MATFVE

Bulk Data Entry Defines material properties for frequency-dependent viscoelastic materials.

Format 1 (`TYPE`=FORMULA)

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
MATFVE	`MID`	`FORMULA`
	`R1`	`I1`	`a`	`R1k`	`I1k`	`b`

Format 2 (`TYPE`=TABLE)

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
MATFVE	`MID`	`TABLE`
	`TID1`	`TID2`	`TID3`	`TID4`

Format 3 (`TYPE`=PRONY)

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
MATFVE	`MID`	`PRONY`			`gD1`	`tD1`	`gB1`	`tB1`
	`gD2`	`tD2`	`gD3`	`tD3`	`gD4`	`tD4`	`gD5`	`tD5`
	`gB2`	`tB2`	`gB3`	`tB2`	`gB4`	`tB4`	`gB5`	`tB5`

Format 4 (`TYPE`=PRELOAD)

(1)	(2)	(3)	(4)	(5)
MATFVE	`MID`	`PRELOAD`
	`EUNIAXI`
	`El`	`Es`	`f`	$ε$
	etc.
	`EVOLUME`
	`Kl`	`Ks`	`f`	`J`
	etc.

Example

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
MATVE	2	PRONY			0.25	5e-2	0.25	5e-2

Definition

Field	Contents	SI Unit Example
`MID`	Unique material identification number. No default (Integer > 0)
`TYPE`	Frequency-dependent visco-elastic material model type. FORMULA 4 TABLE 5 PRONY 6 PRELOAD 7 No default
`R1`	Real part of the deviatoric part for the FORMULA type. Default = blank (Real)
`I1`	Imaginary part of the deviatoric part for the FORMULA type. Default = blank (Real)
`a`	A real number for the deviatoric part for the FORMULA type. Default = blank (Real)
`R1k`	Real part of the bulk part for the FORMULA type. Default = blank (Real)
`I1k`	Imaginary part of the bulk part for the FORMULA type. Default = blank (Real)
`b`	A real number for the bulk part for the FORMULA type. Default = blank (Real)
`TID1`	Table ID (`TABLEDi` only) to specify the real part of the deviatoric part. Default = blank (Integer > 0)
`TID2`	Table ID (`TABLEDi` only) to specify the Imaginary part of the deviatoric part. Default = blank (Integer > 0)
`TID3`	Table ID (`TABLEDi` only) to specify the real part of the bulk part. Default = blank (Integer > 0)
`TID4`	Table ID (`TABLEDi` only) to specify the Imaginary part of the bulk part. Default = blank (Integer>0)
`gDi`	Modulus ratio for the $i$ -th deviatoric Prony series. No default (Real > 0.0)
`tDi`	Relaxation time for the $i$ -th deviatoric Prony series. No default (Real > 0.0)
`gBi`	Modulus ratio for the $i$ -th bulk Prony series. No default (Real > 0.0)
`tBi`	Relaxation time for the $i$ -th bulk Prony series. No default (Real > 0.0)
`EUNIAXI`	Continuation line to indicate the storage and loss moduli from uniaxial tests when `TYPE` = PRELOAD.
`EVOLUME`	Continuation line to indicate the storage and loss moduli from volumetric tests when `TYPE` = PRELOAD.
`El`	Uniaxial loss modulus. No default (Real)
`Es`	Uniaxial storage modulus. No default (Real)
`f`	Frequency. No default (Real ≥ 0.0)
$ε$	Uniaxial nominal strain. No default (Real)
`Kl`	Bulk loss modulus. No default (Real)
`Ks`	Bulk storage modulus. No default (Real)
`J`	Volume ratio between current and original volumes. No default (Real > 0.0)

Comments

The long-term response is given by an elastic material description, which needs to have the same MID. MATHE/MAT1/MAT9 are supported.
CHEXA, CTETRA, CPENTA, CPYRA elements are supported.
Considering a function of deviatoric relaxation in the time-domain, $g * (t)$ .(1)
$g * (t) = \sum_{i} \frac{G_{i}}{G_{\infty}} e^{- \frac{t}{τ_{i}}}$

The subscript $i$ indicates the $i$ -th component in the Prony series.

$G_{\infty}$

Long-term deviatoric modulus input.

$G_{i}$

Deviatoric modulus ratio.

$τ_{i}$

Relaxation time.

The Fourier transform of this function is:(2)
$\tilde{g} * (ω) = F (g * (t)) = R + i I$

Where, $F$ is the Fourier transformation. Equation 2 is for the frequency-dependent deviatoric relaxation. Similarly, the equation for the frequency-dependent bulk relaxation can be written in an analogous manner. (3)
$\tilde{k} * (ω) = F (k * (t)) = R_{k} + i I_{k}$

After Fourier transformation, the Real and Imaginary parts $R$ , $I$ and $R_{k}$ , $I_{k}$ are frequency-dependent and can be input in four different ways (FORMULA, TABLE, PRONY, or PRELOAD).
When TYPE=FORMULA: (4)
$R = R 1 * f^{- a}$
(5)
$I = I 1 * f^{- a}$
(6)
$R_{k} = R 1 k * f^{- b}$
(7)
$I_{k} = I 1 k * f^{- b}$

Where,

$f$

Frequency.

$R$ , $I$

Real and imaginary parts of the Fourier transform of the deviatoric relaxation function.

$R_{k}$ , $I_{k}$

Real and imaginary parts of the Fourier transform of the bulk relaxation function.
When TYPE=TABLE:

TID1

Specify $ω R$ as a function of the frequency $f$ .

TID2

Specify $ω I$ as a function of the frequency $f$ .

TID3

Specify $ω R_{k}$ as a function of the frequency $f$ .

TID4

Specify $ω I_{k}$ as a function of the frequency $f$ .

Where,

$ω$

Angular frequency.

$R$ , $I$

Real and imaginary parts of the Fourier transform of the deviatoric relaxation function.

$R_{k}$ , $I_{k}$

Real and imaginary parts of the Fourier transform of the bulk relaxation function.
When TYPE=PRONY, the data inputs have the same meaning as the MATVE card. The storage and loss moduli are determined as follows, after a Fourier transform of the time-domain Prony series. (8)
$G_{s} = (G_{\infty} + \sum_{i} \frac{G_{i} τ_{i}^{2} ω^{2}}{1 + τ_{i}^{2} ω^{2}})$
(9)
$K_{s} = (K_{\infty} + \sum_{i} \frac{K_{i} τ_{i}^{2} ω^{2}}{1 + τ_{i}^{2} ω^{2}})$
(10)
$G_{l} = (\sum_{i} \frac{G_{i} τ_{i} ω}{1 + τ_{i}^{2} ω^{2}})$
(11)
$K_{l} = (\sum_{i} \frac{K_{i} τ_{i} ω}{1 + τ_{i}^{2} ω^{2}})$

Where,

$G_{s}$ , $G_{l}$

Deviatoric storage and loss moduli.

$K_{s}$ , $K_{l}$

Bulk storage and loss moduli.

$G_{\infty}$ , $K_{\infty}$

Long-term material property input.

$G_{i}$ , $K_{i}$

Modulus ratios.

$τ_{i}$

Relaxation time.

$ω$

Angular frequency.

(12)
$ω I = 1 - \frac{G_{s}}{G_{\infty}}$
(13)
$ω R = \frac{G_{l}}{G_{\infty}}$
(14)
$ω I_{k} = 1 - \frac{K_{s}}{K_{\infty}}$
(15)
$ω R_{k} = \frac{K_{l}}{K_{\infty}}$

Where,

$ω$

Angular frequency.

$R$ , $I$

Real and imaginary parts of the Fourier transform of the deviatoric relaxation function.

$R_{k}$ , $I_{k}$

Real and imaginary parts of the Fourier transform of the bulk relaxation function.
When TYPE= PRELOAD:

EUNIAXI

Test data to specify uniaxial loss modulus, uniaxial storage modulus, the frequency $f$ , uniaxial nominal strain.

EVOLUME

Test data to specify bulk loss modulus, bulk storage modulus, the frequency $f$ , volume ratio (current volume/initial volume).
For all types, deviatoric component and bulk component specifications cannot be blank at the same time.
Only Direct Frequency Response Analysis is supported.
A nonlinear LGDISP analysis needs to precede the direct frequency response analysis which establishes the base state for the direct frequency analysis. STATSUB(PRELOAD) in the Subcase Information section for the direct frequency analysis needs to point to this nonlinear LGDISP analysis. A dummy nonlinear LGDISP analysis without loadings will mean that the base state is the initial configuration.
The time domain and the frequency domain viscoelastic behavior cannot be specified together. That is, MATVE and MATFVE cannot be used together.

MATFVE

Format 1 (TYPE=FORMULA)

Format 2 (TYPE=TABLE)

Format 3 (TYPE=PRONY)

Format 4 (TYPE=PRELOAD)

Example

Definition

Comments

Format 1 (`TYPE`=FORMULA)

Format 2 (`TYPE`=TABLE)

Format 3 (`TYPE`=PRONY)

Format 4 (`TYPE`=PRELOAD)