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Calculating strain energy density in cyclic loading of rubber-like materials

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Posts: 30
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Eminent Member
Joined: 5 years ago

For monotonic loading, obtaining the strain energy density data is straightforward: calculating the area under the stress-strain curve. 

However, obtaining the same for cyclic loading appears to be tricky. Do I have to calculate differently for the loading and unloading curves? I tried this but I get unusual curves. 

Any idea on the correct method of obtaining the strain energy density data for cyclic loading? I will appreciate it. I need this data to model the Mullins effect. 

Thanks in advance, 


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Posts: 3998
Joined: 5 years ago

The same approach should apply for cyclic loading. The easiest way to do it numerically is to do it incrementally one data point at a time. 

Note that MCalibration can plot strain energy density (and it should work for most material models ?). Here's a figure for a hyperelastic + Mullins model.

Note that the strain energy function for a Mullins model is a bit different since the damage is not "visible" until unloading.


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Eminent Member
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@jorgen Many thanks, appreciated.