Elastic materials having the capacity to dissipate the mechanical energy due to viscous effects are characterized as viscoelastic materials. For multi-axial 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

where G0 and K0 are the initial shear and bulk moduli (t = 0) given by: G0 = E/2(1+v) and K0 = E/3(1-2v).

gi, ki, tiG, and tiK are the i-th shear and bulk moduli and corresponding times.

The effect of temperature on the material behavior is introduced through the time-temperature correspondence principle. The mathematical form of the principle is:

where g t is the reduced time and g is the shift function. The WLF (Williams-Landel-Ferry) 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 G1 or K1 moduli at time t1. At time t = 0, the program automatically computes G0 or K0 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.

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