/MAT/LAW28 (HONEYCOMB)

Block Format Keyword This law describes a three dimensional nonlinear elasto-plastic material, usually used to model honeycomb or foam material.

Nonlinear elasto-plastic behavior can be specified for each othrotropic direction and shear as function of strain or volumetric strain. All degrees of freedom are uncoupled and the material is fully compressible. Tension and shear strain based failure criteria can be specified.

Format

(1)	(3)	(5)
/MAT/LAW28/`mat_ID`/`unit_ID` or /MAT/HONEYCOMB/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$
`E`₁₁	`E`₂₂	`E`₃₃
`G`₁₂	`G`₂₃	`G`₃₁

Failure plastic strain and yield stress in normal direction 11, 22, 33:

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`fct_ID`₁₁	`fct_ID`₂₂	`fct_ID`₃₃	`Iflag`₁	`Fscale`₁₁		`Fscale`₂₂		`Fscale`₃₃
$ε_{\max 11}$		$ε_{\max 22}$		$ε_{\max 33}$

Shear failure plastic strain and shear yield stress in direction 12, 23, 31:

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`fct_ID`₁₂	`fct_ID`₂₃	`fct_ID`₃₁	`Iflag`₂	`Fscale`₁₂		`Fscale`₂₃		`Fscale`₃₁
$ε_{\max 12}$		$ε_{\max 23}$		$ε_{\max 31}$

Definitions

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)
$ρ_{i}$	Initial material density (Real)	$[\frac{kg}{m^{3}}]$
`E`₁₁	Young's modulus in orthotropic dimension 1 (Real)	$[Pa]$
`E`₂₂	Young's modulus in orthotropic dimension 2 (Real)	$[Pa]$
`E`₃₃	Young's modulus in orthotropic dimension 3 (Real)	$[Pa]$
`G`₁₂	Shear modulus in direction 12 (Real)	$[Pa]$
`G`₂₃	Shear modulus in direction 23 (Real)	$[Pa]$
`G`₃₁	Shear modulus in direction 31 (Real)	$[Pa]$
`fct_ID`₁₁	Yield stress function identifier in direction 11 (Integer)
`fct_ID`₂₂	Yield stress function identifier in direction 22 (Integer)
`fct_ID`₃₃	Yield stress function identifier in direction 33 (Integer)
`Iflag`₁	Strain formulation for yield functions 11, 22, and 33 6 (Integer) = 0 (Default) Yield stress is a function of $μ$ (volumetric strains) = 1 Yield stress is a function of $ε$ (strains) = -1 Yield stress is a function of - $ε$ .
`Fscale`₁₁	Scale factor for yield stress function in direction 11 Default = 1.0 (Real)	$[Pa]$
`Fscale`₂₂	Scale factor for yield stress function in direction 22 Default = 1.0 (Real)	$[Pa]$
`Fscale`₃₃	Scale factor for yield stress function in direction 33 Default = 1.0 (Real)	$[Pa]$
$ε_{\max 11}$	Failure strain in tension in direction 11 (Real)
$ε_{\max 22}$	Failure strain in tension in direction 22 (Real)
$ε_{\max 33}$	Failure strain in tension in direction 33 (Real)
`fct_ID`₁₂	Shear yield stress function identifier in direction 12 (Integer)
`fct_ID`₂₃	Shear yield stress function identifier in direction 23 (Integer)
`fct_ID`₃₁	Shear yield stress function identifier in direction 31 (Integer)
`Iflag`₂	Strain formulation for shear yield functions 12, 23, and 31 (Integer) = 0 (Default) Yield stress is a function of $μ$ (volumetric strains) = 1 Yield stress is a function of $\dot{ε}$ (strains) = -1 Yield stress is a function of - $\dot{ε}$ .
`Fscale`₁₂	Scale factor for shear yield function 12 Default = 1.0 (Real)	$[Pa]$
`Fscale`₂₃	Scale factor for shear yield function 23 Default = 1.0 (Real)	$[Pa]$
`Fscale`₃₁	Scale factor for shear yield function 31 Default = 1.0 (Real)	$[Pa]$
$ε_{\max 12}$	Failure strain in shear direction 12 (Real)
$ε_{\max 23}$	Failure strain in shear direction 23 (Real)
$ε_{\max 31}$	Failure strain in shear direction 31 (Real)

Example (Steel)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/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/HONEYCOMB/1/1
Steel
#              RHO_I
              7.8E-9
#               E_11                E_22                E_33
              200000              200000              200000
#               G_12                G_23                G_31
              100000              100000              100000
# fct_ID11  fct_ID22  fct_ID33    Iflag1            Fscale11            Fscale22            Fscale33
         1         1         1         0                   0                   0                   0
#          Eps_max11           Eps_max22           Eps_max33
                   0                   0                   0
# fct_ID12  fct_ID23  fct_ID31    Iflag2            Fscale12            Fscale23            Fscale31
         2         2         2         0                   0                   0                   0
#          Eps_max12           Eps_max23           Eps_max31
                   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
FUNCTION: 1
#                  X                   Y
                   0                 200 
                  .5                 200 
                 1.5              200000 
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/2
FUNCTION: 2
#                  X                   Y
                   0                 100 
                  .5                 100 
                 1.5              100000 
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

This material law requires solid orthotropic property /PROP/TYPE6 (SOL_ORTH). Material is compatible with hexa and tetra elements, including 10-node tetrahedron elements. Refer to Material Compatibility for more compatibility information.
Material orthotropic coordinate system for each element (directions 1, 2, and 3) are specified in the property card /PROP/TYPE6 either through a given skew system or related to element coordinate system.

Figure 1.
All element degrees of freedom are fully uncoupled.
Elastic case example:

$σ_{11} = E_{11} ε_{11}$

$σ_{12} = G_{12} ε_{12}$

$σ_{22} = E_{22} ε_{22}$

$σ_{23} = G_{23} ε_{23}$

$σ_{33} = E_{33} ε_{33}$

$σ_{31} = G_{31} ε_{31}$

For each tension/compression and shear direction, the true stress as function of a true volumetric strain

μ

, or a true strain

ε

can be specified.

Sign conventions for strain are:

The stress values should always be positive. The following sign conventions for strain are used:

Strain Definition	Compression	Tension
Volumetric strain (`Iflag`₁ =0)	+	-
Strain (`Iflag`₁ =1)	-	+
Strain (`Iflag`₁ =-1)	+	-

For large strain formulations (I_solid> 1):(1)
$μ = (\frac{ρ}{ρ_{0}} - 1) = (\frac{V_{0}}{V} - 1) ε = \ln \frac{l}{l_{0}}$

For small strains (I_solid = 1):(2)
$μ = - (ε_{1} + ε_{2} + ε_{3}) ε_{i} = \frac{l_{i} - l_{i 0}}{l_{i 0}}$

Where, $l_{0}$ is the initial length.
When switching from a volumetric strain formulation to a strain formulation, Iflag₁ = -1 or Iflag₂ = -1 allows the same function definition to be retained.
If one of the tension strain or shear strain failures is reached, the element is deleted.