Viscoelastic Model
Elastic materials having the capacity to dissipate the mechanical energy due to viscous effects are characterized as viscoelastic materials. For multiaxial stress state, the constitutive relation can be written as:
where e and f are the deviatoric and volumetric strains; G(t  t
) and K(t  t
) are shear and bulk relaxation functions. The relaxation functions can then be represented by the mechanical model, (shown in this figure
) which is usually referred to as a Generalized Maxwell Model having the expressions as the following:
where G
0 and K
0 are the initial shear and bulk moduli (t = 0) given by: G
0
= E/2(1+v) and K
0
= E/3(12v).
g
i, k
i, t
i
G, and t
i
K are the ith shear and bulk moduli and corresponding times.
The effect of temperature on the material behavior is introduced through the timetemperature correspondence principle. The mathematical form of the principle is:
where g t is the reduced time and g is the shift function. The WLF (WilliamsLandelFerry) equation is used to approximate the function:
where TO is the reference temperature which is usually picked as the Glass transition temperature; C1 and C2 are material dependent constants.
The required parameters include the following:
Parameter

Symbol

Description

Linear Elastic Parameters

EX

Elastic modulus

NUxy

Poisson's ratio

GXY (optional)

Shear modulus

Relaxation Function Parameters

G1, G2, G3,..., G8

represent g1, g2, ...,g8 in the Generalized Maxwell Model equations

TAUG1, TAUG2, ....., TAUG8

represent t1g, t2g,..., t8g in the Generalized Maxwell Model equations

K1, K2, ..., K8

represent k1, k2, ...,k8 in the Generalized Maxwell Model equations

TAUK1, TAUK2, ..., TAUK8

represent t1k, t2k,..., t8k in the Generalized Maxwell Model equations

WLF Equation Parameters

REFTEMP

represents T0 in the WLF equation

VC1

represents C1 in the WLF equation

VC2

represents C2 in the WLF equation

When defining a shear or bulk relaxation curve under the Tables & Curves tab, the first point of the curve is the G
1
or K
1
moduli at time t
1. At time t = 0, the program automatically computes G
0
or K
0 from the Elastic modulus and Poisson's ratio.
The viscoelastic material model can be used with the draft and high quality solid and thick shell elements.