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Identifying fracture energy in ductile damage in ABAQUS


I am trying to find out how to identify specified parameters of ductile damage material in its stress-strain curve in Abaqus. I created a one-element model with a dimension of 1x0.2x1 (0.2 in y-direction) and simulated a tensile test in y-direction with a displacement condition of 0.02mm.

I have the following parameters for the material:
Elastic modulus = 250
Yield stress σ: 50
Fracture energy rate for the damage evolution: 2.5

I specified a very low fracture strain so there is nearly no plastic yielding. As a result, I have a stress-strain curve (in y-direction) where it goes linearly up to one point and immediately linearly down until it reaches zero stress (stiffness degradation until fracture).

I can recognize the elastic modulus in the initial slope, and the yield stress in the peak point where it reaches the damage initiation. However, I cannot identify the specified fracture energy rate anywhere. The Abaqus manual gives the following relation between displacement and energy release rate in a linear form of damage evolution: u = 2G / σ

This is how I tried to compute the G: The strain at failure is 0.57, so the displacement at failure would be u = 0.57 * 0.2 = 0.0114. I expected G to be 2.5, but with the equation it would be G = 0.285

What's my mistake here? Thank you in advance.

Kind regards

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Now I figured out that it might have something to do with the characteristic length of the element. I thought this would be the thickness of the element (in this case 0.2), but apparently it's not that simple.

I found papers citing a relation proposed by Bazant and Oh: characteristic length L = sqr(A) / cos(theta), where A is the area associated with the integration point (I thought in this case is 1x1), and theta is the angle between the mesh line along which the crack band advances and the crack direction. This is where I get confused, as I just created a one-element model without specifying any crack line.

Even if I assume that this theta is zero, it would be u = ε * L = ε * 1 = 0.57, and with the equation before G would be G = 14.25, which is not the value I specified for the material.

So now the question: how do I get the characteristic length of my element?

Thank you in advance

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