Updated Lagrangian finite element formulations of various biological soft tissue non-linear material models: a comprehensive procedure and review

Abstract

Simplified material models are commonly used in computational simulation of biological soft tissue as an approximation of the complicated material response and to minimize computational resources. However, the simulation of complex loadings, such as long-duration tissue swelling, necessitates complex models that are not easy to formulate. This paper strives to offer the updated Lagrangian formulation comprehensive procedure of various non-linear material models for the application of finite element analysis of biological soft tissues including a definition of the Cauchy stress and the spatial tangential stiffness. The relationships between water content, osmotic pressure, ionic concentration and the pore pressure stress of the tissue are discussed with the merits of these models and their applications.

Keywords:

• Biological soft tissue
• updated Lagrangian finite element formulation
• poro-hyperelastic non-linear material model
• pore pressure
• multiphasic

Funding

This work was partially supported by the National Science Foundation [grant number 1148897].

Disclosure statement

No potential conflict of interest was reported by the authors.