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7.2 Maxwell Chain

The direct input of the Maxwell Chain model is specified by the number of units in the chain, and for each unit the elasticity (optionally age or temperature dependent or both) and the relaxation [§19.1]. DIANA can generate direct input from indirect input of relaxation or creep curves [§7.4]. User-specified direct input overrules any form of indirect input for the current material index.

(syntax)

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

MAXWEL

specifies viscoelasticity with the Maxwell Chain model, nchain is the number of units n_c in the chain [§19.1]. ( n_c $\leq$ 10 )

SUPIST

suppresses the application of initial stresses, as defined for the initial state evaluation of the nonlinear analysis [Vol. Analysis Procedures], in Maxwell creep evaluation.^7.1If you set this option, then DIANA will store the initial stresses on the analysis database (the FILOS file) for the corresponding elements and subtract these from the total stresses in the Maxwell stress evaluation. That means that the initial stresses will not relax. If you don't set this option (the default), then only the total stresses will be applied in the Maxwell stress evaluation.

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

mwnr

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:

RELTIM

rt the relaxation time $\lambda_{{\alpha}}^{}$ . Relaxation time is not applied to the first unit of the Maxwell chain. If no relaxation 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 (n $\leq$ 30 )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.
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: are the Young's moduli E_t for element ages t (n $\leq$ 30 )respectively. 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 time.

Direct Maxwell input (file.dat)

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

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

Aging and temperature influence (file.dat)

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

Unit 1: with age independent Young's modulus E = 20000 .
Unit 2: with 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 dashpot relaxation time $\lambda_{{\alpha}}^{}$ = 10 .
Unit 4: with 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 dashpot relaxation time $\lambda_{{\alpha}}^{}$ = = 100 .
Unit 5: calls the user-supplied subroutine with keyword FRAC5.

Next: 7.3 Kelvin Chain Up: 7. Viscoelasticity Previous: 7.1.2 Young Hardening Concrete Contents Index

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

Copyright (c) 2008 by TNO DIANA BV.