6.1.2 Tension Softening

Next: 6.1.3 Shear Retention Up: 6.1 Smeared Cracking Previous: 6.1.1 Tension Cut-off Contents Index

Subsections

6.1.2.1 Ambient Influence

6.1.2 Tension Softening

Figure 6.2 shows the available tension softening models. See also §18.1.1 for background theory.

**Figure 6.2:** Tension softening - Smeared cracking
$\begin{figure}\begin{footnotesize}\setlength{\unitlength}{1cm} \begin{picture... ...enterline{\raise 5.7cm\box\graph} } \end{picture}\end{footnotesize} \end{figure}$

Brittle cracking (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...xtsf{\tiny {80}}}\\ * \>\>\texttt{TENSIO}\>\texttt{0} \end{tabbing} \end{figure}$

TENSIO: 0 indicates brittle cracking [§18.1.1.1]. No further values are necessary.

Linear tension softening - based on ultimate strain (syntax)

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

Linear tension softening - based on fracture energy (syntax)

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

TENSIO

1 indicates linear tension softening [§18.1.1.2].

TENVAL

eu is the ultimate strain $\varepsilon_{{\mathrm{u}}}^{{\mathrm{cr}}}$ of the diagram. For reinforced concrete, take $\varepsilon_{{\mathrm{u}}}^{{\mathrm{cr}}}$ = $\sigma_{{\mathrm{y,steel}}}^{}$ /E_steel . For unreinforced concrete, take $\varepsilon_{{\mathrm{u}}}^{{\mathrm{cr}}}$ = 2G_f/f_th_cr , with G_f the fracture energy and h_cr the estimated numerical crack bandwidth.

GF

gf is the fracture energy. In this case DIANA calculates the ultimate crack strain as

$\displaystyle \varepsilon_{{\mathrm{u}}}^{{\mathrm{cr}}}$ = $\displaystyle {\frac{{ 2 G_{\mathrm{f}} }}{{ f_{\mathrm{t}} h }}}$

(6.1)

with h is the crack bandwidth. By default DIANA assumes a value of h related to the area or the volume of the element. You may overrule the default by specifying the crack bandwidth explicitly via the CRACKB input data item [§6.3].

Multilinear tension softening (syntax)

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

TENSIO: 2 indicates multilinear tension softening [§18.1.1.3].
TENVAL: specifies a diagram with two values for each point: st1 ...stn (n $\leq$ 5 )are the tensile stresses $\sigma_{{nn}}^{}$ normal to the crack, et1 ...etn are the tensile crack strains $\varepsilon_{{nn}}^{{\mathrm{cr}}}$ normal to the crack. The diagram may also contain ascending parts (hardening). The last (zero) branch must also be specified, via a point far away with zero stress and very high strain.

Nonlinear tension softening (Moelands and Reinhardt) (syntax)

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

TENSIO: 3 indicates nonlinear tension softening according to Moelands and Reinhardt [§18.1.1.4].
GF: gf is the fracture energy G_f . This model also requires the crack bandwidth h . By default DIANA assumes a value of h related to the area or the volume of the element. You may overrule the default by specifying the crack bandwidth explicitly via the CRACKB input data item [§6.3].

Nonlinear tension softening (Hordijk et al.) (syntax)

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

TENSIO: 5 indicates nonlinear tension softening according to Hordijk, Cornelissen and Reinhardt [§18.1.1.5].
TENVAL: c1 and c2 are the factors c₁ and c₂ . [c₁ = 3 , c₂ = 6.93 ]
GF: gf is the fracture energy G_f . This model also requires the crack bandwidth h . By default DIANA assumes a value of h related to the area or the volume of the element. You may overrule the default by specifying the crack bandwidth explicitly via the CRACKB input data item [§6.3].

6.1.2.1 Ambient Influence

The tension softening criterion may be specified depending on ambient values for temperature, concentration or maturity. In this case the criterion must be specified with TENSIO as indicated in the previous section followed by the data records in this section.

Linear tension softening - based on ultimate strain (syntax)

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

eua ...euz: (z $\leq$ 30 )are the ultimate strains $\varepsilon_{{\mathrm{u}}}^{{\mathrm{cr}}}$ respectively valid for the corresponding ambient values. It is not necessary to specify the constant value for $\varepsilon_{{\mathrm{u}}}^{{\mathrm{cr}}}$ with TENVAL.
TEMTEN: specifies temperature influence, tea ...tez are temperatures T .
CONTEN: specifies concentration influence, coa ...coz are concentrations C .
MATTEN: specifies maturity influence, mva ...mvz are maturity variables M .

(file.dat)

'MATERI'
  1   TENSIO 1
      TEMTEN     0.0  0.001
               400.0  0.001
              1000.0  0.002

Linear tension softening - based on fracture energy (syntax)

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

gfa ...gfz: (z $\leq$ 30 )are the fracture energies G_f respectively valid for the corresponding ambient values. It is not necessary to specify the constant value for G_f with GF.
TEMGF1: specifies temperature influence, tea ...tez are temperatures T .
CONGF1: specifies concentration influence, coa ...coz are concentrations C .
MATGF1: specifies maturity influence, mva ...mvz are maturity variables M .

(file.dat)

'MATERI'
  1   TENSIO 1
      MATGF1     0.0  0.02
                 0.1  0.03
                 1.0  0.05

Multilinear tension softening (syntax)

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

etna ...etnz: (z $\leq$ 30 )are the tensile crack strains $\varepsilon_{{nn}}^{{\mathrm{cr}}}$ normal to the crack for the last branch of the softening model, respectively valid for the corresponding ambient value. DIANA scales the other tensile crack strains proportionally to the values et of TENVAL. The tensile stresses st1 to stn of the tension softening model are scaled proportionally to the ft1 to ftn values of the tension cut-off model [§6.1.1.1].
TEMTEN: specifies temperature influence, tea ...tez are temperatures T .
CONTEN: specifies concentration influence, coa ...coz are concentrations C .
MATTEN: specifies maturity influence, mva ...mvz are maturity variables M .

Nonlinear tension softening (syntax)

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

TENSIO tnr: specifies the tension softening model: 3 for nonlinear tension softening according to Moelands and Reinhardt, or 5 for nonlinear tension softening according to Hordijk et al.
TENVAL: specifies parameters for the softening model: ft is the tensile strength f_t , gf is the fracture energy G_f , h is the estimated numerical crack bandwidth h_cr , c1 and c2 are the factors c₁ and c₂ [c₁ = 3 , c₂ = 6.93 ] (only for nonlinear tension softening according to Hordijk et al.).
gfa ...gfz: are the fracture energy values G_f , (z $\leq$ 30 ) respectively valid for the corresponding ambient values. DIANA derives value ft of the tension softening model from the values of the tension cut-off model [§6.1.1.1]. Factors h, c1 and c2 are considered to remain constant, i.e., no ambient influence on these factors.
TEMTEN: specifies temperature influence, tea ...tez are temperatures T .
CONTEN: specifies concentration influence, coa ...coz are concentrations C .
MATTEN: specifies maturity influence, mva ...mvz are maturity variables M .

User-supplied - based on ultimate strain (syntax)

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

USRTEN: specifies that the ambient influence on the tension softening model is determined via a user-supplied subroutine [§11.3.3]. DIANA passes the keyword usrkey to the first argument of this subroutine.

User-supplied - based on fracture energy (syntax)

$\begin{figure}\centering \begin{tabbing} \texttt{'MATERI'} \\ [-1.0ex] \rule{14... ...\>\texttt{USRGF1}\>\texttt{\textit{usrkey}}$_{w}\,$ \end{tabbing} \end{figure}$

USRGF1: specifies that the ambient influence on the tension softening model is determined via a user-supplied subroutine [§11.3.7]. DIANA passes the keyword usrkey to the first argument of this subroutine.

Next: 6.1.3 Shear Retention Up: 6.1 Smeared Cracking Previous: 6.1.1 Tension Cut-off Contents Index

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

Copyright (c) 2008 by TNO DIANA BV.