- #1

FEAnalyst

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- TL;DR Summary
- Are there analytical solutions for simple solid mechanics problems (e.g. bending of a beams, torsions of shafts, internal pressure in pipes) involving hyperelastic material?

Hi,

I have recently become interested in analytical solutions of various advanced solid mechanics problems, mostly nonlinear ones. I consider simple geometries and loads (like bending of beams, torsion of shafts, or internal pressure in pipes), but for nonlinear materials. I have learned that hand calculations for such cases are possible even when plasticity or creep conditions become involved. The results are in very good agreement with FEA. However, there is still at least one major issue left that puzzles me - hyperelasticity. Are there any analytical solutions at all for such materials (considering simple geometries and loads)? If so, what kinds of problems can be solved this way - only axial tension/compression or maybe also bending, torsion etc.? And where to look for such solutions? So far I have not been able to find anything concrete, but I am missing literature where examples of this type would be presented.

I'm not sure which hyperelastic material model could be used for calculations like that but I assume that if they are possible at all then neo-Hookean material might be the right choice as it seems to be the simplest model, with only two constants involved: https://en.wikipedia.org/wiki/Neo-Hookean_solid

Thank you in advance for any help.

I have recently become interested in analytical solutions of various advanced solid mechanics problems, mostly nonlinear ones. I consider simple geometries and loads (like bending of beams, torsion of shafts, or internal pressure in pipes), but for nonlinear materials. I have learned that hand calculations for such cases are possible even when plasticity or creep conditions become involved. The results are in very good agreement with FEA. However, there is still at least one major issue left that puzzles me - hyperelasticity. Are there any analytical solutions at all for such materials (considering simple geometries and loads)? If so, what kinds of problems can be solved this way - only axial tension/compression or maybe also bending, torsion etc.? And where to look for such solutions? So far I have not been able to find anything concrete, but I am missing literature where examples of this type would be presented.

I'm not sure which hyperelastic material model could be used for calculations like that but I assume that if they are possible at all then neo-Hookean material might be the right choice as it seems to be the simplest model, with only two constants involved: https://en.wikipedia.org/wiki/Neo-Hookean_solid

Thank you in advance for any help.