HyperWorks Solvers

Tsai-Wu Formulation (Iform =0)

Tsai-Wu Formulation (Iform =0)

Previous topic Next topic Expand/collapse all hidden text  

Tsai-Wu Formulation (Iform =0)

Previous topic Next topic JavaScript is required for expanding text JavaScript is required for the print function  

Block Format Keyword

/MAT/LAW25 - Orthotropic Shell and Solid Material Tsai-Wu Formulation (Iform =0)

Description

This law describes the composite shell and solid material using the Tsai-Wu formulation. The material is assumed to be orthotropic-elastic before the Tsai-Wu criterion is reached. The material becomes nonlinear afterwards. For solid elements, the material is assumed to be linearly elastic in the transverse direction. The Tsai-Wu criterion limit can be set dependent on the plastic work and strain rate to model material hardening. Strain and plastic energy criterion for brittle damage and failure are available. A simplified delamination criterion based on out-of-plane shear angle can be used.

Format

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

/MAT/LAW25/mat_ID/unit_ID or /MAT/COMPSH/mat_ID/unit_ID

mat_title

 

 

 

 

 

 

 

 

E11

E22

Iform

 

E33

G12

G23

G31

E1f1

E1f2

E1t1

E1m1

E1t2

E1m2

dmax

 

Composite Plasticity Hardening

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

symbol_Wp_ref

Ioff

 

Ratio

 

 

b

n

fmax

 

 

 

 

 

Composite Yield Stress in Tension Compression

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

symbol_a_14

 

Yield Stress in Shear and Strain Rate

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

c

ICC

 

 

Delamination

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

d3max

 

 

 

 

 

Strain Rate Filtering

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

Fsmooth

Fcut

 

 

 

 

 

 

 

hmtoggle_plus1Flag Definition

Field

Contents

SI Unit Example

mat_ID

Material identifier

(Integer, maximum 10 digits)

 

unit_ID

Optional unit identifier

(Integer, maximum 10 digits)

 

mat_title

Material title

(Character, maximum 100 characters)

 

Initial density

(Real)

symbol_kg

E11

Young‘s modulus in direction 1

(Real)

E22

Young’s modulus in direction 2

(Real)

Poisson’s ratio

(Real)

 

Iform

Formulation flag (Comment 1)

(Integer)

= 0: Tsai-wu formulation

 

E33

Young’s modulus in direction 33 (Comment 4)

(Real)

G12

Shear modulus in direction 12

(Real)

G23

Shear modulus in direction 23

(Real)

G31

Shear modulus in direction 31

(Real)

E1f1

Maximum tensile strain for element deletion in material direction 1

Default = 1.2 x 1030 (Real)

 

E1f2

Maximum tensile strain for element deletion in material direction 2

Default = 1.2 x 1030 (Real)

 

E1t1

Tensile failure strain in the material direction 1 at which stress starts to reduce (Comment 6)

Default = 1.0 x 1030  (Real)

 

E1m1

Maximum tensile strain in material direction 1 at which the stress at the element is set to zero, if dmax = 1 (Comment 6)

Default = 1.1 x 1030  (Real)

 

E1t2

Tensile failure strain in the material direction 2 at which the stress starts to reduce

Default = 1.0 x 1030  (Real)

 

E1m2

Maximum tensile strain in material direction 2 at which the stress in the element is set to zero, if dmax=1.

Default = 1.1 x 1030  (Real)

 

dmax

Maximum damage factor dmax < 1) (Comment 6)

Default = 0.999  (Real)

 

Maximum plastic work per unit shell volume

Default = 1030 (Real)

symbol_Jm3

symbol_Wp_ref

Reference plastic work per unit shell volume (Comment 16)

Default = 1.0  (Real)

symbol_Jm3

Ioff

Flag that controls shell and thick shell element deletion depending on failure modes in the element layers.

(Integer)

0: shell is deleted if for one element layer.

= 1: shell is deleted if for all element layers.

= 2: shell is deleted if for each element layer,

= 3: shell is deleted if for each element layer,

= 4: shell is deleted if for each element layer, condition 1 and condition 2 are satisfied.

= 5: shell is deleted if for all element layers, condition 1 or condition 2 is satisfied.

= 6: shell is deleted if for each element layer condition 1 or condition 2 is satisfied.

 

Ratio

Ratio parameter which controls the deletion of shell elements based on the number of failed layers.

Default = 1.0  (Real)

< 0.0: the element will be deleted if all of the layers but one fail (that is, the number of layers that did not fail is equal to 1) (Comment 8)

> 0.0: the element will be deleted if:

 

b

Plastic hardening parameter

Default = 0.0  (Real)

 

n

Plastic hardening exponent

Default = 1.0  (Real)

 

fmax

Maximum value of the Tsai-Wu criterion limit

Default = 1030  (Real)

Yield stress in tension in direction 1

Default = 0.0  (Real)

Yield stress in tension in direction 2

Default = 0.0  (Real)

Yield stress in compression in direction 1

Default = 0.0  (Real)

Yield stress in compression in direction 2

Default = 0.0  (Real)

symbol_a_14

Reduction factor for F12 coefficient calculation in Tsai-Wu criterion

Default set to 1.0  (Real)

 

Yield stress in compression in 45 degree of fiber direction

Default = 0.0  (Real)

Yield stress in tension in 45 degree of fiber direction

Default = 0.0  (Real)

c

Strain rate coefficient for plastic work criteria

(Real)

= 0: there is no strain rate dependency

 

Reference strain rate

If , no strain rate effect

(Real)

fail_johnson

ICC

Strain rate effect flag (Comment 10)

(Integer)

= 0: Default set to 1

= 1: Strain rate effect on fmax is taken into account, no effect of strain rate on

= 2: There is no strain rate effect on both fmax and

= 3: There is strain rate effect on both fmax and

= 4: Strain rate effect on is taken into account, but there is no effect of strain rate on fmax

 

symbol_yini

Out-of-plane shear strain when delamination begins (Comment 11)

Default = 1030  (Real)

 

symbol_ymax

Out-of-plane shear strain when delamination ends and the element is deleted (Comment 11)

Default = 1.1 * 1030  (Real)

 

d3max

Maximum delamination damage factor (d3max < 1) (Comment 11)

Default = 1.0  (Real)

 

Fsmooth

Strain rate filtering flag

(Integer)

= 0: strain rate smoothing is inactive (default)

= 1: strain rate smoothing is active

 

Fcut

Cutoff frequency for strain rate filtering

Default = 1030  (Real)

symbol_Hz

hmtoggle_plus1Example (Composite)

#RADIOSS STARTER

/UNIT/1

unit for mat

#              MUNIT               LUNIT               TUNIT

                   g                  mm                  ms

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

/MAT/COMPSH/1/1

composite example

#              RHO_I

             .001506

#                E11                 E22                NU12     Iform                           E33

              144000               10000                 .25         0                         20000

#                G12                 G23                 G31              EPS_f1              EPS_f2

                4200                4200                4200                   0                   0

#             EPS_t1              EPS_m1              EPS_t2              EPS_m2                dmax

                   0                   0                   0                   0                   0

#              Wpmax               Wpref      Ioff                         ratio

             1000000                   0         0                             0

#                  b                   n                fmax

                   0                   0             1000000

#            sig_1yt             sig_2yt             sig_1yc             sig_2yc               alpha

               10100               10100               10100               10100                   0

#           sig_12yc            sig_12yt                   c          Eps_rate_0       ICC

               10068               10068                   0                   0         0

#          GAMMA_ini           GAMMA_max               d3max

                   0                   0                   0

#  Fsmooth                Fcut

         0                   0

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

#enddata

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

hmtoggle_plus1Comments
1.The formulation flag Iform should be set to 0, for the Tsai-Wu formulation.
2.This material requires orthotropic shell properties (/PROP/SH_ORTH, /PROP/SH_COMP or /PROP/SH_SANDW). These properties specify the orthotropic directions, therefore, it is not compatible with the isotropic shell property (/PROP/TYPE1).
3.This material is available with under-integrated Q4 and fully-integrated BATOZ shell formulations. It is not available with QEPH shell formulation.
4.This material is compatible with orthotropic solid property (/PROP/SOL_ORTH), the orthotropic thick shell property (/PROP/TSH_ORTH) and the composite thick shell property (/PROP/TSH_COMP). These properties specify the orthotropic directions. It is assumed that for solids and thick shells, the material is elastic in transverse direction and the E33 value must be specified in such cases.
5.The material is assumed to be elastic until the Tsai-Wu criterion is fulfilled. After exceeding the Tsai-Wu criterion limit , the material becomes non-linear:

Where, , and are the stresses in the material coordinate system.

The coefficients of the Tsai-Wu criterion are determined from the limiting stresses when the material becomes nonlinear in directions 1, 2 or 12 (shear) in compression or tension, as follows:

   

   

       

Where, the superscripts c and t represent compression and tension, respectively. This criterion represents a second order closed three-dimensional Tsai-Wu surface in , and space.

F is the variable Tsai-Wu criterion limit defined as a function of plastic work (Wp) and the true strain rate (E2):

Where, symbol_Wp_ref is the reference plastic work, b is the plastic hardening parameter, n is the plastic hardening exponent, is the reference true strain rate, and c is the strain rate coefficient.

This Tsai-Wu surface is scaled outwards homothetically in all directions, due to increase in Wp and E2.

6.Damage between and is controlled by the damage factor di, which is given by the following equation:

in directions, i = 1, 2.

Stress is reduced according to damage parameter . Damage is reversible between and . When , damage is set to dmax and it is not updated further. Element deletion is controlled by the Ioff flag.

7.For the plastic work failure criterion, and are defined as follows:

and

When , the stress is set to zero in the layer. Element deletion is controlled by the Ioff flag.

8.This Ratio field can be used to provide stability to composite shell components. It allows you to delete unstable elements wherein all layers but one have failed. This last layer may cause instability during simulation, due to a low stiffness value. This option is available for strain and plastic energy based brittle failure.
9.Tensile strain and energy failure criterion of LAW25 is not available for orthotropic shells with /PROP/TYPE9.
10.The ICC flag defines the effect of strain rate on the maximum plastic work and on the Tsai-Wu criterion limit. For ICC = 2, 3 and 4, the plastic work failure criterion is:

11.The simple delamination criterion is based on the evaluation of out-of-plane shear strains ( and ). Element stresses and are gradually reduced when the resultant out-of-plane shear lies within . The element is completely removed (fails) if the value of becomes greater than the value of dmax (specified on this material card) in one of the shell layers.
12.Failure criterion in LAW25 is not applicable to solid elements. To determine failure for solid elements /FAIL card should be used.
13.For shell and thick shell composite parts, with /PROP/SH_COMP, /PROP/SH_SANDW, /PROP/TSH_ORTH or /PROP/TSH_COMP, material is defined directly in the property card. The failure criteria defined within this material (for example, LAW25) are accounted for. Material referred to in the corresponding /PART card is only used for time step and interface stiffness calculation.

From version 14.0 global material properties (membrane stiffness, bending stiffness, mass, and inertia) are calculated based on the material properties and layup (thicknesses) given in /PROP/TYPE11 card. They are used for stability, mass and interface stiffness. A material is still required at part definition level, but is only used for pre- and post- (visualization “by material”) and its physical characteristics are ignored. The previous formulation where stiffness and mass were calculated from the material associated to the part is still used, if the version number of the input file is 13.0 or earlier.

14.To post-process this material in the animation file, the following Engine cards should be used:

/ANIM/SHELL/EPSP - for plastic work output
/ANIM/SHELL/TENS/STRAIN – for strain tensor output in the elemental coordinate system
/ANIM/SHELL/TENS/STRESS – for stress tensor output in the elemental coordinate system
/ANIM/SHELL/PHI – angle between elemental and first material direction
/ANIM/SHELL/FAIL – number of failed layers.

15.To post-process this material in the time-history file, the following special definitions in /TH/SHEL or /TH/SH3N card should be used:

PLAS (or EMIN and EMAX) for minimum and maximum plastic work in the shell

WPLAYJJ (JJ=0 to 99) for plastic work in a corresponding layer

16.The unit of symbol_Wp_ref is an energy per unit of volume. If the default value (0) is encountered, the default value is 1 unit of the model (example: or ). For proper conversion of this value if changing units in pre- and post-, it is advised to replace the default value by the true value (1), so that the value of symbol_Wp_ref will be automatically converted. Leaving thesymbol_Wp_ref  field to “0” may result in errors in case of automatic conversion.

Note that a local unit system can be created for the material to avoid conversion.

See Also:

Material Compatibility

Law Compatibility with Failure Model

/VISC/PRONY

Elastic-Plastic Orthotropic Composite Shells in Theory Manual

Failure message in FAQ