$\underset{=}{Q}$	Stress-like internal variable	σ	Cauchy stress tensor
$\underset{=}{H}$	Algorithmic solution of Q	B	Strain interpolation matrix
Dk, Ci	Polynomial parameters	Ωe	Volume of element
ψ	Free energy function	T1, T2	Tensile stiffness in two directions of yarn
tn, tn+1	Times at the beginning and end of the nth time increment	Mχ1, Mχ2	Bending moments in two directions of yarn
Δtn	nth time increment	B1, B2	Material parameters related to bending
		α, β	Thermo-dependent parameters