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Next: 6.2.3 Compressive Behavior Up: 6.2 Total Strain Crack Previous: 6.2.1 Basic Properties   Contents   Index

Subsections

6.2.2 Tensile Behavior

For the tensile behavior of a Total Strain crack model you may choose a predefined function [§6.2.2.1], or customize it via a user-supplied subroutine [§6.2.2.2]. See §20.2.5 for background theory.

6.2.2.1 Predefined Tension Softening Functions

For a Total Strain crack model you can choose a predefined tension softening function by specifcation of the curve name and appropriate parameters.

    (syntax)


\begin{figure}\centering
\begin{tabbing}
\texttt{'MATERI'}
\\ [-1.0ex]
\rule{14...
...cdots\;\)\hspace{14ex}\=\emph{tensile parameters} {]} \end{tabbing} \end{figure}


TENCRV
curve specifies a predefined tension softening function [Fig.6.4]. [LINEAR] Beyond the tensile strength ft the shape of these curves is like the tension softening curves for the multi-directional fixed crack models. See §20.1.1 for background theory.
Figure 6.4: Predefined tension softening for Total Strain crack model
\begin{figure}
\setlength{\unitlength}{1cm}
\begin{footnotesize}
\begin{picture...
...nterline{\raise 15.2cm\box\graph}
}
\end{picture}\end{footnotesize}
\end{figure}

Tensile parameters.
If you specified the basic properties via the CEB-FIP Model Code 1990 [§6.2.1.1], CEB-FIP Model Code 2010 [§6.2.1.2], Eurocode 2 EN 1992-1-1 [§6.2.1.3], ACI 209R-92 [§6.2.1.4], AASHTO [§6.2.1.5], JCI [§6.2.1.6], JSCE [§6.2.1.7], KCI [§6.2.1.8], or NEN 6720/A4 [§6.2.1.9] code regulations then DIANA can determine all tensile parameters without further input. Else you must specify the tensile parameters, depending on the softening function, as outlined in the following.


Elastic    (syntax)


\begin{figure}\centering
\begin{tabbing}
\texttt{'MATERI'}
\\ [-1.0ex]
\rule{14...
...\tiny {80}}}\\ *
\>\>\texttt{TENCRV}\>\texttt{ELASTI} \end{tabbing} \end{figure}


ELASTI
for elastic behavior in tension, i.e., no cracking [Fig.6.4a].


Ideal and brittle    (syntax)


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


CONSTA
for ideal behavior [Fig.6.4b].

BRITTL
for brittle behavior [Fig.6.4c].

TENSTR
ft is the tensile strength ft .

RESTST
sigres is the residual tensile strength, below which the tensile strength stress will not drop for large strains in case of brittle behavior.

TEM$ \sqcup$ $ \sqcup$ $ \sqcup$
influence by temperature: a1 to an are tempreatures T . The temperature-time dependency must be specified via input table 'TEMPER'1.2.1].

CON$ \sqcup$ $ \sqcup$ $ \sqcup$
influence by concentration: a1 to an are concentrations C . The concentration-time dependency must be specified via input table 'CONCEN'1.2.2].

MAT$ \sqcup$ $ \sqcup$ $ \sqcup$
influence by maturity: a1 to an are maturity variables M . The maturity-time dependency must be specified via input table 'MATURI'1.2.3].

PRE$ \sqcup$ $ \sqcup$ $ \sqcup$
influence by pressure: a1 to an are pressures P . The pressure-time dependency must be specified via input table 'PRESSU'1.2.4].

$ \sqcup$ $ \sqcup$ $ \sqcup$ TST
influence on the tensile strength: ft1 to ftn are the ft values for the ambient values a1 to an.

USRTST
tensile strength determined via subroutine USRTST13.3.5].


Linear tension softening - based on ultimate strain    (syntax)


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


LINEPS
for ultimate strain based linear softening [Fig.6.4d].

TENSTR
ft is the tensile strength ft .

EPSULT
eu is the Mode-I ultimate tensile strain $ \varepsilon_{{\mathrm{u}}}^{}$ as depicted in Figure 6.4d.

RESTST
sigres is the residual tensile strength, below which the tensile strength stress will not drop for large strains.

TEM$ \sqcup$ $ \sqcup$ $ \sqcup$
influence by temperature: a1 to an are tempreatures T . The temperature-time dependency must be specified via input table 'TEMPER'1.2.1].

CON$ \sqcup$ $ \sqcup$ $ \sqcup$
influence by concentration: a1 to an are concentrations C . The concentration-time dependency must be specified via input table 'CONCEN'1.2.2].

MAT$ \sqcup$ $ \sqcup$ $ \sqcup$
influence by maturity: a1 to an are maturity variables M . The maturity-time dependency must be specified via input table 'MATURI'1.2.3].

PRE$ \sqcup$ $ \sqcup$ $ \sqcup$
influence by pressure: a1 to an are pressures P . The pressure-time dependency must be specified via input table 'PRESSU'1.2.4].

$ \sqcup$ $ \sqcup$ $ \sqcup$ TST
influence on the tensile strength: ft1 to ftn are the ft values for the ambient values a1 to an.

$ \sqcup$ $ \sqcup$ $ \sqcup$ EPU
influence on the Mode-I ultimate tensile strain: eu1 to eun are the $ \varepsilon_{{\mathrm{u}}}^{}$ values for the ambient values a1 to an.

USRTST
tensile strength determined via subroutine USRTST13.3.5].

USREPU
Mode-I ultimate tensile strain determined via subroutine USREPU13.3.6].


Tension softening curves - 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}


LINEAR
for linear softening [Fig.6.4e].

EXPONE
for exponential softening [Fig.6.4f].

HORDYK
for softening according to Hordijk et al. [Fig.6.4g].

JSCESO
for softening according to Japan Society of Civil Engineers (JSCE) [71] [Fig.6.4i].

TENSTR
ft is the tensile strength ft .

GF1
gf1 is the Mode-I fracture energy GfI . The linear, exponential, and Hordijk softening curves also require 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].
Note that combinations of a small Mode-I fracture energy GfI and a large crack bandwidth h may lead to a decreased tensile strength ft . For direct input of GF1 and TENSTR this is checked and warnings will be issued. However, for input of GfI and ft with ambient influence no warning is issued and the tensile strength ft is lowered without notice.

RESTST
sigres is the residual tensile strength, below which the tensile strength stress will not drop for large strains in case of linear softening, exponential softening, or softening according to Hordijk et al.

TEM$ \sqcup$ $ \sqcup$ $ \sqcup$
influence by temperature: a1 to an are tempreatures T . The temperature-time dependency must be specified via input table 'TEMPER'1.2.1].

CON$ \sqcup$ $ \sqcup$ $ \sqcup$
influence by concentration: a1 to an are concentrations C . The concentration-time dependency must be specified via input table 'CONCEN'1.2.2].

MAT$ \sqcup$ $ \sqcup$ $ \sqcup$
influence by maturity: a1 to an are maturity variables M . The maturity-time dependency must be specified via input table 'MATURI'1.2.3].

PRE$ \sqcup$ $ \sqcup$ $ \sqcup$
influence by pressure: a1 to an are pressures P . The pressure-time dependency must be specified via input table 'PRESSU'1.2.4].

$ \sqcup$ $ \sqcup$ $ \sqcup$ TST
influence on the tensile strength: ft1 to ftn are the ft values for the ambient values a1 to an.

$ \sqcup$ $ \sqcup$ $ \sqcup$ GF1
influence on the Mode-I tensile fracture energy: gf11 to gf1n are the GfI values for the ambient values a1 to an.

USRTST
tensile strength determined via subroutine USRTST13.3.5].

USRGF1
Mode-I tensile fracture energy determined via subroutine USRGF113.3.7].


Multi-linear    (syntax)


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


A multi-linear diagram fully describes the stress-strain relationship, therefore input of the tensile strength ft is not necessary.

MULTLN
for a multi-linear diagram [Fig.6.4h].

TENPAR
are the points of the multi-linear diagram: n pairs of values ( $ \sigma$$ \varepsilon$ ); ( 1 $ \leq$ n $ \leq$ 100 )s0 ...sn are the tensile stresses $ \sigma$ , e0 ...en are the corresponding total strains $ \varepsilon$ . In general the curve should start with a linear elastic slope from the origin to the tensile strength ft as in Figure 6.4h.


JSCE tension stiffening    (syntax)


\begin{figure}\centering
\begin{tabbing}
\texttt{'MATERI'} \\ [-1.0ex]
\rule{14...
...\
\>\>\texttt{CPOWER}\>\texttt{\textit{c}}\(_{r}\,\) \end{tabbing} \end{figure}


JSCETS
for Japan Society of Civil Engineers (JSCE) tension stiffening [71] [Fig.6.4j]:

$\displaystyle \sigma$ = ft($\displaystyle \varepsilon_{{\mathrm{tu}}}^{}$/$\displaystyle \varepsilon$)c (6.3)

TENSTR
ft is the tensile strength ft .

EPSTU
etu is the end of plateau strain $ \varepsilon_{{\mathrm{tu}}}^{}$ . [ $ \varepsilon_{{\mathrm{tu}}}^{}$ = 0.0002 ]

CPOWER
c is the power c . [c = 0.4 ]


CEB-FIP Model Code 1990    (syntax)


\begin{figure}\centering
\begin{tabbing}
\texttt{'MATERI'} \\ [-1.0ex]
\rule{14...
...}\>\texttt{DMAX}\>\texttt{\textit{dmax}}\(_{i}\,\){]} \end{tabbing} \end{figure}


MC1990
for tension softening according to Paragraph 2.1.4.4.2 of the European CEB-FIP Model Code 1990 [26] [Fig.6.4k]:

TENSTR
ft is the tensile strength ft .

GF1
gf1 is the Mode-I fracture energy GfI . By default DIANA assumes a value of the crack bandwidth 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].
Note that combinations of a small Mode-I fracture energy GfI and a large crack bandwidth h may lead to a decreased tensile strength ft . This is checked and warnings will be issued.

DMAX
dmax is the maximum aggregate size of concrete in mm. Possible maximum aggregate sizes are 8, 16, or 32 mm. [ dmax = 16 mm]


CEB-FIP Model Code 2010    (syntax)


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


MC2010
for tension softening according to Paragraph 5.1.8.2 of the European CEB-FIP Model Code 2010 [27] [Fig.6.4l]:

TENSTR
ft is the tensile strength ft .

GF1
gf1 is the Mode-I fracture energy GfI . By default DIANA assumes a value of the crack bandwidth 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].
Note that combinations of a small Mode-I fracture energy GfI and a large crack bandwidth h may lead to a decreased tensile strength ft . This is checked and warnings will be issued.


CEB-FIP fiber reinforced concrete model    (syntax)


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


FRCCON
for the fiber reinforced concrete modelas defined by the CEB-FIB working groups [Fig.6.4m]. The model can be either specified as function of the total strain or as function of the crack opening.

FRCEPS
ft is the tensile strength ft , fr1 and epsr1 represent the first reference point in the stress-strain curve ( $ \varepsilon_{{\mathrm{R1}}}^{}$, fR1 ), fr3 and epsr3 represent the second reference point in the stress-strain curve ( $ \varepsilon_{{\mathrm{R3}}}^{}$, fR3 ), and epsu is the ultimate strain $ \varepsilon_{{\mathrm{u}}}^{}$ [Fig.6.4m].

FRCCMD
ft is the tensile strength ft , fr1 and cmodr1 represent the first reference point in the stress-crack opening curve ( cmdR1, fR1 ), fr3 and cmodr3 represent the second reference point in the stress-crack opening curve ( cmdR3, fR3 ), and cmodu is the ultimate crack opening cmdu . The crack strain is obtained by dividing the crack opening by 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].


6.2.2.2 User-supplied Tension Softening

DIANA offers the user-supplied subroutine mechanism for cases where the tensile stress-strain relationship cannot be input by one of the predefined curves as described in the previous section.

    (syntax)


\begin{figure}\centering
\begin{tabbing}
\texttt{'MATERI'}
\\ [-1.0ex]
\rule{14...
...{USRPAR}\>\texttt{\textit{usrpar}}\(_{r\ldots}\,\){]} \end{tabbing} \end{figure}


USRCRV
specifies that the function of the tensile stress is determined via a user-supplied subroutine [§13.3.1].

USRPAR
usrpar is a series of parameters of the user-supplied curve which DIANA passes to the subroutine.


next up previous contents index
Next: 6.2.3 Compressive Behavior Up: 6.2 Total Strain Crack Previous: 6.2.1 Basic Properties   Contents   Index
DIANA-9.6 User's Manual - Material Library
First ed.

Copyright (c) 2015 by TNO DIANA BV.