An irreversible constitutive model for fibrous soft biological tissue: A 3-D microfiber approach with demonstrative application to abdominal aortic aneurysms

Understanding the failure and damage mechanisms of soft biological tissue is critical to a sensitive and specific characterization of tissue injury tolerance and its relation to biological responses. Despite increasing experimental and analytical efforts, failure-related irreversible effects of soft biological tissue are still poorly understood. There is still no clear definition of what “damage” of a soft biological material is, and conventional macroscopic indicators, as known from damage of engineering materials for example, may not identify the tissue’s tolerance to injury appropriately. To account for the complex three-dimensional arrangement of collagen, a microfiber model approach is applied, where constitutive relations for collagen fibers are integrated over the unit sphere, which in turn defines the tissue’s macroscopic properties. A collagen fiber is represented by a bundle of proteoglycan cross-linked collagen fibrils that undergoes irreversible deformations when exceeding its elastic tensile limit. The proposed constitutive model is able to predict strain stiffening at physiological strain levels and does not exhibit a clear macroscopic elastic limit, two typical features known from soft biological tissue testing. An elastic-predictor/plastic-corrector implementation of the model is followed and constitutive parameters are estimated from in vitro test data from a particular abdominal aortic aneurysm (AAA). Damage-based structural instabilities of the AAA under different inflation conditions are investigated, where the collagen orientation density has been estimated from its in vivo stress state.