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# ABAQUS - Energy balance of implicit simulation including cohesive element

## ABAQUS - Energy balance of implicit simulation including cohesive element

(OP)
Hi all,

I am having trouble with my 2D simulation work, therefore, hope there is anyone who can help me with this.

To briefly explain my model, I am working on the penetration of the hyperelastic body. The rigid body is piercing the soft matter along the predetermined crack path where cohesive elements are assigned.
However, the energy outputs do not seem to satisfy the energy balance condition.
The simulation is a quasi-static analysis with a dynamic implicit step. Since the friction is ignored in my model, the energy balance equation can be simplified as follows:

ETOTAL = ALLKE + ALLIE - ALLWK , where ALLIE = ALLSE + ALLDMD + ALLAE

with other outputs zero.

As it is shown in the attached file, when the penetration begins (cohesive element starts to fail), a discrepancy between external work and internal energy occurs and total energy becomes negative...
I am currently guessing this is caused by some errors when cohesive elements are included in the crack propagation problem.

Does anyone know why this kind of problem I am facing?
When I checked the slope of ALLDMD - Crack length plot, it was only half of the fracture toughness I assigned for the cohesive element (thickness is 1). I couldn't understand why I get this result...

I would appreciate any help or idea.

Details of model:
*Dynamic implicit (quasi-static)
*Soft matter: NH model
*Cohesive element: bilinear cohesive law
*Zero thickness cohesive elements are tied with soft bodies, rigid body is inserted along the crack path
*Interaction property: Normal (hard contact), Tangential (frictionless)
*Displacement B.C. assigned to rigid body (ramp)

### RE: ABAQUS - Energy balance of implicit simulation including cohesive element

Do the contour plots on the deformed shape of the model look reasonable ? Please attach pictures showing them, if it’s not a problem. Is this analysis based on some research paper ? If yes, can you share the title ?

Apart from checking for errors in the current analysis, you may have to try a slightly different approach, for example with cohesive contact.

### RE: ABAQUS - Energy balance of implicit simulation including cohesive element

(OP)
Hello, @FEA way

I guess the contour plots seem reasonable. The analysis is based on the paper "Detailed finite element modelling of deep needle insertions into a soft tissue phantom using a cohesive approach".

Do you know if the total energy is generally constant throughout the crack propagation simulation with simple loading such as pure shear fracture when cohesive elements are included?

I just want to know if this is an inherent error related to the cohesive elements before moving on to try different methods...

### RE: ABAQUS - Energy balance of implicit simulation including cohesive element

Request output of all the energies available for this analysis (*Energy output, variable=all) then plot them all (together, in various combinations and one by one). There’s a great chance that you will find the cause of the problem this way.

If we take a closer look at the available energies, here’s more or less what we get for the end of the analysis (ignoring energies that are almost zero):

ETOTAL = ALLIE - ALLWK
ALLIE = ALLSE + ALLDMD

ALLIE = 0.1 + 0.35 = 0.45
ETOTAL = 0.45 - 0.55 = -0.1

So you can probably narrow down your focus to those 3 energies instead of looking at ETOTAL.

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