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7.3 Kelvin Chain

The direct input of the Kelvin Chain model form is specified by the number of units in the chain, and for each unit the elasticity and the viscosity [§19.2.1]. The elasticity may be age or temperature dependent or both. DIANA can generate direct input from indirect input of creep curves [§7.4]. Direct input of chain parameters overrules any form of indirect input for the current material index.

(syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...}\>\texttt{RETTIM}\>\texttt{\textit{rt}}$_{r}\,${]} \end{tabbing} \end{figure}$

KELVIN

specifies viscoelasticity with the Kelvin Chain model, nchain is the number of units n_c ( n_c $\leq$ 10 )in the chain [§19.2.1].

The following data must be specified for each unit of the chain.

kvnr

is the chain unit number for which the following properties are valid. Don't forget the leading comma!

The syntax for the four types of input is outlined below. Note that age dependency and ambient influence may be combined.

All types of input may be supplemented with:

RETTIM

rt the retardation time $\lambda_{{\alpha}}^{}$ . If no retardation time is specified, then DIANA assumes a spring with appropriate Young's modulus. No damping is applied in this case.

Constant (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...\\ \>\>\texttt{YOUNG}\>\texttt{\textit{e}}$_{r}\,$ \end{tabbing} \end{figure}$

YOUNG: e is Young's modulus E .

Age dependent (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...}}$_{r}\,$ \ldots{]} \texttt{\textit{en}}$_{r}\,$ \end{tabbing} \end{figure}$

TIME t0 ...tn: are the element ages t (n $\leq$ 30 )at which Young's modulus is specified. The element age is independent of a user-specified starting time, see the note in §7.4.2.
YOUNG e0 ...en: are the Young's moduli E_t at the specified element ages respectively.

Ambient influence (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...textit{mvz}}$_{r}\,$ \texttt{\textit{ez}}$_{r}\,$ \end{tabbing} \end{figure}$

ea ...ez: (z $\leq$ 30 )are the Young's moduli E for the corresponding ambient values respectively.
TEMYOU: specifies temperature influence on Young's modulus, tea ...tez are temperatures T .
CONYOU: specifies concentration influence on Young's modulus, coa ...coz are concentrations C .
MATYOU: specifies maturity influence on Young's modulus, mva ...mvz are maturity variables M .

Time dependent and ambient influence (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...}$_{r}\,$ \ldots{]} \texttt{\textit{ezn}}$_{r}\,$ \end{tabbing} \end{figure}$

e_0 ...e_n: (n $\leq$ 30 )are the respective Young's moduli E_t for element ages t . Values ea_ are for ambient value __a, values eb_ for ambient value __b etc. until ez_ for ambient value __z. (z $\leq$ 30 )For example in TEMYOU, value eb1 is Young's modulus E_{T_b, t₁} for temperature T_b at element age t₁ .
TIME t0 ...tn: are the element ages t at which Young's modulus is specified. The element age is independent of a user-specified starting time, see the note in §7.4.2.
TEMYOU: specifies temperature influence on Young's modulus, tea ...tez are temperatures T .
CONYOU: specifies concentration influence on Young's modulus, coa ...coz are concentrations C .
MATYOU: specifies maturity influence on Young's modulus, mva ...mvz are maturity variables M .

User-supplied (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...\>\texttt{USRYOU}\>\texttt{\textit{usrkey}}$_{w}\,$ \end{tabbing} \end{figure}$

USRYOU: specifies that the ambient influence on Young's modulus is determined via a user-supplied subroutine [§11.1.1]. DIANA passes the keyword usrkey to the first argument of this subroutine. The ambient influence can be any function of temperature, concentration, maturity and element age.

Direct Kelvin input (file.dat)

'MATERI'
  1  YOUNG   15718.
     POISON  0.2
     KELVIN  5
  ,1 YOUNG   6030.
  ,2 YOUNG   1520.0
     RETTIM  0.4
  ,3 YOUNG   2463.5
     RETTIM  4.
  ,4 YOUNG   3743.
     RETTIM  100.
  ,5 YOUNG   1961.5
     RETTIM  400.

The parameters in the above example describe a particular Kelvin Chain.

Aging and temperature influence (file.dat)

'MATERI'
 2  YOUNG   37000.
     POISON  0.2
     KELVIN  5
  ,1 YOUNG   20000.
  ,2 TIME    0. 10.
     YOUNG   5000. 7000.
  ,3 TEMYOU    0. 6000.
             100. 4000.
             200. 3000.
     RETTIM  10.
  ,4 TIME          0.    10.
     TEMYOU    0. 6000. 8000.
             100. 5000. 7000.
             200. 3000. 4000.
     RETTIM  100.
  ,5 USRYOU  FRAC5

Unit 1: with age independent Young's modulus E = 20000 without dashpot.
Unit 2: with element age dependent Young's modulus: E_t=0 = 5000 , E_t=10 = 7000 , without dashpot.
Unit 3: with temperature dependent Young's modulus: E_T=0 = 6000 ,
E_T=100 = 4000 , E_T=200 = 3000 , with retardation time $\lambda_{{\alpha}}^{}$ = 10 .
Unit 4: with element age and temperature dependent Young's modulus:
E_{(t=0, T=0)} = 6000 , E_{(t=10, T=0)} = 8000 , E_{(t=0, T=100)} = 5000 , E_{(t=10, T=100)} = 7000 , E_{(t=0, T=200)} = 3000 , E_{(t=10, T=200)} = 4000 , with retardation time $\lambda_{{\alpha}}^{}$ = 100 .
Unit 5: calls the user-supplied subroutine with keyword FRAC5.

Next: 7.4 Determination of Chain Up: 7. Viscoelasticity Previous: 7.2 Maxwell Chain Contents Index

DIANA-9.3 User's Manual - Material Library
First ed.

Copyright (c) 2008 by TNO DIANA BV.