/VISC/PRONY

Block Format Keyword This is an isotropic visco-elastic Maxwell model that can be used to add visco-elasticity to certain shell and solid element material models. The visco-elasticity is input using a Prony series.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/VISC/PRONY/mat_ID/unit_ID
M   K v MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGlbWaaS baaSqaaiaadAhaaeqaaaaa@3855@            
Read only if M > 0, each pair of shear relaxation and shear decay per line
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
G i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaWGPbaabeaaaaa@37DE@ β i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHYoGyda WgaaWcbaGaamyAaaqabaaaaa@3A23@ K i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaWGPbaabeaaaaa@37DE@ β ki MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHYoGyda WgaaWcbaGaam4AaiaadMgaaeqaaaaa@3B13@    

Definitions

Field Contents SI Unit Example
mat_ID Material identifier which refers to the viscosity card

(Integer, maximum 10 digits)

 
unit_ID Unit Identifier

(Integer, maximum 10 digits)

 
M Maxwell model order (number of Prony coefficients)

Default = 0 (Integer)

 
K v MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGlbWaaS baaSqaaiaadAhaaeqaaaaa@3855@ Viscous bulk modulus 3 Only used if K i = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaWGPbaabeaakiabg2da9iaaicdaaaa@39A8@

Default = 0. (Real)

[ Pas ]
G i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaWGPbaabeaaaaa@37DE@ Shear relaxation modulus for ith term (i=1, M)

(Real)

[ Pa ]
β i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHYoGyda WgaaWcbaGaamyAaaqabaaaaa@3A23@ Decay shear constant for ith term (i=1, M)

(Real)

[ 1 s ]
K i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacaWGPbaabeaaaaa@37DE@ Bulk relaxation modulus for ith term (i=1, M) 3

(Real)

[ Pa ]
β k i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHYoGyda WgaaWcbaGaam4AaiaadMgaaeqaaaaa@3B13@ Decay bulk constant for ith term (i=1, M)

(Real)

[ 1 s ]

Comments

  1. For shell elements this model is available with /MAT/LAW66 and /MAT/LAW25 (COMPSH).

    For solid elements it is available with hyperelastic material laws /MAT/LAW42 (OGDEN), /MAT/LAW69, /MAT/LAW82, /MAT/LAW88 and /MAT/LAW92.

  2. The viscosity effect is taken into account by using a Prony series. The deviatoric viscous stress is given by the convolution integral of the form:(1)
    S ij = 0 t 2 G ( t s ) dev [ ε ij ] s ds
    with(2)
    G ( t ) = i = 1 M G i e β i t

    and dev [ ε ij ] denotes the deviatoric part of strain tensor.

    Shear decay:(3)
    β i = ( 1 τ i )
    Where,
    τ i
    Relaxation time
  3. For the viscous pressure, two formulations are available:
    • If the bulk relaxation modulus is K i > 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGlbWaaS baaSqaaiaadMgaaeqaaOGaeyOpa4JaaGimaaaa@3A14@ , the viscous pressure is computed as:(4)
      P = 0 t K ( s ) ε ˙ v o l d s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbGaey ypa0JaeyOeI0Yaa8qmaeaacaWGlbWaaeWaaeaacaWGZbaacaGLOaGa ayzkaaGafqyTduMbaiaadaWgaaWcbaGaamODaiaad+gacaWGSbaabe aaaeaacaaIWaaabaGaamiDaaqdcqGHRiI8aOGaamizaiaadohaaaa@46EF@

      with ε ˙ v o l = t r a c e ( ε ˙ ) = ε ˙ x x + ε ˙ y y + ε ˙ z z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacuaH1oqzga GaamaaBaaaleaacaWG2bGaam4BaiaadYgaaeqaaOGaeyypa0JaamiD aiaadkhacaWGHbGaam4yaiaadwgadaqadaqaaiqbew7aLzaacaaaca GLOaGaayzkaaGaeyypa0JafqyTduMbaiaadaWgaaWcbaGaamiEaiaa dIhaaeqaaOGaey4kaSIafqyTduMbaiaadaWgaaWcbaGaamyEaiaadM haaeqaaOGaey4kaSIafqyTduMbaiaadaWgaaWcbaGaamOEaiaadQha aeqaaaaa@5271@ and K( t )= 1 M K i e β ki t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGlbWaae WaaeaacaWG0baacaGLOaGaayzkaaGaeyypa0ZaaabmaeaacaWGlbWa aSbaaSqaaiaadMgaaeqaaOGaamyzamaaCaaaleqabaGaeyOeI0Iaeq OSdi2aaSbaaWqaaiaadUgacaWGPbaabeaaliaadshaaaaabaGaaGym aaqaaiaad2eaa0GaeyyeIuoaaaa@46E2@

    • If the bulk relaxation modulus is K i = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGlbWaaS baaSqaaiaadMgaaeqaaOGaeyypa0JaaGimaaaa@3A12@ and the viscous bulk modulus K ν > 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4samaaBa aaleaacqaH9oGBaeqaaOGaeyOpa4JaaGimaaaa@3A76@ , the viscous pressure is computed as:(5)
      P = K v ε ˙ v o l MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbGaey ypa0JaeyOeI0Iaam4samaaBaaaleaacaWG2baabeaakiqbew7aLzaa caWaaSbaaSqaaiaadAhacaWGVbGaamiBaaqabaaaaa@3FE3@
  4. Starting with Radioss version 2017, identical results are obtained using the same Prony coefficents Gi in /VISC/PRONY and viscoelastic materials /MAT/LAW34 (BOLTZMAN), /MAT/LAW40 (KELVINMAX), and /MAT/LAW42 (OGDEN). In previous Radioss versions, 2 Gi had to be input into /VISC/PRONY to get equivalent results.