Prefer an exhaustive text book which is written as an introductory text and explain the concept of strain energy in details and multiple models, derivation and limitations.
Hi,
I am not sure you will find easily this information on text books, however, I am sure you can find few PhD thesis using hyperelastic models for soft biological tissues. You can nevertheless find easily hyperelastic theory for polymers (which is the same theory)
Some key aspects of this are :
- Usual strain energy derives from classical thermoelasticity for hyperelastic materials.
- limitations are based on the fact that hyperelastic behavior depends on identification parameters on simple test such as simple tension or biaxial tension not valid on complex load scenarios
Application to soft tissue depends on two factors : (i) hypothesis of homogeneity of the structure, (ii) validity of tissue microstructureal behavior to the model you use.
Regards,
Hello,
if you're interested in modelling of rubber then textbooks by R. W. Ogden (e.g . Non-Linear Elastic Deformations) and coauthors (e.g. G.A. Holzapfel).
The holly book for living tissues is Y. C. Fung. Biomechanics. Mechanical Properties of Living Tissues.
P. Wriggers Nonlinear Finite Element Methods gives more in depth "mathematical formulation", although most of the literature presents theoretical background in depth and describes standard hyper-elastic models (compressible and in compressible) . Almost any recent FEM book has a chapter with a decent overview of finite deformations.
There are also books with more "engineering approach" to nonlinear elasticity with eg. source code for Matlab eg. http://www2.mae.ufl.edu/nkim/INFEM/.
de Souza Neto, et al. Computational Methods for Plasticity: Theory and Applications also provide many examples with code.
BTW. In general (our observations) Yeoh's model gives the best results for for living tissues (eg. human skin).
Regards,
Zlatko
Dear Shah,
For cells, the Maxwell model is the most used to describe the viscoelastic nature phenomena. I believe that for tissues as well. I would like to particularly indicate this book: Understanding viscoelasticity: an introduction to Rheology (Nhan Phan Thien).
I do not think the knowledge on the biomechanical modelling of soft tissues are that developed yet to establish a reliable exhaustive book. I have seen chapters on different books and also some papers which dealt with hyperelastic modelling of soft tissues. I can recommend the ones I mostly use for my reference on modelling brain and spinal cord tissues:
- Holzapfel, Gerhard A. "Nonlinear solid mechanics: a continuum approach for engineering science." Meccanica 37.4 (2002): 489-490.
- Weiss, Jeffrey A., Bradley N. Maker, and Sanjay Govindjee. "Finite element implementation of incompressible, transversely isotropic hyperelasticity." Computer methods in applied mechanics and engineering 135.1 (1996): 107-128.
- Studies in Mechanobiology, Tissue Engineering and Biomaterials
these are a few, and also I am a real fan of Abaqus manuals, there I always find very interesting practical notes about modelling soft tissues.
Shervin
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