I wish to formulate a FEM computational algorithm to solve problems which involve both large deformations (hyperelastic) and time dependent (viscoelastic) stress-strain relationships observed in the case of soft tissues. The constitutive equation that I preferably wish to solve is the generalized standard-linear-solid one.
Paper [1] models the hyperelastic behaviour of arteries where the Maxwell model was used to represent the viscoelastic effect. In [2], a Kelvin-Voigt type model was used to represent the viscoelastic effect of ligaments. In both papers, FEM approach was used to obtain solutions.
In your case, since you are using a standard linear solid (a material which uses the combination of a Maxwell material and a Kelvin-Voigt material) then you can try to use ideas from these 2 papers.
(Also, look at the references therein. The Introduction in [2] gives some examples in the literature of such work which might be of some help to you).
[1] Title: A viscoelastic model for fiber-reinforced composites at finite strains: Continuum basis, computational aspects and applications
Authors: Holzapfel G.A., Gasser T.C
Journal: Computer Methods in Applied Mechanics and Engineering, Volume 190, Issue 34, 25 Pages 4379–4403 (2001)
[2] Title: An anisotropic visco-hyperelastic model for ligaments at finite strains. Formulation and computational aspects
Authors: Peña E., Calvo B., Martínez M.A, Doblaré M,
Journal: International Journal of Solids and Structures 44 pages 760–778 (2007)
Paper [1] models the hyperelastic behaviour of arteries where the Maxwell model was used to represent the viscoelastic effect. In [2], a Kelvin-Voigt type model was used to represent the viscoelastic effect of ligaments. In both papers, FEM approach was used to obtain solutions.
In your case, since you are using a standard linear solid (a material which uses the combination of a Maxwell material and a Kelvin-Voigt material) then you can try to use ideas from these 2 papers.
(Also, look at the references therein. The Introduction in [2] gives some examples in the literature of such work which might be of some help to you).
[1] Title: A viscoelastic model for fiber-reinforced composites at finite strains: Continuum basis, computational aspects and applications
Authors: Holzapfel G.A., Gasser T.C
Journal: Computer Methods in Applied Mechanics and Engineering, Volume 190, Issue 34, 25 Pages 4379–4403 (2001)
[2] Title: An anisotropic visco-hyperelastic model for ligaments at finite strains. Formulation and computational aspects
Authors: Peña E., Calvo B., Martínez M.A, Doblaré M,
Journal: International Journal of Solids and Structures 44 pages 760–778 (2007)
You could refer to Prof. Bonnet's Book in Continuum Mechanics to start.
Thanks Layal. The references are indeed helpful. However I have a doubt in the first reference. How do we determine the non dimensional free-energy factors "beta_inf" associated with the relaxation times when we evaluate the viscoelastic isochoric components of the free energy function? I am unable to figure out a relationship for the same.
Hi Shakti,
I'm not sure where he get the free energy factors from in Tables 1 and 2. It will be useful though because in your case they will be different since you're dealing with a different material.
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