PSI - Issue 13

Vera Turkova / Procedia Structural Integrity 13 (2018) 982–987

985

Vera Turkova/ Structural Integrity Procedia 00 (2018) 000 – 000

4



      

11 1 D C C 

1 11 C D D  (

1 11 C D D C D D   1 22 ( (

2 2 (

)

)

)

0 0 0 0 0 0

 1                          2 3 4 5 6







 

1

2

22

33

            

2      4 5 6

1 11 C D D C D D   1 11 ( (

22 1 D C C 

) )

2 2 (

)

)

 



 

22

2

33 

(7)

1 22 C D D  (

33 1 D C C

)

2 2 (

) 0 0 0



 



 

3                  

33

33

2

0 0 0

0 0 0

0 0 0

0 0



0

0



0 0



1 C and 2 C are chosen so that the stress 11  drops to zero when

11 1.0 D  for uniaxial tension in

The values of

1 C

C

1.5

  and

 



[7]. In the following calculations these values of material constants are used.

direction 1.

2

3. Finite element modeling and calculations

Abaqus provides an extensive number of user subroutines that allow us adapting Abaqus to particular problem requirements. User subroutines provide an extremely powerful and flexible tool for analysis [22]. 3.1. User subroutine UMAT in Simulia Abaqus To define any complex, constitutive models for materials that cannot be modeled with the available Abaqus standard material models we use subroutine UMAT (User material). The material model developer should be concerned only with the development of the material model and not the development and maintenance of the software. Solution-dependent state variables (SDVs) are values that can be defined to evolve with the solution of an analysis. An example of a solution-dependent state variable for UMAT subroutine in this particular work is damage parameter. 3.2. The analysis of active damage zones in structures The objective of this work is the analysis of active damage zone in the vicinity of the crack tip in various types of cracked specimens. The models are implemented in Simulia Abaqus using UMAT subroutine. Damage distribution in a 3D elastic rod. The elaborated UMAT subroutine was applied to the simplest possible model – a 3D elastic rod rigidly fixed at the one end. Additional complexity was not included in the model in order to compare this problem results with standard Abaqus material model. The rod is subjected to uniaxial loading in direction 1.

11  without UMAT; (c) stress component

22  without UMAT;

Fig. 1. (a) equivalent stresses in the model without UMAT; (b) stress component

33  without UMAT; (f) equivalent stresses in the model with UMAT; (g) stress component 11  with UMAT; (h) stress component 22  with UMAT; (i) stress component 33  with UMAT.

(d) stress component