MATVE

Bulk Data Entry Defines material properties for nonlinear viscoelastic materials.

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  

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  

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.
 
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)

 

Comments

  1. The CHEXA, CTETRA, CPENTA, and CPYRA elements are currently supported.
  2. The instantaneous response can be provided by MAT1, MAT9 or MATHE entries, which should have the same MID as the MATVE entry.
  3. The linear viscoelastic material (Model = PRONY) is represented by the generalized Maxwell model. The material response is given by the following convolution representation.(1)
    σ = 0 t g ( t s ) σ ˙ 0 d s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4WdmNaey ypa0Zaa8qmaeaacaWGNbWaaeWaaeaacaWG0bGaeyOeI0Iaam4CaaGa ayjkaiaawMcaaiqbeo8aZzaacaWaaSbaaSqaaiaaicdaaeqaaOGaam izaiaadohaaSqaaiaaicdaaeaacaWG0baaniabgUIiYdaaaa@468B@
    Where,
    g ( t ) = γ + i γ i e t τ i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4zamaabm aabaGaamiDaaGaayjkaiaawMcaaiabg2da9iabeo7aNnaaBaaaleaa cqGHEisPaeqaaOGaey4kaSYaaabuaeaacqaHZoWzdaWgaaWcbaGaam yAaaqabaGccaWGLbWaaWbaaSqabeaacqGHsisldaWcaaqaaiaadsha aeaacqaHepaDdaWgaaadbaGaamyAaaqabaaaaaaaaSqaaiaadMgaae qaniabggHiLdaaaa@4A64@
    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 component in the Prony series. A maximum of 5 components are allowed.
    γ i
    Modulus ratio
    τ i
    Relaxation time
    σ 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaaicdaaeqaaaaa@38A0@
    Instantaneous stress response
  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 the user 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, the user 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:(2)
    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:(3)
    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:(4)
    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.