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General consitutive modeling framework for anisotropic pro-visco-hyperelastic materials?

azadpoor's picture

Modeling the constitutive behavior of biological tissues often involves anisotropy, hyperelasticity, viscoelasticity, and poroelasticity. I am looking for a good monograph/paper/textbook that presents a general constitutive modeling framework where these aspects are presented in an interconnected way. Most references treat these aspects separately, perhaps devoting a chapter to every aspect. My preferred way of treatment starts with presentation of hyperelasticity and then extending it to visco-hyperelasticity by modification of the strain energy function and perhaps separation (decoupling) of the terms describing the hyperelastic part and the viscous part. The next step is extension of the visco-hyperelastic model to poro-visco-hyperelasticity by extending the formulation to the case of biphasic materials. The anisotropic aspects are also very important for me, because they play an important role.
I need a good presentation of the theory for teaching purposes. Is anybody aware of any good reference? Other approaches to poro-visco-hyperelasticity could be also interesting. There are some papers that present some parts of the theory, but I am more interested in monograph-like references, because they are probably better for teaching purposes.


Dear Amir,

I did some work at that field. Here is a paper concerning finite deformation anisotropy connected with viscoplastic Bodner-Partom model

I recommend you book

Yuriy I. Dimitrienko: Nonlinear Mechanics and Large Inelastic Deformations.


Jozef Bocko





azadpoor's picture

Thank you Jozef, but the sources you mentioned do not integrate it with poro-elasticity. Any idea about a good source for teaching the integration of visco-hyperelasticity with poro-elasticity?

Try book

Anandarajah: Computational Methods in Elasticity and Plasticity, Springer, 2010

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