10.4 Material Section

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Multiple material sections may be defined with an input file. Each material section is identified by its own name. A particular name must not be referenced by a *solid/*beam/*shell section ($\rightarrow $10.5, 10.6, 10.7). In that case the respective material will be ignored. This is for an easy switching between different materials within an input data set.

The section keyword *MATERIAL must have an option

NAME=<name>

specifies a unique name



*MATERIAL has own sub-keywords. A first sub-keyword *DENSITY indicates the specific mass of the respective material. It has one data line specifying the value. Specific mass should not be confused with the specific weight, both differ by earth acceleration. The chosen mass unit has to be consistent with the units for length, force and time. If the keyword *DENSITY is not given a zero mass is assumed and dynamic calculations, if activated, are performed as quasistatic.

Each section keyword *MATERIAL must have exactly one material type keyword which has to be placed after the *DENSITY keyword, if there is one specified. The following material types are currently available:

material type

 

material

sym. tang.

Book ($\rightarrow $ https:://www.concrete-fem.com)

keyword

 

dimensions

stiffness

Sections

*ELASTIC

linear elasticity

1D, 2D, 3D

+

2.4, 6.3.1

 

+ phase field approach with option PHASE_FIELD

1D

na

7.5.2

 

+ visco-elasticity with option VISCO

1D

na

3.2

*ELASTICLT

linear elasticity with limited tensile strength

1D, 2D

-

8.2

 

and smeared crack

 

+ strong discontinuity approach with option SDA

2D (,3D)

-

7.7

 

replacing smeared crack

*MISES

Mises elasto-plasticity

1D, 2D, 3D

-

2.4, 6.5.1

*ISODAMAGE

isotropic damage

1D, 2D, 3D

-

6.6

*MICRODAMAGE

microplane damage

1D, 2D, 3D

-

6.8

*RCBEAM

plane reinforced concrete cross section

$M,\, N,\, V$

+

4.1.3

*RESHEET

plate with reinforcement sheet

1D

+

8.3

*NLSLAB

nonlinear model for Kirchhoff slabs

$m$

na

9.8

*RCSHELL

continuum based shell with reinforcement sheets

3D / 1D

-

10.7.1

*SPRING

nonlinear spring

$\tau $

na

3.6

*BOND

nonlinear bond

$\tau ,\, p$

+

8.5




The following combinations between element types and material types are currently implemented (* is wild card):

 

B21*

B23*

T*

S1D2

CP*

SB3

SH*

C3D*

*ELASTIC

+

+

+

+

+

+

+

+

PHASE_FIELD

-

-

+

-

-

-

-

-

VISCO

-

-

+

-

-

-

-

-

*ELASTICLT

-

-

+

-

+

-

+

-

SDA

-

-

-

-

+

-

-

(+)

*MISES

-

+

+

-

+

-

+

+

*ISODAMAGE

-

-

+

-

+

-

+

+

*MICRODAMAGE

-

-

+

-

+

-

+

+

*RCBEAM

+

+

-

-

-

-

-

-

*RESHEET

-

-

-

-

+

-

-

-

*NLSLAB

-

-

-

-

-

+

-

-

*RCSHELL

-

-

-

-

-

-

+

-

*SPRING

-

-

-

+

-

-

-

-

*BOND

-

-

-

-

+

-

-

-




The material types are used with examples (see Section 5) as listed in the following:

 

3.1

3.2

3.4

4.1

4.2

4.3

4.4

4.5

4.6

4.8

4.9

5.2

X.X

5.3

6.2

6.3

6.4

7.1

7.2

7.5

7.6

8.1

8.2

8.3

8.4

9.1

9.2

9.3

9.4

9.5

10.1

10.2

*ELASTIC

-

-

-

-

-

-

-

-

-

-

-

+

-

-

-

-

-

-

-

-

-

+

-

+

-

+

+

+

-

-

+

-

PHASE_FIELD

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

+

-

-

-

-

-

-

-

-

-

-

-

-

VISCO

-

+

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

*ELASTICLT

-

-

+

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

+

-

-

-

-

-

-

-

-

+

SDA

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

+

-

-

-

-

-

-

-

-

-

-

-

*MISES

-

-

+

-

-

-

-

-

-

-

-

-

+

+

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

*ISODAMAGE

+

-

-

-

-

-

-

-

-

-

-

-

-

-

+

+

-

+

+

-

-

-

-

-

+

-

-

-

-

-

-

+

*MICRODAMAGE

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

+

-

-

-

-

-

-

-

-

-

-

-

-

-

-

+

*RCBEAM

-

-

-

+

+

+

+

+

+

+

+

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

*RESHEET

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

*NLSLAB

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

+

+

-

-

*SPRING

-

-

+

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

*BOND

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

+

+

-

-

-

-

-

-

-



Each material type keyword has its specific data lines which are described in the following.

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*ELASTIC

The data line describes the following properties

$E$,

$\nu $,

$\alpha _T$


with

$E$

Young’s modulus

$\nu $

Poisson’s ratio

$\alpha _T$

thermal expansion coefficient

Element output provides standard data, see Section 12.3.

*ELASTIC may have an option VISCO which allows for visco-elasticity of the Kelvin-Voigt-type, see Book 3.2. This is currently implemented for elements of type T* only. This option requires two more items in the data line which now takes the form

$E$,

$\nu $,

$\alpha _T$,

$\varphi $,

$\zeta $


with

$E$

Young’s modulus

$\nu $

Poisson’s ratio

$\alpha _T$

thermal expansion coefficient

$\varphi $

creep coefficient

$\zeta $

creep time



Element output provides standard data, see Section 12.3.

*ELASTIC may have a further option PHASE_FIELD which activates the phase-field approach for resolution of strain localizations, see Book 7.5.2. This is currently implemented for elements of type T* only. This option requires three more data in the data line which now takes the form

$E$,

$\nu $,

$\alpha _T$,

$G_f$,

$l$,

$\eta _{s}$


with

$E$

Young’s modulus

$\nu $

Poisson’s ratio

$\alpha _T$

thermal expansion coefficient

$G_f$

fracture toughness

$l$

characteristic length

$\eta _{s}$

stress viscosity – might be necessary for convergence, see Book A.1 (currently trial and error, default should be 0!)



Element output provides standard data, see Section 12.3, and additionally the value of damage variable $d$ as last item of integration point data lines.

The options VISCO and PHASEFIELD cannot be combined.

*ELASTICLT

The data line describes the following properties

$E$,

$\nu $,

$f_{ct}$,

$G_f$,

$L_w$,

$\alpha _{res}$,

$\eta _s$


with

$E$

Young’s modulus

$\nu $

Poisson’s ratio

$f_{ct}$

uniaxial tensile strength

$G_f$

crack energy

$L_w$

width of weak section – currently effective only for 1D material approach

 

generally corresponds to crack band width $b_w$ (material property!) but must not

$\alpha _{res}$

residual crack traction related to uniaxial tensile strength in case of macro crack

$\eta _c$

crack traction viscosity – might be necessary for convergence, see Book A.1 (currently trial and error, default should be 0!)



*ELASTICLT has distinct states which are reported to the execution report, see Section 12.2, when a state change occurs

0

uncracked

1

cracked loading branch

2

cracked unloading branch

3

crack closure

4

fully cracked with zero crack traction



Element output provides standard data, see Section 12.3.

*ELASTICLT may have an option SDA which activates the strong discontinuity approach (SDA) to describe crack formation by allowing for displacement discontinuities instead of smeared cracks, see Book 7.7. This is appropriate for continuum elements of type C* only. This is currently implemented as fixed crack for element types CP* and under construction for C3D*. This option requires a modified data line

$E$,

$\nu $,

$f_{ct}$,

$G_f$,

$\alpha _{sr}$,

$\phi _{md}$,

$\eta _{s}$,

$\eta _{s}$


with

$E$

Young’s modulus

$\nu $

Poisson’s ratio

$f_{ct}$

uniaxial tensile strength

$G_f$

crack energy

$\alpha _{sr}$

shear retention factor $0\le \alpha _{sr} \le 1$

 

as far as can be seen results are quite sensitive with respect to this factor, i.e. small values $\alpha _{sr}\ll 1$ seem to be appropriate

$\phi _{md}$

minimum deviation (angle degree unit) for secondary fixed cracking according to Rankine criterion

 

$\phi _{md}=-1$ prevents dual cracking

$\eta _{s}$

stress viscosity – might be necessary for convergence, see Book A.1 (currently trial and error, default should be 0!)

$\eta _c$

crack traction viscosity for discrete cracks – might be necessary for convergence, see Book A.1 (currently trial and error, default should be 0!)



Regarding ordinary integration points the element output provides standard data, see Section 12.3. Regarding integration points along discontinuity lines, additional data lines are provided, see also Section 12.3.

*MISES

The data line describes the following properties

$E$,

$\nu $,

$f_y$,

$f_u$,

$\epsilon _u$,

$\alpha _T$,

$\alpha _{s1D}$


with

$E$

Young’s modulus

$\nu $

Poisson’s ratio, not used for 1D

$f_y$

yield stress in case of uniaxial stress

$f_u$

failure stress in case of uni axial stress

$\epsilon _u$

strain corresponding to $f_u$

$\alpha _T$

thermal expansion coefficient

$\alpha _{s1D}$

parameter to smooth transition in yield point – for 1D stress-strain only

 

generally $\alpha _{s1D}=0$ $\rightarrow $ sharp transition, try $\alpha _{s1D}\approx 0.1$ in case of convergence problems



Element output provides standard data, see Section 12.3, and additionally

for B* elements types

longitudinal stresses $\sigma _x$ at lower and upper edge as last two items of integration point data lines

for other element types

the value of the current yield stress $f_y$ as last item of integration point data lines

*ISODAMAGE

The data line describes the following properties

$E_0$,

$\nu $,

$f_c$,

$f_{ct}$,

$LimTY$,

$\alpha _{biax}$,

$r_{confined},$

$\alpha _{confined}$,

$RegTY$,

$R$ or $G_f$,

$\eta _{s}$,

$\eta _{c}$


with

$E_0$

initial Young’s modulus

$\nu $

Poisson’s ratio

$f_c$

uniaxial compressive strength

$f_{ct}$

uniaxial tensile strength

$LimTY$

type of triaxial strength surface

 

choose $LimTy=1$ – other values reserved for further extensions

$\alpha _{biax}$

biaxal compressive strength related to uniaxial compressive strength

$r_{confined}$

circumferential stress related to longitudinal stress (compression) of confined cylinder specimen

$\alpha _{confined}$

longitudinal strength related to uniaxial compressive strength of confined cylinder specimen under the condition $r_{confined}$

$RegTY$

regularization type

 

$RegTY=0$: no regularization

 

$RegTY=1$: gradient damage

 

$RegTY=2$: crack band

$R$

characteristic length for $RegTY=1$

$G_f$

cack energy for $RegTY=2$ – be careful with units!

 

value is ignored for $RegTY=0$

$\eta _{s}$

stress viscosity – might be necessary for convergence (currently trial and error, default should be 0!)

$\eta _{c}$

crack traction viscosity for smeared cracks / SDA – might be necessary for convergence (currently trial and error, default should be 0!)



Some care has to be taken in choosing the relations of $f_c - E_0$, $f_c - f_{ct}$, $r_{confined} - \alpha _{confined}$ and the value of $\alpha _{biax}$. There might be unfeasible choices.

As an example with units [MN,m]

  36300.,0.2,   40.,3.5,  1,1.2,0.2,2.0,  2,150.e-6,  0., 0.

should make sense, e.g., for C40 according to MC2010.

Element output provides standard data, see Section 12.3, and additionally the value of isotropic damage $D$ as last item of integration point data lines.

*MICRODAMAGE

The data line describes the following properties

$E_0$,

$\nu $,

$LimTY$,

$f_{ct}$,

$\alpha _{ct}$,

$x$,

$y$,

$RegTY$,

$R$,

$\eta _{s}$,

$\eta _{c}$


with

$E_0$

initial Young’s modulus

$\nu $

Poisson’s ratio

$LimTY$

type of triaxial strength surface

 

choose $LimTy=2$ – other values reserved for further extensions

$f_{ct}$

uniaxial tensile strength

$\alpha _{ct}$

a measure of uniaxial compressive strength related to uniaxial tensile strength

 

this does not exactly reproduce the ratio, some inverse trial and error has to be applied to calibrate for a target

$x$

currently not used, set $x=0$ – reserved for further extensions

$y$

currently not used, set $y=0$ – reserved for further extensions

$RegTY$

regularization type

 

$RegTY=0$: no regularization

 

$RegTY=2$: crack band

$G_f$

cack energy for $RegTY=2$ – be careful with units!

 

value is ignored for

  \[ RegTY=0 \]    

$\eta _{s}$

stress viscosity – might be necessary for convergence (currently trial and error, start with 0.0!)

$\eta _{c}$

crack traction viscosity for smeared cracks / SDA – might be necessary for convergence (currently trial and error, start with 0.0!)



As an example with units [MN,m]

   363000., 0.20,   2, 3.0, 13.0,   0., 0.,   0, 150.e-06,   0., 0.

should make sense, e.g., for C40 according to MC2010.

Element output provides standard data, see Section 12.3, and additionally an averaged damage value over all microplanes of an integration point.

*RCBEAM

This must be combined with geometric reinforcement data defined in a *BEAM SECTION, see Section 10.6. The first data line describes the following concrete properties

$E_c$,

$f_c$,

$\epsilon _{c1}$,

$\epsilon _{cu1}$,

$f^{ts}_{ct}$,

$n$

$\alpha _T$

$\varphi $

$1/\zeta $

$f_{ct}$


with

$E_c$

Young’s modulus

$f_c$

compressive strength

$\epsilon _{c1}$

strain corresponding to compressive strength

$\epsilon _{cu1}$

ultimate strain in case of uniaxial stress

$f^{ts}_{ct}$

nominal tensile strength – for tension stiffening

 

value comes only into play if tension stiffening is activated in *BEAM SECTION, see Section 10.6

$n$

number of layers for integration of nonlinear stress-strain relation

 

$n=1$ uses a linear relation without tension

 

$n=1$ is mandatory to compute creep of concrete

 

$n=50$ is generally used for nonlinear uniaxial concrete behavior

$\alpha _T$

thermal expansion coefficient

$\varphi $

creep coefficient

$1/\zeta $

$\zeta \rightarrow $ creep time

$f_{ct}$

tensile strength – to consider concrete tensile strength in moment-curvature relations

 

value is generally set to 0 according to common standards



Tensile strength values $f^{ts}_{ct}$ and $f_{ct}$ are used in different contexts and may be chosen independent from each other.

The second data line describes the reinforcing steel properties and is the same as for the *MISES data line.

Element output provides standard data for beam elements, see Section 12.3, and additionally edge strains [‰]: concrete edge strain at the compressed edge and strain of reinforcement with the largest lever arm at the tension edge.

*RESHEET

This material type provides a reinforcement like plane sheet with uniaxial Mises elasto-plasticity. The data line describes the following properties

$E$,

$\varphi $,

$f_y$,

$f_u$,

$\epsilon _u$,

$\alpha _T$


with

$E$

Young’s modulus

$\varphi $

orientation of reinforcement with respect to global $x$-direction in degrees

$f_y$

yield strength in case of uniaxial stress

$f_u$

failure strength in case of uniaxial stress

$\epsilon _u$

strain corresponding to $f_u$

$\alpha _T$

thermal expansion coefficient



which to a large degree corresponds to the *MISES data line but be aware of the second item $\varphi $.

Only one data line is allowed corresponding to one reinforcement sheet. Further reinforcement sheets have to be defined with further *RESHEET material sections.

Element output provides standard data for 2D continuum elements, see Section 12.3.

*NLSLAB

This material type provides a bilinear moment-curvature relation for usage with Kirchhoff-slabs. This includes elasto-plastic behavior with unloading, i.e. elastic behavior of plastic cross sections prior to unloading. As slabs are statically indeterminate internally an elasto-plastic behavior should not be expected in a straightforward way. The data line describes the following properties

$k_x$,

$k_y$,

$m_{fx}$,

$m_{fy}$,

$k_{Tx}$,

$k_{Ty}$,

$m_{ux}$,

$m_{uy}$,

$\alpha $


with

$k_x$

initial bending stiffness in global $x$-direction

$k_y$

initial bending stiffness in global $y$-direction

$m_{fx}$

final / yield-moment of initial branch in global $x$-direction

$m_{fy}$

final / yield moment of initial branch in global $y$-direction

$k_{Tx}$

hardening bending stiffness in global $x$-direction

$k_{Ty}$

hardening bending stiffness in global $y$-direction

$m_{ux}$

final / ultimate-moment of hardening branch in global $x$-direction

$m_{uy}$

final / ultimate moment of hardening branch in global $y$-direction

$\alpha $

factor for twisting stiffness



This is applied with absolute values for both positive moments (lower side tension) and negative moments (upper side tension) in the same way. Different definitions for positive and negative moments can be given with an expanded data line

$k^{pos}_x$,

$k^{pos}_y$,

$m^{pos}_{fx}$,

$m^{pos}_{fy}$,

$k^{pos}_{Tx}$,

$k^{pos}_{Ty}$,

$m^{pos}_{ux}$,

$m^{pos}_{uy}$,

$\alpha $,

$k^{neg}_x$,

$k^{neg}_y$,

$m^{neg}_{fx}$,

$m^{neg}_{fy}$,

$k^{neg}_{Tx}$,

$k^{neg}_{Ty}$,

$m^{neg}_{ux}$,

$m^{neg}_{uy}$


whereby the upper index $pos$ indicates positive parameters and $neg$ negative parameters. See also the Book Sections 9.8.2, 9.8.3 for a further specification of these values.

Element output provides standard data for slabs, see Section 12.3.

*RCSHELL

This material type is appropriate for the continuum based shell with element type SH4 and must be combined with geometric reinforcement data defined in a *SHELL SECTION, see Section 10.7. The first seven items of the following data line correspond to the *MISES data line to be applied to uniaxial reinforcement behavior. The last item refers to a biaxial material law.

$E$,

$\nu $,

$f_y$,

$f_u$,

$\epsilon _u$,

$\alpha _T$,

$\alpha _{s1D}$,

$MATN$


with

$E$

Young’s modulus

$\nu $

Poisson’s ratio, not used for 1D

$f_y$

yield stress in case of uniaxial stress

$f_u$

failure stress in case of uni axial stress

$\epsilon _u$

strain corresponding to $f_u$

$\alpha _T$

thermal expansion coefficient

$\alpha _{s1D}$

parameter to smooth transition in yield point – for 1D stress-strain only

 

generally $\alpha _{s1D}=0$ $\rightarrow $ sharp transition, try $\alpha _{s1D}\approx 0.1$ in case of convergence problems

$MATN$

name of a material of type *ELASTICLT or *ISODAMAGE or *MICRODAMAGE

 

the respective material has to be explicitly defined with a material type specification



Element output provides standard data for shells, see Section 12.3.

*SPRING

This material type provides a force $t$ depending on a relative displacement $s$. This is basically described by cubic splines. It behaves in the same way in the negative and positive range. The data line describes the following properties

$x$,

$s_1$,

$t_1$,

$s_2$,

$t_2$,

$s_0$,

$k_0$


with

$x$

currently not used

$s_1$

prescribed relative displacement

$t_1$

force prescribed with $s_1$

 

$\textrm{d}t/\textrm{d}s=0$ for $s=s_1$

$s_2$

prescribed relative displacement, $s_2>s_1$

$t_2$

force prescribed with $s_2$

 

$\textrm{d}t/\textrm{d}s=0$ for $s \ge _2$

$s_0$

end of starting range of relative displacement with linear stiffness $k_0$ up to $s_0$

 

may be set to $s_0=0$ starting with a cubic spline with initial slope $k_0$

$k_0$

initial constant stiffness $\textrm{d}t/\textrm{d}s$ for $0\le s \le s_0$



In case of decreasing $|s|$ the same force path is followed in reverse direction as for increasing $|s|$.

Element output provides standard data for springs, see Section 12.3.

*BOND

*BOND is an extension of *SPRING. It has the same behavior in case of loading, i.e. increasing $|s|$. But regarding unloading with decreasing $|s|$ this type *BOND follows a ‘damage’-characteristic, i.e. a linear path from largest $|s|_{m}$ in the current loading path to $s=0, t=0$. The $t_s$-relation moves on this linear path as long as $|s|<|s|_{m}$ including a $s$-sign reversal where necessary. The loading path is continued like *SPRING in case $|s|>|s|_m$. This increases $|s|_m$ directly connected to $|s|$, i.e. $|s|_m$ is a state variable.

First data line describes the following properties

$x$,

$k_{lat}$


with

$x$

currently not used

$k_{lat}$

linear stiffness related to lateral relative displacements of connected parts

 

connected parts are generally a bulk material (e.g. concrete) and an embedded reinforcement

 

in order to prevent a mutual penetration this should be a relatively high value with respect to the implied penalty method

 

to check the relative lateral displacements see following output description



The second data line is same as for *SPRING.

Element output provides standard data for bond elements, see Section 12.3.

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