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 ii -th deviatoric Prony series.

Default = Blank (Real > 0.0)

tDi Relaxation time for the ii -th deviatoric Prony series.

Default = Blank (Real > 0.0)

gBi Modulus ratio for the ii -th bulk Prony series.

Default = Blank (Real > 0.0)

tBi Relaxation time for the ii -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 ( σσ ) here is given by the following convolution representation, for deviatoric deformation.
    σ=t0g(ts)˙σ0dsσ=t0g(ts)˙σ0ds
    Where,
    g(t)=G(t)G0g(t)=G(t)G0
    Normalized modulus
    G0G0
    Instantaneous modulus
    G(t)G(t)
    Time-dependent modulus
    Similarly,
    J(t)J(t)
    Time-dependent compliance
    j(t)j(t)
    Normalized compliance

    They satisfy j(t)=G0J(t)j(t)=G0J(t) .

    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 ( GG ) and the following equation is used for calculation of the material property incorporating relaxation:

    g(t)=g+igietτig(t)=g+igietτi

    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 ( G0G0 ) and the following equation is used for calculation of the material property incorporating relaxation:

    g(t)=1igi[1etτi]g(t)=1igi[1etτi]

    The subscript ii indicates the ii -th term in the Prony series. A maximum of 5 terms are allowed.

    Where,
    gigi
    Prony material parameters.
    τiτi
    Relaxation time.
    gigi and τiτi
    Values determined from curve fitting, if RTEST is given or they can be directly input via Model=PRONY.

    ˙σ0=G0˙ε˙ε=dεdt

    Where,
    σ0
    Instantaneous stress response.
    ε
    Strain as a function of time.
    g
    Indicates the normalized modulus.
    G
    Indicates the modulus for relaxation.
    j
    Indicates the normalized compliance.
    J
    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 is assumed to act on both networks and is decomposed into elastic ( FeB ) and inelastic ( FcrB ) parts in network B as:

    F=FA=FeB.FcrB

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

    FeB.˙FcrB.Fcr1B.Fe1B=˙εvBSBˉσB

    The Bergström-Boyce hardening formulation is given by:

    ˙εvB=A(˜λ1+E)cˉσmB

    Where,
    ˉσB=SB:SB
    ˜λ=13I:(FcrB.(FcrB)T)
    SB
    Deviatoric part of the Cauchy stress tensor in network B.
    FcrB
    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,

    t0g(s)j(ts)ds=t

    If the Laplace transform, L , is written as:

    ˆf(s)=L(f(t))=0f(t)estdt

    The Laplace transforms of the functions g and f satisfy ˆg(s)ˆj(s)=1s2 , Then the calibration to a Prony series will be carried out based on the relaxation test.
    g
    Normalized modulus
    j
    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).