/PROP/TYPE27 (SPR_BDAMP)

Block Format Keyword Describes a damper spring property with one translational DOF. Damper force is bounded by stiffness force.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/PROP/TYPE27/prop_ID/unit_ID or /PROP/SPR_BDAMP/prop_ID/unit_ID
prop_title
Mass sens_ID Isflag Ileng Itens Ifail
K C n δ min 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aa0 baaSqaaiGac2gacaGGPbGaaiOBaaqaaiaaigdaaaaaaa@3B35@ δ max 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aa0 baaSqaaiGac2gacaGGPbGaaiOBaaqaaiaaigdaaaaaaa@3B35@
gap       Fsmooth Fcut
fct_ID1 fct_ID2 Ascale1 Fscale1 Ascale2 Fscale2

Definition

Field Contents SI Unit Example
prop_ID Property identifier.

(Integer, maximum 10 digits)

unit_ID (Optional) Unit Identifier.

(Integer, maximum 10 digits)

prop_title Property title.

(Character, maximum 100 characters)

Mass Mass.

(Real)

[ kg ] (Ileng = 0)

[ kg m ] (Ileng = 1)

sens_ID Sensor identifier.
= 0
Spring is active.

(Integer)

Isflag Sensor flag.
= 0
Spring element activated when sens_ID activates and cannot be deactivated.
= 1
Spring element deactivated when sens_ID activates and cannot be activated.
= 2
Spring element activated or deactivated state matches the sensor state and can switch back and forth. The spring initial length ( l 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiBamaaBa aaleaacaaIWaaabeaaaaa@37AD@ ) is based on the spring length at the activation time.

(Integer)

Ileng Input per unit length flag.
= 0
Spring properties are input as explained in the definition table.
= 1
Some inputs are per unit length.

(Integer)

Itens Tensile behavior flag.
= 0
The spring only works in compression. No stiffness or damping in tension.
= 1
The spring also works in tension with the defined stiffness and damping.

(Integer)

Ifail Failure model flag.
=1
Displacement criterion (Ileng = 0).
Strain criterion (Ileng = 1).
= 2
Force criterion.

(Integer)

K Linear loading and unloading stiffness.

(Real)

[ N m ] (Ileng = 0)

[ N m 2 ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaad6eaaeaacaWGTbWaaWbaaSqabeaacaaIYaaaaaaaaOGa ay5waiaaw2faaaaa@3AB1@ (Ileng = 1)

C Linear damping coefficient.

Default = 0.0 (Real)

[ Ns m ] (Ileng = 0)

[ N s m 2 ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaad6eacaWGZbaabaGaamyBamaaCaaaleqabaGaaGOmaaaa aaaakiaawUfacaGLDbaaaaa@3BA9@ (Ileng = 1)

n Exponent for nonlinear stiffness force.

Default = 1.0 (Real)

δ min 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aa0 baaSqaaiGac2gacaGGPbGaaiOBaaqaaiaaigdaaaaaaa@3B35@ Negative failure limit.

Default = -1020 (Real)

Ifail = 1: Failure displacement (Ileng = 0)

Failure strain (Ileng = 1)

[ m ] (Ileng = 0)
Ifail = 2: Failure force. [ N ]
δ max 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiTdq2aa0 baaSqaaiGac2gacaGGPbGaaiOBaaqaaiaaigdaaaaaaa@3B35@ Positive failure limit.

Default = 1020 (Real)

Ifail = 1: Failure displacement (Ileng = 0)

Failure strain (Ileng = 1)

[ m ] (Ileng = 0)
Ifail = 2: Failure force. [ N ]
gap Minimum gap before activation.

Default = 0.0 (Real)

[ m ] (Ileng = 0)
Fsmooth Spring force filtering flag.
= 0
No filtering.
= 1
Spring force is filtered using the cutoff frequency Fcut.

(Integer)

Fcut Cutoff frequency for spring force filtering.

Default = 100 kHz (Real)

[Hz]
fct_ID1 Nonlinear stiffness force function identifier:
Ileng = 0
A function of spring elongation f(δ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacI cacqaH0oazcaGGPaaaaa@39E0@ .
Ileng = 1
A function of engineering strain f(ε) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacI cacqaH1oqzcaGGPaaaaa@39E2@ .

(Integer)

fct_ID2 Damping force function identifier:
Ileng = 0
A function of spring velocity g( δ ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4zamaabm aabaGafqiTdqMbaiaaaiaawIcacaGLPaaaaaa@3A1A@ .
Ileng = 1
A function of strain rate g( ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4zamaabm aabaGafqyTduMbaiaaaiaawIcacaGLPaaaaaa@3A1C@ .

(Integer)

Ascale1
Ileng = 0
Elongation scale factor for the stiffness function f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaaaa@36E2@ .
Ileng = 1
Engineering strain scale factor for the stiffness function f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaaaa@36E2@ .

Default = 1.0 (Real)

[ m ] (Ileng = 0)
Fscale1 Ordinate scale factor for the stiffness function f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaaaa@36E2@ .

Default = 1.0 (Real)

[ N ]
Ascale2
Ileng = 0
Velocity scale factor for the damping function g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaaaa@36E2@ .
Ileng = 1
Strain rate scale factor for the damping function g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaaaa@36E2@ .

Default = 1.0 (Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaad2gaaeaacaWGZbaaaaGaay5waiaaw2faaaaa@39E3@ (Ileng = 0)

[ 1 s ] (Ileng = 1)

Fscale2 Ordinate scale factor for the stiffness function g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaaaa@36E2@ .

Default = 1.0 (Real)

[ N ]

Comments

  1. The spring has one translational degree of freedom in the local x direction which is defined between node N1 and N2 of the spring.
  2. Force computation is activated by default in compression ( δ < 0), and in tension only if Itens = 1. The spring force value is obtained as follows, where Ileng = 0:
    • Stiffness part:

      { F K ( δ ) = s i g n ( δ ) K | δ | n if f c t _ I D 1 = 0 F K ( δ ) = F s c a l e 1 f ( δ A s c a l e 1 ) otherwise MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaeaafa qabeGadaaabaGaamOramaaBaaaleaacaWGlbaabeaakiaacIcacqaH 0oazcaGGPaGaeyypa0Jaam4CaiaadMgacaWGNbGaamOBaiaacIcacq aH0oazcaGGPaGaeyyXICTaam4saiabgwSixpaaemaabaGaeqiTdqga caGLhWUaayjcSdWaaWbaaSqabeaacaWGUbaaaaGcbaGaaeyAaiaabA gaaeaacaWGMbGaam4yaiaadshacaGGFbGaamysaiaadseadaWgaaWc baGaaGymaaqabaGccqGH9aqpcaaIWaaabaGaamOramaaBaaaleaaca WGlbaabeaakiaacIcacqaH0oazcaGGPaGaeyypa0JaamOraiaadoha caWGJbGaamyyaiaadYgacaWGLbGaaGymaiabgwSixlaadAgadaqada qaamaalaaabaGaeqiTdqgabaGaamyqaiaadohacaWGJbGaamyyaiaa dYgacaWGLbGaaGymaaaaaiaawIcacaGLPaaaaeaacaqGVbGaaeiDai aabIgacaqGLbGaaeOCaiaabEhacaqGPbGaae4Caiaabwgaaeaaaaaa caGL7baaaaa@79E2@

      Where, n 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBaiabgw MiZkaaigdaaaa@394A@ .

    • Damping part:

      { F D ( δ ˙ )=C δ ˙ if fct_I D 2 =0 F D ( δ ˙ )=Fscale2g( δ ˙ Ascale2 ) otherwise MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaeaafa qabeGadaaabaGaamOramaaBaaaleaacaWGebaabeaakiaacIcacuaH 0oazgaGaaiaacMcacqGH9aqpcaWGdbGaeyyXICTafqiTdqMbaiaaae aacaqGPbGaaeOzaaqaaiaadAgacaWGJbGaamiDaiaac+facaWGjbGa amiramaaBaaaleaacaaIYaaabeaakiabg2da9iaaicdaaeaacaWGgb WaaSbaaSqaaiaadseaaeqaaOGaaiikaiqbes7aKzaacaGaaiykaiab g2da9iaadAeacaWGZbGaam4yaiaadggacaWGSbGaamyzaiaaikdacq GHflY1caWGNbWaaeWaaeaadaWcaaqaaiqbes7aKzaacaaabaGaamyq aiaadohacaWGJbGaamyyaiaadYgacaWGLbGaaGOmaaaaaiaawIcaca GLPaaaaeaacaqGVbGaaeiDaiaabIgacaqGLbGaaeOCaiaabEhacaqG PbGaae4CaiaabwgaaeaaaaaacaGL7baaaaa@6C9B@

    • Global force:

      { F(δ, δ ˙ )= F K (δ)+ F D ( δ ˙ ) if | F D ( δ ˙ ) |<| F K (δ) | F(δ)=2 F K (δ) otherwise MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaeaafa qabeGadaaabaGaamOraiaacIcacqaH0oazcaGGSaGafqiTdqMbaiaa caGGPaGaeyypa0JaamOramaaBaaaleaacaWGlbaabeaakiaacIcacq aH0oazcaGGPaGaey4kaSIaamOramaaBaaaleaacaWGebaabeaakiaa cIcacuaH0oazgaGaaiaacMcaaeaacaqGPbGaaeOzaaqaamaaemaaba GaamOramaaBaaaleaacaWGebaabeaakiaacIcacuaH0oazgaGaaiaa cMcaaiaawEa7caGLiWoacqGH8aapdaabdaqaaiaadAeadaWgaaWcba Gaam4saaqabaGccaGGOaGaeqiTdqMaaiykaaGaay5bSlaawIa7aaqa aiaadAeacaGGOaGaeqiTdqMaaiykaiabg2da9iaaikdacqGHflY1ca WGgbWaaSbaaSqaaiaadUeaaeqaaOGaaiikaiabes7aKjaacMcaaeaa caqGVbGaaeiDaiaabIgacaqGLbGaaeOCaiaabEhacaqGPbGaae4Cai aabwgaaeaaaaaacaGL7baaaaa@70A8@

  3. If the Ileng flag is activated (Ileng = 1), the above computations become:
    • Stiffness part:

      { F K ( ε ) = s i g n ( ε ) K | ε | n if f c t _ I D 1 = 0 F K ( ε ) = F s c a l e 1 f ( ε A s c a l e 1 ) otherwise MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaeaafa qabeGadaaabaGaamOramaaBaaaleaacaWGlbaabeaakiaacIcacqaH 1oqzcaGGPaGaeyypa0Jaam4CaiaadMgacaWGNbGaamOBaiaacIcacq aH1oqzcaGGPaGaeyyXICTaam4saiabgwSixpaaemaabaGaeqyTduga caGLhWUaayjcSdWaaWbaaSqabeaacaWGUbaaaaGcbaGaaeyAaiaabA gaaeaacaWGMbGaam4yaiaadshacaGGFbGaamysaiaadseadaWgaaWc baGaaGymaaqabaGccqGH9aqpcaaIWaaabaGaamOramaaBaaaleaaca WGlbaabeaakiaacIcacqaH1oqzcaGGPaGaeyypa0JaamOraiaadoha caWGJbGaamyyaiaadYgacaWGLbGaaGymaiabgwSixlaadAgadaqada qaamaalaaabaGaeqyTdugabaGaamyqaiaadohacaWGJbGaamyyaiaa dYgacaWGLbGaaGymaaaaaiaawIcacaGLPaaaaeaacaqGVbGaaeiDai aabIgacaqGLbGaaeOCaiaabEhacaqGPbGaae4Caiaabwgaaeaaaaaa caGL7baaaaa@79EC@

    • Damping part:

      { F D ( ε ˙ ) = C ε ˙ if f c t _ I D 2 = 0 F D ( ε ˙ ) = F s c a l e 2 g ( ε ˙ A s c a l e 2 ) otherwise MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaeaafa qabeGadaaabaGaamOramaaBaaaleaacaWGebaabeaakiaacIcacuaH 1oqzgaGaaiaacMcacqGH9aqpcaWGdbGaeyyXICTafqyTduMbaiaaae aacaqGPbGaaeOzaaqaaiaadAgacaWGJbGaamiDaiaac+facaWGjbGa amiramaaBaaaleaacaaIYaaabeaakiabg2da9iaaicdaaeaacaWGgb WaaSbaaSqaaiaadseaaeqaaOGaaiikaiqbew7aLzaacaGaaiykaiab g2da9iaadAeacaWGZbGaam4yaiaadggacaWGSbGaamyzaiaaikdacq GHflY1caWGNbWaaeWaaeaadaWcaaqaaiqbew7aLzaacaaabaGaamyq aiaadohacaWGJbGaamyyaiaadYgacaWGLbGaaGOmaaaaaiaawIcaca GLPaaaaeaacaqGVbGaaeiDaiaabIgacaqGLbGaaeOCaiaabEhacaqG PbGaae4CaiaabwgaaeaaaaaacaGL7baaaaa@6CA3@

    • Global force:

      { F ( ε , ε ˙ ) = F K ( ε ) + F D ( ε ˙ ) if | F D ( ε ˙ ) | < | F K ( ε ) | F ( ε ) = 2 F K ( ε ) otherwise MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaeaafa qabeGadaaabaGaamOraiaacIcacqaH1oqzcaGGSaGafqyTduMbaiaa caGGPaGaeyypa0JaamOramaaBaaaleaacaWGlbaabeaakiaacIcacq aH1oqzcaGGPaGaey4kaSIaamOramaaBaaaleaacaWGebaabeaakiaa cIcacuaH1oqzgaGaaiaacMcaaeaacaqGPbGaaeOzaaqaamaaemaaba GaamOramaaBaaaleaacaWGebaabeaakiaacIcacuaH1oqzgaGaaiaa cMcaaiaawEa7caGLiWoacqGH8aapdaabdaqaaiaadAeadaWgaaWcba Gaam4saaqabaGccaGGOaGaeqyTduMaaiykaaGaay5bSlaawIa7aaqa aiaadAeacaGGOaGaeqyTduMaaiykaiabg2da9iaaikdacqGHflY1ca WGgbWaaSbaaSqaaiaadUeaaeqaaOGaaiikaiabew7aLjaacMcaaeaa caqGVbGaaeiDaiaabIgacaqGLbGaaeOCaiaabEhacaqGPbGaae4Cai aabwgaaeaaaaaacaGL7baaaaa@70B8@

  4. You can define a compression gap activation as defined on the following scheme:


    Figure 1.
    If the gap is defined (gap ≠ 0.0) the force computation is activated once the spring compression is bigger than the specified gap.(1)
    { F ( δ + | g a p | , δ ˙ ) 0 if δ < | g a p | F ( δ + | g a p | , δ ˙ ) = 0 otherwise MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaeaafa qabeGadaaabaGaamOraiaacIcacqaH0oazcqGHRaWkdaabdaqaaiaa dEgacaWGHbGaamiCaaGaay5bSlaawIa7aiaacYcacuaH0oazgaGaai aacMcacqGHGjsUcaaIWaaabaGaaeyAaiaabAgaaeaacqaH0oazcqGH 8aapcqGHsisldaabdaqaaiaadEgacaWGHbGaamiCaaGaay5bSlaawI a7aaqaaiaadAeacaGGOaGaeqiTdqMaey4kaSYaaqWaaeaacaWGNbGa amyyaiaadchaaiaawEa7caGLiWoacaGGSaGafqiTdqMbaiaacaGGPa Gaeyypa0JaaGimaaqaaiaab+gacaqG0bGaaeiAaiaabwgacaqGYbGa ae4DaiaabMgacaqGZbGaaeyzaaqaaaaaaiaawUhaaaaa@6911@
    Note: Defining a gap value implies that the spring only works in compression and thus, Itens = 0, if the gap is defined. If Ileng = 1, the gap is homogeneous to a compressive strain.
  5. The switching between the two forces computation’s formula can lead to a noisy spring response. To address this issue, you can use filtering on the spring force computation, allowing a smooth transition between the two spring states (damped and undamped). To do so, the force filtering flag Fsmooth and the cutoff frequency Fcut can be used as:
    • If Fcut ≠ 0.0, the filtering is activated (Fsmooth is automatically set to 1), and the filtering uses the cutoff frequency provided by you.
    • If Fsmooth =1 and Fcut = 0.0, the filtering is activated and a default cutoff frequency of 100 kHz is used.
    • If Fsmooth =0 and Fcut = 0.0, no filtering is used.
    If the filtering is activated, the spring force is computed as:(2)
    F n f i l t e r = α F n + ( 1 α ) F n 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaWGUbaabeaakmaaCaaaleqabaGaamOzaiaadMgacaWGSbGa amiDaiaadwgacaWGYbaaaOGaeyypa0JaeqySdeMaamOramaaBaaale aacaWGUbaabeaakiabgUcaRiaacIcacaaIXaGaeyOeI0IaeqySdeMa aiykaiaadAeadaWgaaWcbaGaamOBaiabgkHiTiaaigdaaeqaaaaa@4B73@

    Where, α = 2 π Δ t F c u t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqbaeqabeWaaa qaaiaadAeadaWgaaWcbaGaamOBaaqabaGcdaahaaWcbeqaaiaadAga caWGPbGaamiBaiaadshacaWGLbGaamOCaaaakiabg2da9iabeg7aHj aadAeadaWgaaWcbaGaamOBaaqabaGccqGHRaWkcaGGOaGaaGymaiab gkHiTiabeg7aHjaacMcacaWGgbWaaSbaaSqaaiaad6gacqGHsislca aIXaaabeaaaOqaaiaabEhacaqGPbGaaeiDaiaabIgaaeaacqaHXoqy cqGH9aqpcaaIYaGaeqiWdaNaeyyXICTaeuiLdqKaamiDaaaacqGHfl Y1caWGgbGaam4yaiaadwhacaWG0baaaa@5F0B@