Hyperelastic problems - analytical solutions?

  • Thread starter Thread starter FEAnalyst
  • Start date Start date
  • Tags Tags
    Analytical
AI Thread Summary
The discussion centers on the search for analytical solutions to hyperelastic problems in solid mechanics, particularly for simple geometries and loads like tension and compression. The participant has successfully found hand calculations for nonlinear materials but struggles with hyperelasticity, seeking literature that includes exemplary stress/strain calculations. They express interest in the neo-Hookean model due to its simplicity but note a lack of resources that provide practical examples. Recommendations for books and manuals focused on hyperelastic materials are requested, especially those that include calculation examples similar to those found in older Polish texts. The conversation highlights a gap in accessible literature for analytical solutions in hyperelasticity, particularly for more complex loading scenarios.
FEAnalyst
Messages
348
Reaction score
149
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.
 
Engineering news on Phys.org
Hi, I never dealt directly with hyperlastic materials, but a nice book that I came across some years ago had a chapter dedicated to hyperelasticity. The book is this one:

Notes on Continuum Mechanics

It is very dense from the mathematical point of view, but it might help! It presents not only the model you mentioned, but also other ones.
 
Thank you for the recommendation, I was not familiar with this publication. However, what I need is a book with exemplary stress/strain calculations involving hyperelastic material models. And all the books I've found so far (including this one) only discuss the material models themselves. I am looking for a source that will be equivalent to what helped me hand calculate problems involving plasticity and creep. Those were old Polish books in a "collection of tasks" form. I don't know if such publications are available in English and if they cover hyperelasticity as well but maybe there are also some textbooks focusing on theory but featuring occasional exemplary calculations (like a typical "mechanics of materials" or "solid mechanics" guide). Maybe I should look for something more practical, like a manual for the design of hyperelastic (polymer/rubber) components (such as gaskets).

Anyway, I will be very grateful for any other recommendations. It may not be possible to solve more complex loading scenarios (bending, torsion) involving hyperelastic materials but it should be possible to solve at least simple tension/compression analytically. I guess that it's just a matter of obtaining stress-strain curve for uniaxial tension from material model's constants. The problem is that those models use description based on strain energy density instead of directly providing stress-strain relationship.
 
Thread 'What type of toilet do I have?'
I was enrolled in an online plumbing course at Stratford University. My plumbing textbook lists four types of residential toilets: 1# upflush toilets 2# pressure assisted toilets 3# gravity-fed, rim jet toilets and 4# gravity-fed, siphon-jet toilets. I know my toilet is not an upflush toilet because my toilet is not below the sewage line, and my toilet does not have a grinder and a pump next to it to propel waste upwards. I am about 99% sure that my toilet is not a pressure assisted...
After over 25 years of engineering, designing and analyzing bolted joints, I just learned this little fact. According to ASME B1.2, Gages and Gaging for Unified Inch Screw Threads: "The no-go gage should not pass over more than three complete turns when inserted into the internal thread of the product. " 3 turns seems like way to much. I have some really critical nuts that are of standard geometry (5/8"-11 UNC 3B) and have about 4.5 threads when you account for the chamfers on either...
Thread 'Physics of Stretch: What pressure does a band apply on a cylinder?'
Scenario 1 (figure 1) A continuous loop of elastic material is stretched around two metal bars. The top bar is attached to a load cell that reads force. The lower bar can be moved downwards to stretch the elastic material. The lower bar is moved downwards until the two bars are 1190mm apart, stretching the elastic material. The bars are 5mm thick, so the total internal loop length is 1200mm (1190mm + 5mm + 5mm). At this level of stretch, the load cell reads 45N tensile force. Key numbers...
Back
Top