MATBRT

Bulk Data Entry Defines the material properties for Brittle Damage material models.

Format

(1)	(2)	(3)
MATBRT	`MID`
	`CRACK`	`OPTION`
	`V1`	`V2`
	etc.	etc.
	`SHEAR`	`OPTION`
	`V3`	`V4`
	etc.	etc.
	`FAILURE`	`NDIR`
	`V5`	`PFAIL`

Example

(1)	(2)	(3)
MATBRT	2
	`CRACK`	ENER
	250.0	0.4

Definitions

Field	Contents	SI Unit Example
`MID`	Material identification number. No default (Integer > 0)
`CRACK`	Flag indicating that parameters for tensile cracking behavior are to follow. 3
`OPTION`	The following options are available for tensile crack behavior (Mode I): STRN Crack opening is expressed in the form of positive principal stress versus crack opening strain. DISP Crack opening is expressed in the form of positive principal stress versus crack opening displacement. ENER Crack opening is expressed in the form of positive principal stress and fracture energy. blank (Default) 3
`V1`, `V2`	Values of `V1` and `V2` depend on the `OPTION` chosen for tensile crack behavior. 3	$[Pa]$ $[Pa]$ for `V1` $[m]$ $[m]$ for `V2` if `OPTION`= DISP or ENER
`SHEAR`	Flag indicating that the parameters for shear cracking behavior are to follow. 4
`OPTION`	The following options are available for shear crack behavior (Mode II): RFAC Crack opening is expressed in the form of retention factor versus crack opening variable. The variable is strain if `CRACK` `OPTION`=STRN is specified; it is displacement if `CRACK` `OPTION`=DISP or ENER. PLAW Crack opening is expressed in the form of power law factor and maximal crack opening variable. The variable is strain if `CRACK` `OPTION`=STRN is specified; it is displacement if `CRACK` `OPTION`=DISP or ENER. blank (Default) 4
`V3`, `V4`	Values of `V3` and `V4` depend on the `OPTION` chosen for shear crack behavior. 4	$[m]$ $[m]$ for `V4` if `OPTION`= DISP or ENER
`FAILURE`	Flag indicating parameters for defining the limit of element deletion with the crack opening.
`NDIR`	Number of directions that should reach the critical crack opening value (`V5`) before element deletion. 1 (Default) 1 or 2 Shells 1, 2, or 3 Solids
`V5`	If the `CRACK` `OPTION`=STRN, defines the value of critical strain crack opening ( $ε_{c r i t}^{c k}$ $ε_{c r i t}^{c k}$ ). If the `CRACK` `OPTION`=DISP or ENER, defines the value of critical displacement crack opening ( $u_{c r i t}^{c k}$ $u_{c r i t}^{c k}$ ) Default = blank (Real)	$[m]$ $[m]$ for `V5` if `OPTION`= DISP or ENER
`PFAIL`	Percentage of failed integration points prior to element deletion. Default = 1.0

Comments

MATBRT is currently supported only for explicit dynamic analysis (NLEXPL).
A MATBRT entry should have the same MID as a MAT1 entry in the same model. The MAT1 entry is used to define the linear isotropic elastic behavior prior to crack initiation. The curves defined in the comments below define only the cracking behavior post crack initiation.
For tensile crack, there is no change to compression behavior and only tensile cracking is considered. CRACK defines the tensile crack behavior (Mode I):

STRN

Crack opening is expressed in the form of positive principal stress ( $σ_{t}^{I}$ $σ_{t}^{I}$ ) versus crack opening strain ( $ε_{n n}^{c k}$ $ε_{n n}^{c k}$ ). The series of values (V1, V2) define a table of ( $σ_{t}^{I}$ $σ_{t}^{I}$ , $ε_{n n}^{c k}$ $ε_{n n}^{c k}$ ).

Figure 1. STRN Option for Tensile CRACK

DISP

Crack opening is expressed in the form of positive principal stress ( $σ_{t}^{I}$ $σ_{t}^{I}$ ) versus crack opening displacement ( $u_{n n}^{c k}$ $u_{n n}^{c k}$ ). The series of values (V1, V2) define a table of ( $σ_{t}^{I}$ $σ_{t}^{I}$ , $u_{n n}^{c k}$ $u_{n n}^{c k}$ ).

Figure 2. DISP Option for Tensile CRACK

ENER

Crack opening is expressed in the form of positive principal stress ( $σ_{t u}^{I}$ $σ_{t u}^{I}$ ) and fracture energy ( $G_{f}^{I}$ $G_{f}^{I}$ ). The value of V1 is $σ_{t u}^{I}$ $σ_{t u}^{I}$ and V2 is $G_{f}^{I}$ $G_{f}^{I}$ .

Figure 3. ENER Option for Tensile Crack
For shear crack, the SHEAR flag defines the shear crack behavior (Mode II):

RFAC

Crack opening is expressed in the form of retention factor ( $ρ$ $ρ$ ) versus crack opening variable chosen for CRACK OPTION (STRN= $ε_{n n}^{c k}$ $ε_{n n}^{c k}$ , DISP or ENER= $u_{n n}^{c k}$ $u_{n n}^{c k}$ ). The series of values (V3, V4) defines a table of ( $ρ$ $ρ$ , $ε_{n n}^{c k}$ $ε_{n n}^{c k}$ ) or ( $ρ$ $ρ$ , $u_{n n}^{c k}$ $u_{n n}^{c k}$ ).

(1)
$G_{s h e a r}^{d a m a g e d} = ρ * G_{s h e a r}$ $G_{s h e a r}^{d a m a g e d} = ρ * G_{s h e a r}$

Where $ρ$ $ρ$ is a function of $ε_{n n}^{c k}$ $ε_{n n}^{c k}$ or $u_{n n}^{c k}$ $u_{n n}^{c k}$ ; the range of $ρ$ $ρ$ is from 1.0 to 0.0.

Figure 4. RFAC Option for SHEAR Cracking with STRN Option in CRACK Definition

Figure 5. RFAC Option for SHEAR Cracking with DISP/ENER Option in CRACK Definition

The shear modulus is multiplied by the variable $ρ$ $ρ$ during the crack propagation.

PLAW

Retention factor $ρ$ $ρ$ is expressed in the form of a power law. This power law evolves following the crack opening variable chosen in the CRACK definition (STRN= $ε_{n n}^{c k}$ $ε_{n n}^{c k}$ , DISP or ENER= $u_{n n}^{c k}$ $u_{n n}^{c k}$ ):
$G_{s h e a r}^{d a m a g e d} = {(1 - \frac{ε_{n n}^{c k}}{ε_{\max}^{c k}})}^{p} G_{s h e a r}$ $G_{s h e a r}^{d a m a g e d} = {(1 - \frac{ε_{n n}^{c k}}{ε_{\max}^{c k}})}^{p} G_{s h e a r}$
or,
$G_{s h e a r}^{d a m a g e d} = {(1 - \frac{u_{n n}^{c k}}{u_{\max}^{c k}})}^{p} G_{s h e a r}$ $G_{s h e a r}^{d a m a g e d} = {(1 - \frac{u_{n n}^{c k}}{u_{\max}^{c k}})}^{p} G_{s h e a r}$

Two parameters are expected. The value of V3 is $ε_{\max}^{c k}$ $ε_{\max}^{c k}$ or $u_{\max}^{c k}$ $u_{\max}^{c k}$ , the maximal crack opening variable, and V4 is $ρ$ $ρ$ , the power exponent.

Figure 6. PLAW Option for SHEAR Cracking with STRN Option in CRACK Definition

Figure 7. PLAW Option for SHEAR Cracking with DISP/ENER Option in CRACK Definition
FAILURE defines the limit of element deletion with the crack opening. Each principal stress over all directions of the element is used to compute a specific crack opening variable. NDIR is the number of principal directions that have reached the critical crack opening variable value V5 triggering the element deletion; at least 1 direction is mandatory. For shells there can be a maximal of 2 directions, and for solids 3 directions.