6.2.2 Tensile Behavior

Next: 6.2.3 Shear 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 §18.2.5 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 f_t the shape of these curves is like the tension softening curves for the Smeared cracking models. See §18.1.1 for background theory.

**Figure 6.4:** Predefined tension softening for Total Strain crack model
$\begin{figure} \setlength{\unitlength}{1cm} \begin{footnotesize} \begin{picture... ...enterline{\raise 7.2cm\box\graph} } \end{picture}\end{footnotesize} \end{figure}$

Tensile parameters.

If you specified the basic properties via a Model Code [§6.2.1.1], 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 f_t .
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 f_t values for the ambient values a1 to an.
USRTST: tensile strength determined via subroutine USRTST [§11.3.5].

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}$

LINEAR: for linear softening [Fig.6.4d].
TENSTR: ft is the tensile strength f_t .
EPSULT: eu is the Mode-I ultimate tensile strain $\varepsilon_{{\mathrm{u}}}^{}$ as depicted in Figure Figure 6.4d.
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 f_t 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 USRTST [§11.3.5].
USREPU: Mode-I ultimate tensile strain determined via subroutine USREPU [§11.3.6].

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.6.4d].
EXPONE: for exponential softening [Fig.6.4e].
HORDYK: for softening according to Hordijk et al. [Fig.6.4f].
TENSTR: ft is the tensile strength f_t .
GF1: gf1 is the Mode-I fracture energy G_f^I . 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 G_f^I and a large crack bandwidth h may lead to a decreased tensile strength f_t . For direct input of GF1 and TENSTR this is checked and warnings will be issued. However, for input of G_f^I and f_t with ambient influence no warning is issued and the tensile strength f_t is lowered without notice.
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 f_t 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 G_f^I values for the ambient values a1 to an.
USRTST: tensile strength determined via subroutine USRTST [§11.3.5].
USRGF1: Mode-I tensile fracture energy determined via subroutine USRGF1 [§11.3.7].

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 f_t is not necessary.

MULTLN: for a multi-linear diagram [Fig.6.4g].
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 f_t as in Figure 6.4g.

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 [§11.3.1].
USRPAR: usrpar is a series of parameters of the user-supplied curve which DIANA passes to the subroutine.

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

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

Copyright (c) 2008 by TNO DIANA BV.