MATVE

Bulk Data Entry Defines material properties for nonlinear viscoelastic materials.

Attention: Valid for Implicit and Explicit Analysis

Format A: Prony Series (Model=PRONY)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATVE MID Model gD1 tD1 gB1 tB1
gD2 tD2 gD3 tD3 gD4 tD4 gD5 tD5
gB2 tB2 gB3 tB3 gB4 tB4 gB5 tB5

Format B: Bergström-Boyce (Model=BBOYCE)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATVE MID Model Sb A C m E

Format C (Model=RTEST)

Format for separate shear and volumetric test data for relaxation:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATVE MID Model etol npmax
SHEAR slong
gs(t) t
etc
BULK blong
gk(t) t
etc
Format for combined shear and volumetric test data for relaxation:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATVE MID Model etol npmax
COMB slong blong
gs(t) gk(t) t
etc

Format D (Model=CTEST)

Format for separate shear and volumetric test data for creep:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATVE MID Model etol npmax
SHEAR slong
js(t) t
etc
BULK blong
jk(t) t
etc
Format for combined shear and volumetric test data for creep:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATVE MID Model etol npmax
COMB slong blong
js(t) jk(t) t
etc

Format E (Model=UPRN)

Format for unlimited Prony series:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATVE MID Model
gD1 tD1 gB1 tB1
gD2 tD2 gB2 tB2
etc

Example A: Prony Series (Model=PRONY)

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

Example B: Bergström-Boyce (Model=BBOYCE)

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
MATVE 2 BBOYCE 2.0 0.1 -0.7 5.0 0.01

Example E: Unlimited Prony Series (Model=UPRN)

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

Definitions

Field Contents SI Unit Example
MID Unique material identification number.

No default (Integer > 0)

Model Viscoelastic material model type.
PRONY (Default)
Linear viscoelastic model based on Prony series.
BBOYCE
Bergström-Boyce model.
RTEST
Relaxation test data for Prony series.
CTEST
Creep test data for Prony series.
UPRN
Unlimited Prony series.
gDi Modulus ratio for the i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGPbaaaa@39C5@ -th deviatoric Prony series.

Default = Blank (Real > 0.0)

tDi Relaxation time for the i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGPbaaaa@39C5@ -th deviatoric Prony series.

Default = Blank (Real > 0.0)

gBi Modulus ratio for the i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGPbaaaa@39C5@ -th bulk Prony series.

Default = Blank (Real > 0.0)

tBi Relaxation time for the i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGPbaaaa@39C5@ -th bulk Prony series.

Default = Blank (Real > 0.0)

Sb Stress scaling factor that defines the ratio of the stress carried by network B to that carried by network A under identical elastic stretching. 7

No default (Real > 0.0)

A Effective creep strain rate. 7

No default (Real > 0.0)

C Negative exponent characterizes the creep strain dependence of the effective creep strain rate in network B. 7

No default (-1.0 ≤ Real ≤ 0.0)

m Positive exponent characterizes the effective stress dependence of the effective creep strain rate in network B. 7

No default (Real ≥1.0)

E Material parameter to regularize the creep strain rate in the vicinity of the undeformed state. 7

Default = 0.01 (Real ≥0.0)

SHEAR Continuation line to indicate test data from shear relaxation/creep tests are to follow.
BULK Continuation line to indicate test data from volumetric relaxation/creep tests are to follow.
COMB Continuation line to indicate test data from both shear and volumetric relaxation/creep tests are to follow.
t Time; should be specified in an ascending order.

No default (Real > 0.0)

gs(t) Normalized shear modulus.

No default (0.0 ≤ Real ≤ 1.0)

gk(t) Normalized bulk modulus.

No default (0.0 ≤ Real ≤ 1.0)

js(t) Normalized shear compliance.

No default (1.0 ≤ Real)

jk(t) Normalized bulk compliance.

No default (1.0 ≤ Real)

etol Error tolerance for CTEST/RTEST material calibration.
0.0
Implies that the tolerance is automatically controlled.

Default = 0.0 (0.0 ≤ Real)

npmax Maximum number of terms in the Prony series for CTEST/RTEST material calibration.

Default = 13 (1 ≤ Integer ≤ 13)

slong Long term normalized Shear modulus for RTEST.

Default = blank (0.0 < Real < 1.0)

Long term normalized Shear compliance for CTEST.

Default = blank (1.0 < Real)

blong Long term normalized Bulk modulus for RTEST.

Default = blank (0.0 < Real < 1.0)

Long term normalized Bulk compliance for CTEST.

Default = blank (1.0 < Real)

Comments

  1. The CHEXA, CTETRA, CPENTA, and CPYRA elements are currently supported.
  2. The instantaneous or long-term material property can be provided by MAT1, MAT9 or MATHE Bulk Data Entries, which should have the same MID as the MATVE Bulk Data Entry.
  3. The linear viscoelastic material (Model=PRONY) is represented by the generalized Maxwell model. The material response, indicated by stress ( σ ) here is given by the following convolution representation, for deviatoric deformation.
    σ = 0 t g ( t s ) σ ˙ 0 d s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4WdmNaey ypa0Zaa8qmaeaacaWGhbWaaeWaaeaacaWG0bGaeyOeI0Iaam4CaaGa ayjkaiaawMcaaiqbeo8aZzaacaWaaSbaaSqaaiaaicdaaeqaaOGaam izaiaadohaaSqaaiaaicdaaeaacaWG0baaniabgUIiYdaaaa@466B@
    Where,
    g ( t ) = G ( t ) G 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4zamaabm aabaGaamiDaaGaayjkaiaawMcaaiabg2da9maalaaabaGaam4ramaa bmaabaGaamiDaaGaayjkaiaawMcaaaqaaiaadEeadaWgaaWcbaGaaG imaaqabaaaaaaa@3F7B@
    Normalized modulus
    G 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4ramaaBa aaleaacaaIWaaabeaaaaa@37A9@
    Instantaneous modulus
    G ( t ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4ramaabm aabaGaamiDaaGaayjkaiaawMcaaaaa@3945@
    Time-dependent modulus
    Similarly,
    J ( t ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsamaabm aabaGaamiDaaGaayjkaiaawMcaaaaa@3948@
    Time-dependent compliance
    j ( t ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsamaabm aabaGaamiDaaGaayjkaiaawMcaaaaa@3948@
    Normalized compliance

    They satisfy j ( t ) = G 0 J ( t ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOAamaabm aabaGaamiDaaGaayjkaiaawMcaaiabg2da9iaadEeadaWgaaWcbaGa aGimaaqabaGccaWGkbWaaeWaaeaacaWG0baacaGLOaGaayzkaaaaaa@3F7B@ .

    If the MTIME field on MAT1/MAT9/MATHE entries is set to LONG (default), then the input material property is considered as the long-term material deviatoric input modulus ( G MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4ramaaBa aaleaacqGHEisPaeqaaaaa@3860@ ) and the following equation is used for calculation of the material property incorporating relaxation:

    g ( t ) = g + i g i e t τ i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4zamaabm aabaGaamiDaaGaayjkaiaawMcaaiabg2da9iaadEeadaWgaaWcbaGa eyOhIukabeaakiabgUcaRmaaqafabaGaam4ramaaBaaaleaacaWGPb aabeaakiaadwgadaahaaWcbeqaaiabgkHiTmaalaaabaGaamiDaaqa aiabes8a0naaBaaameaacaWGPbaabeaaaaaaaaWcbaGaamyAaaqab0 GaeyyeIuoaaaa@48AE@

    If the MTIME field on the MAT1/MAT9/MATHE entries is set to INSTANT, then the input material property is considered as the instantaneous material input ( G 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4ramaaBa aaleaacaaIWaaabeaaaaa@37A9@ ) and the following equation is used for calculation of the material property incorporating relaxation:

    g ( t ) = 1 i g i [ 1 e t τ i ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4zamaabm aabaGaamiDaaGaayjkaiaawMcaaiabg2da9iaaigdacqGHsisldaae qbqaaiaadEgadaWgaaWcbaGaamyAaaqabaGcdaWadaqaaiaaigdacq GHsislcaWGLbWaaWbaaSqabeaacqGHsisldaWcaaqaaiaadshaaeaa cqaHepaDdaWgaaadbaGaamyAaaqabaaaaaaaaOGaay5waiaaw2faaa WcbaGaamyAaaqab0GaeyyeIuoaaaa@4AC5@

    The subscript i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGPbaaaa@39C5@ indicates the i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGPbaaaa@39C5@ -th term in the Prony series. A maximum of 5 terms are allowed.

    Where,
    g i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4ramaaBa aaleaacaWGPbaabeaaaaa@37DD@
    Prony material parameters.
    τ i
    Relaxation time.
    g i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4ramaaBa aaleaacaWGPbaabeaaaaa@37DD@ and τ i
    Values determined from curve fitting, if RTEST is given or they can be directly input via Model=PRONY.

    σ ˙ 0 = G 0 ε ˙ ε ˙ = d ε d t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacuaHdp WCgaGaamaaBaaaleaacaaIWaaabeaakiabg2da9iaadEeadaWgaaWc baGaaGimaaqabaGccuaH1oqzgaGaaaqaaiqbew7aLzaacaGaeyypa0 ZaaSaaaeaacaWGKbGaeqyTdugabaGaamizaiaadshaaaaaaaa@4464@

    Where,
    σ 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaaicdaaeqaaaaa@38A0@
    Instantaneous stress response.
    ε
    Strain as a function of time.
    g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4zaaaa@36E3@
    Indicates the normalized modulus.
    G MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4zaaaa@36E3@
    Indicates the modulus for relaxation.
    j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4zaaaa@36E3@
    Indicates the normalized compliance.
    J MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4zaaaa@36E3@
    Indicates the compliance for creep.
  4. For the isotropic model, the deviatoric and bulk responses can be specified separately. For the anisotropic model, only gDi and tDi are used and the bulk specifications are ignored.
  5. The material relaxation response is controlled by the card VISCO. For example, if you wants to simulate a physical relaxation test, the first subcase can omit the VISCO card so that material response is only the instantaneous elasticity in this subcase. In the next subcase, you can add a VISCO card so that the material response is viscoelastic.
  6. For Implicit Nonlinear Analysis, MATVE is supported for small displacement and large displacement nonlinear analysis.
  7. The nonlinear viscoelastic material (Model = BBOYCE) is supported only for solid elements in Nonlinear Explicit Analysis.

    The response of the material can be represented using an equilibrium hyperelastic network A, and a time-dependent hyperelastic - nonlinear viscoelastic network B. The hyperelastic material models for network A and B can be selected from existing MATHE card.

    The deformation gradient tensor, F MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraaaa@36C1@ is assumed to act on both networks and is decomposed into elastic ( F B e MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaDa aaleaacaWGcbaabaGaamyzaaaaaaa@389F@ ) and inelastic ( F B c r MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaDa aaleaacaWGcbaabaGaam4yaiaadkhaaaaaaa@3994@ ) parts in network B as:

    F = F A = F B e . F B c r MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOraiabg2 da9iaadAeadaWgaaWcbaGaamyqaaqabaGccqGH9aqpcaWGgbWaa0ba aSqaaiaadkeaaeaacaWGLbaaaOGaaiOlaiaadAeadaqhaaWcbaGaam OqaaqaaiaadogacaWGYbaaaaaa@4197@

    The evolution of inelastic deformation gradient on network B is governed by:

    F B e . F ˙ B c r . F B c r 1 . F B e 1 = ε ˙ B v S B σ ¯ B MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaDa aaleaacaWGcbaabaGaamyzaaaakiaac6caceWGgbGbaiaadaqhaaWc baGaamOqaaqaaiaadogacaWGYbaaaOGaaiOlaiaadAeadaqhaaWcba GaamOqaaqaaiaadogacaWGYbGaeyOeI0IaaGymaaaakiaac6cacaWG gbWaa0baaSqaaiaadkeaaeaacaWGLbGaeyOeI0IaaGymaaaakiabg2 da9iqbew7aLzaacaWaa0baaSqaaiaadkeaaeaacaWG2baaaOWaaSaa aeaacaWGtbWaaSbaaSqaaiaadkeaaeqaaaGcbaGafq4WdmNbaebada WgaaWcbaGaamOqaaqabaaaaaaa@517D@

    The Bergström-Boyce hardening formulation is given by:

    ε ˙ B v = A ( λ ˜ 1 + E ) c σ ¯ B m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbai aadaqhaaWcbaGaamOqaaqaaiaadAhaaaGccqGH9aqpcaWGbbGaaiik aiqbeU7aSzaaiaGaeyOeI0IaaGymaiabgUcaRiaadweacaGGPaWaaW baaSqabeaacaWGJbaaaOGafq4WdmNbaebadaqhaaWcbaGaamOqaaqa aiaad2gaaaaaaa@46BB@

    Where,
    σ ¯ B = S B : S B MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4WdmNbae badaWgaaWcbaGaamOqaaqabaGccqGH9aqpdaGcaaqaaiaadofadaWg aaWcbaGaamOqaaqabaGccaGG6aGaam4uamaaBaaaleaacaWGcbaabe aaaeqaaaaa@3E42@
    λ ˜ = 1 3 I : ( F B c r . ( F B c r ) T ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafq4UdWMbaG aacqGH9aqpdaGcaaqaamaalaaabaGaaGymaaqaaiaaiodaaaGaamys aiaacQdadaqadaqaaiaadAeadaqhaaWcbaGaamOqaaqaaiaadogaca WGYbaaaOGaaiOlamaabmaabaGaamOramaaDaaaleaacaWGcbaabaGa am4yaiaadkhaaaaakiaawIcacaGLPaaadaahaaWcbeqaaiaadsfaaa aakiaawIcacaGLPaaaaSqabaaaaa@4812@
    S B MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uamaaBa aaleaacaWGcbaabeaaaaa@37C1@
    Deviatoric part of the Cauchy stress tensor in network B.
    F B c r MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaDa aaleaacaWGcbaabaGaam4yaiaadkhaaaaaaa@3994@
    Inelastic deformation gradient tensor in network B.
  8. When MODEL=RTEST/CTEST:

    Relaxation (RTEST) or Creep (CTEST) test data can be input using these two types. This test data will internally be used to calibrate a Prony series.

    If creep test data are used, then the creep test will be first converted to the relaxation test using the convolution integration,

    0 t g ( s ) j ( t s ) d s = t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa8qCaeaaca WGNbWaaeWaaeaacaWGZbaacaGLOaGaayzkaaGaamOAamaabmaabaGa amiDaiabgkHiTiaadohaaiaawIcacaGLPaaacaWGKbGaam4CaaWcba GaaGimaaqaaiaadshaa0Gaey4kIipakiabg2da9iaadshaaaa@46C0@

    If the Laplace transform, L MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitaaaa@36C8@ , is written as:

    f ^ ( s ) = L ( f ( t ) ) = 0 f ( t ) e s t d t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmOzayaaja WaaeWaaeaacaWGZbaacaGLOaGaayzkaaGaeyypa0Jaamitamaabmaa baGaamOzamaabmaabaGaamiDaaGaayjkaiaawMcaaaGaayjkaiaawM caaiabg2da9maapehabaGaamOzamaabmaabaGaamiDaaGaayjkaiaa wMcaaiaadwgadaahaaWcbeqaaiabgkHiTiaadohacaWG0baaaOGaam izaiaadshaaSqaaiaaicdaaeaacqGHEisPa0Gaey4kIipaaaa@4F28@

    The Laplace transforms of the functions g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitaaaa@36C8@ and f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitaaaa@36C8@ satisfy g ^ ( s ) j ^ ( s ) = 1 s 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4zayaaja WaaeWaaeaacaWGZbaacaGLOaGaayzkaaGabmOAayaajaWaaeWaaeaa caWGZbaacaGLOaGaayzkaaGaeyypa0ZaaSaaaeaacaaIXaaabaGaam 4CamaaCaaaleqabaGaaGOmaaaaaaaaaa@40A6@ , Then the calibration to a Prony series will be carried out based on the relaxation test.
    g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitaaaa@36C8@
    Normalized modulus
    j MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitaaaa@36C8@
    Normalized compliance

    You can input shear test data or volumetric test data, respectively, using the continuation lines SHEAR or BULK. The continuation line COMB will allow both shear and volumetric test data together.

  9. If the number of Prony series is greater than 5, model UPRN, which means unlimited prony series, needs to be used. The first two columns are for the deviatoric part and the next two columns are for the bulk part. The deviatoric part and the bulk part can have different number of Prony series (just using blanks to fill the unused positions).