/MAT/LAW116
Block Format Keyword Describes mixed mode, strain rate dependent material model with damage and failure.
Format
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
/MAT/LAW116/mat_ID/unit_ID | |||||||||
mat_title | |||||||||
Thick | Imass | Idel | Icrit | ||||||
Iorder_I | Ifail_I | ||||||||
Iorder_II | Ifail_II |
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) |
||
Young’s (stiffness) modulus in
normal direction per unit length. (Real) |
||
Shear (stiffness) modulus in
tangent direction per unit length. Default = (Real) |
||
Thick | Reference cohesive
thickness. (Real) |
|
Imass | Mass calculation flag.
(Integer) |
|
Idel | Failure flag indicating the number
of integration points to delete the element (between 1 and
4). Default = 1 (Integer) |
|
Icrit | Yield and damage initiation flag.
(Integer) |
|
Initial critical energy release
rate for mode I (normal direction). (Real) |
||
Upper bound of critical energy
release rate. Indicates the strain rate dependency of
. Default = 0.0 (Real) |
||
Reference (lower bound) strain rate
for GC strain rate dependency. Must be defined if . (Real) |
||
Shape factor for energy release
rate before failure in mode I. (Real) |
||
Initial critical energy release
rate for mode II (shear). (Real) |
||
Upper bound of critical energy
release rate. Indicates the strain rate dependency of
. Default = 0.0 (Real) |
||
Reference (lower bound) strain rate
for GC strain rate dependency. Must be defined if . (Real) |
||
Shape factor for energy release
rate before failure in mode II. (Real) |
||
Static yield stress in mode
I. (Real) |
||
Strain rate dependent yield stress
term in mode I. (Real) |
||
Reference (lower bound) strain rate
value for yield stress rate dependency in mode I. Must be defined . (Real) |
||
Iorder_I | Order of yield stress dependency on
strain rate in mode I.
(Integer) |
|
Ifail_I | Failure criteria defined by
:
(Integer) |
|
Static yield stress in mode
II. (Real) |
||
Strain rate dependent yield stress
term in mode II. (Real) |
||
Reference (lower bound) strain rate
value for yield stress rate dependency in mode II. Must be defined if . (Real) |
||
Iorder_II | Order of yield stress dependency of
strain rate in mode II.
(Integer) |
|
Ifail_II | Failure criteria defined by
:
(Integer) |
▸Example
Comments
- The elastic stiffness is
defined with:Figure 1.Where,
- GP
- Plastic energy under constant stress
- GC
- Total energy
- ={I,II}
- The mode I (normal) and mode II (shear)
The shape of the traction separation law is defined with:- Failure criteria
defined by ratio of fracture energy
(Ifail_i=1)
(1) - Failure criteria
defined by ratio fracture displacements
(Ifail_i=2)
(2)
- The yield stress is defined
as:
- When
Iorder_i=1:
(3) - When
Iorder_i=2:
(4) Where, ={I,II}, the mode I and mode II.
- When
Iorder_i=1:
- The equivalent strain rate
is defined with:
(5) Where,- Normal velocity.
- Shear velocity.
- The rate dependent fracture
energies are defined with:
(6) Where, ={I,II}, the mode I and mode II.
- Yield stress and damage law
scheme:Figure 2.
- For yield and damage based
on quadratic nominal stress (Icrit=1):
- Mixed-mode yield initiation
displacement is:
(7) Where,- ={I,II}, the mode I and mode II.
- Mixed-mode damage
initiation is:
(8) Where,- ={I,II}, the mode I and mode II.
- Mixed-mode yield initiation
displacement is:
- For yield and damage based
on quadratic nominal stress (Icrit=2).
- Mixed-mode yield initiation
displacement is:If :
(9) If :(10) Where,- Displacement is mode I (normal).
- Displacement is mode II (shear).
- Mixed-mode damage
initiation is:If :
(11) If :(12)
- Mixed-mode yield initiation
displacement is:
- The mixed-mode final damage
is (Icrit=1,2):
(13) Where,- Displacement is mixed mode.
- The plastic strain is
defined as:
- Mode I:
(14) Where, is the value from previous time step.
- Mode II:
If
The plastic strain is computed for each direction 1 and 2 in the shear plane.(15) (16)
- Mode I:
- Stress value is reduced
linearly from damage initiation to final damage (
).
(17) The stress reduction is computed in the normal direction as:
If , then .
otherwise, .
For each direction 1 and 2 in the shear plane.(18) (19) - The connection element is deleted when .