/MAT/LAW59 (CONNECT)

Block Format Keyword This law describes the Connection material, which can be used to model spotweld, welding line, glue, or adhesive layers in laminate composite material.

Elastic and elastoplastic behavior in normal and shear directions can be defined. The curves that represent plastic behavior can be specified for different displacement rates. This material is applicable only to solid hexahedron elements (/BRICK) and the element time-step does not depend on element height.

Format

(1)	(2)	(3)	(5)	(6)	(7)
/MAT/LAW59/`mat_ID`/`unit_ID` or /MAT/CONNECT/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$ $ρ_{i}$
`E`		`G`	`Imass`	`Icomp`	`Ecomp`
`N`_{b_fct}	`F`_smooth	`F`_cut

If N_{b_fct} > 0, each true plastic stress versus displacement functions in normal/tangent direction per line

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`Y_fct_ID`_N	`Y_fct_ID`_T	`SR`_ref		`Fscale`_yld

Definition

Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer, maximum 10 digits)
`unit_ID`	Unit Identifier. (Integer, maximum 10 digits)
`mat_title`	Material title. (Character, maximum 100 characters)
$ρ_{i}$ $ρ_{i}$	Density. (Real)	$[\frac{kg}{m^{3}}]$ $[\frac{kg}{m^{3}}]$
`E`	Young's modulus in the normal direction per unit length. (Real)	$[\frac{P a}{m}]$ $[\frac{P a}{m}]$
`G`	Shear modulus in the tangential direction per unit length. (Real)	$[\frac{P a}{m}]$ $[\frac{P a}{m}]$
`Imass`	Mass calculation flag. = 0 (Default) Element mass is calculated using density and volume. = 1 Element mass is calculated using density and (means of upper and lower) area. (Integer)
`Icomp`	Symmetric elasto-plastic behavior in compression. = 0 Symmetric elasto-plastic behavior in tension and compression. = 1 Elasto-plastic behavior defined by input yield function in tension only.
`Ecomp`	Compression modulus per unit length. Default = `E`	$[\frac{P a}{m}]$ $[\frac{P a}{m}]$
`N`_{b_fct}	Number of input functions: true stress versus plastic displacement (normal or tangential). = 0 Material is linear elastic. (Integer)
`F`_smooth	Displacement rate filtering flag. = 0 (Default) No displacement rate filtering. = 1 Displacement rate filtering. (Integer)
`F`_cut	Cutoff frequency for the displacement rate filtering. Default = 10³⁰ (Real)	$[Hz]$ $[Hz]$
`Y_fct_ID`_N	True plastic stress versus displacement in normal direction defined for the reference displacement rate. (Integer)
`Y_fct_ID`_T	True plastic stress versus displacement in tangential direction defined for the reference displacement rate. (Integer)
`SR`_ref	Displacement rate values for which the set of functions are defined. Default = 0.0 (Real)	$[\frac{1}{s}]$ $[\frac{1}{s}]$
`Fscale`_yld	Scale factor for the plastic stress. Default = 1.0 (Real)	$[Pa]$ $[Pa]$

▸Example (Spotweld)

#RADIOSS STARTER
/UNIT/1
unit for mat
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW59/1/1
spotweld
#              RHO_I
              7.9E-9
#                  E                   G     Imass     Icomp               Ecomp
               21000               21000         0         0                   0
#   NB_fct   Fsmooth                Fcut
         1         1                   0
# YFun_IDN  YFun_IDT              SR_ref          Fscale_yld
         1         2                   0                   0
/FAIL/CONNECT/1
#          EPS_MAX_N               EXP_N             ALPHA_N R_fct_IDN     Ifail  Ifail_so      ISYM
                   1                   0                   0         0         0         1         0
#          EPS_MAX_T               EXP_T             ALPHA_T R_fct_IDT
                 1.8                   0                   0         0
#              EIMAX               ENMAX               ETMAX                  Nn                  Nt
                   0                   0                   0                   0                   0
#               Tmax               Nsoft           AREAscale
                   0                   0                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  3. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1
New_function
#                  X                   Y
                   0                 250                                                            
                   1                 350                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/2
New_function
#                  X                   Y
                   0                 350                                                            
                   1                 350                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

This law is compatible with 8-noded hexahedron elements (/BRICK) only. It is only compatible with /PROP/TYPE43.
The stiffness modulus and stresses are defined per displacement in order to be independent from the initial height of the solid element.
For example, $E$ $E$ =210000 MPa/mm means that the normal stress increases by 210000 MPa for each 1 mm of displacement until the yield stress limit specified by the yield stress curve is reached.
The complete element displacement $\bar{u}$ $\bar{u}$ can be subdivided into an elastic portion ${\bar{u}}^{e}$ ${\bar{u}}^{e}$ (before yield stress is reached) and a portion of the plastic displacement ${\bar{u}}^{p l}$ ${\bar{u}}^{p l}$ . Plastic displacement is calculated as:
Normal plastic displacement:(1)
${\bar{u}}_{n}^{p l} = {\bar{u}}_{n} - {\bar{u}}_{n}^{e} = {\bar{u}}_{n} - \frac{σ_{n}^{t r u e}}{E}$ ${\bar{u}}_{n}^{p l} = {\bar{u}}_{n} - {\bar{u}}_{n}^{e} = {\bar{u}}_{n} - \frac{σ_{n}^{t r u e}}{E}$

Shear plastic displacement:(2)
${\bar{u}}_{s}^{p l} = {\bar{u}}_{s} - {\bar{u}}_{s}^{e} = {\bar{u}}_{s} - \frac{σ_{s}^{t r u e}}{E}$ ${\bar{u}}_{s}^{p l} = {\bar{u}}_{s} - {\bar{u}}_{s}^{e} = {\bar{u}}_{s} - \frac{σ_{s}^{t r u e}}{E}$

Total normal (shear) displacement is the sum of plastic normal (shear) displacement and elastic normal (shear) displacement.

The plastic displacement is accounted for when the normal and tangent yield stress curves are specified. These are usually non-decreasing functions, which represent true stress as a function of the plastic displacement either in normal or in shear direction. The first abscissa value of the function should be "0" and the first ordinate value is the yield stress. The functions may have a stress decrease portion to model material damage.
If Icomp =0, the material behavior is elasto plastic in both tension and compression, the compression modulus is given by Ecomp (which by default is equal to $E$ $E$ ).
If Icomp =1, the material is nonlinear elasto plastic in tension and linear in compression. The compression modulus is given by Ecomp. The normal and shear degrees of freedom are uncoupled and the shear behavior is always symmetrical.
The height of the solid element can be equal to zero.
All nodes of the solid elements must be connected to other shells or solid elements, secondary nodes of rigid body (/RBODY) or secondary nodes of tied interface (/INTER/TYPE2).
When all nodes of the solid element become free, the element is deleted.
The rupture criteria for this material are defined by /FAIL/CONNECT.