Difference between revisions of "J Integrals"
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where n1,n2 are starting and ending node numbers and n3 is an increment. If you use the <code>grad</code> option the formulation uses <math>\nabla\mathbf{u}</math> under the integral sign instead of the deformation gradient <math>\mathbf{F}</math>. | where n1,n2 are starting and ending node numbers and n3 is an increment. If you use the <code>grad</code> option the formulation uses <math>\nabla\mathbf{u}</math> under the integral sign instead of the deformation gradient <math>\mathbf{F}</math> formulation. | ||
== Simple Example == | == Simple Example == | ||
A simple example of an edge crack | A simple example of an edge crack | ||
<pre> | |||
FEAP * * Simple Test of JINT for an elastic problem * * | |||
0 0 0 2 2 4 | |||
PARAmeter | |||
n = 4 | |||
MATErial 1 | |||
SOLId | |||
ELAStic ISOTropic 200e3 0.3 | |||
MATErial 2 | |||
SOLId | |||
ELAStic ISOTropic 200e3 0.3 | |||
MATErial 3 | |||
SOLId | |||
ELAStic ISOTropic 200e3 0.3 | |||
BLOCk | |||
CART 4*n 8*n | |||
MATE 1 | |||
1 1 -1 | |||
2 2 -1 | |||
3 2 1 | |||
4 1 1 | |||
BLOCk | |||
CART 4*n 4*n | |||
MATE 2 | |||
1 0 0 | |||
2 1 0 | |||
3 1 1 | |||
4 0 1 | |||
BLOCk | |||
CART 4*n 4*n | |||
MATE 3 | |||
1 0 -1 | |||
2 1 -1 | |||
3 1 0 | |||
4 0 0 | |||
EBOUndary | |||
2 -1 1 1 | |||
2 1 1 1 | |||
EDISplacement | |||
2 1 0 1 | |||
END | |||
tie,mate,1,2 | |||
tie,mate,1,3 | |||
batch | |||
tang,,1 ! Solve for the (linear) elastic solution | |||
plot outl ! Plot mesh showing crack | |||
plot jint ! Add J-integral computations to the plot | |||
jint,,273 ! Output J-int at crack tip node using F | |||
jint,grad,273 ! Output J-int at crack tip node using grad(u) | |||
end | |||
inte | |||
stop | |||
</pre> | |||
Latest revision as of 07:13, 13 April 2018
Use of the J-integral calculator
(This is an experimental feature, please test carefully to make sure you understand what it does.)
When solving elastic problems FEAP has a built-in feature that computes the nodal values of the J-integral; i.e. it will compute the variation of the systems potential energy with respect to variations in the nodal positions. The negative of this is the energy release rate. To use this feature, at the Macro prompt simply type JINT. To plot the J-integral vectors, enter the plot phase, and type JINT.
Note that one will see non-zero values at most nodes. This indicates that the mesh can be optimized to lower the computed energy. However, if there is a singularity in the problem, then there will be a dominant J-integral vector at the singularity that can be interpreted as the energy release rate. See
JINT Syntax Macro phase
jint,<grad>,<n1,n2,n3> jint,all
where n1,n2 are starting and ending node numbers and n3 is an increment. If you use the grad option the formulation uses under the integral sign instead of the deformation gradient formulation.
Simple Example
A simple example of an edge crack
FEAP * * Simple Test of JINT for an elastic problem * *
0 0 0 2 2 4
PARAmeter
n = 4
MATErial 1
SOLId
ELAStic ISOTropic 200e3 0.3
MATErial 2
SOLId
ELAStic ISOTropic 200e3 0.3
MATErial 3
SOLId
ELAStic ISOTropic 200e3 0.3
BLOCk
CART 4*n 8*n
MATE 1
1 1 -1
2 2 -1
3 2 1
4 1 1
BLOCk
CART 4*n 4*n
MATE 2
1 0 0
2 1 0
3 1 1
4 0 1
BLOCk
CART 4*n 4*n
MATE 3
1 0 -1
2 1 -1
3 1 0
4 0 0
EBOUndary
2 -1 1 1
2 1 1 1
EDISplacement
2 1 0 1
END
tie,mate,1,2
tie,mate,1,3
batch
tang,,1 ! Solve for the (linear) elastic solution
plot outl ! Plot mesh showing crack
plot jint ! Add J-integral computations to the plot
jint,,273 ! Output J-int at crack tip node using F
jint,grad,273 ! Output J-int at crack tip node using grad(u)
end
inte
stop