Biomechanics of Planar Collagenous Soft Tissues: Heterogeneities and Averaged Material Descriptions

Abstract

The overarching goal of this thesis is to advance the understanding of biomechanical heterogeneities and averaged material description of planar collagenous soft biological tissues through experimental, constitutive, and computational approaches, while also refining and adapting existing methods to better suit the specific characteristics and complexities of soft tissues. Despite decades of research documenting the mechanical heterogeneity of soft tissues, existing frameworks have yet to be fully reconciled with the experimental evidence. As the first objective, reindeer back skin and velvet (antler skin) are mechanically tested using a biaxial tensile testing machine, providing a basis for demonstrating the significance of regional mechanical heterogeneity. Motivated to accurately represent each tissue region, the second objective evaluates the concept of averaged material descriptions, specifically ``response averaging" and ``parameter averaging", across various hyperelastic constitutive models, ranges of deformations, and test types, to accurately represent groups of specimens. These findings are further used in the third objective to study whether it is possible to accurately describe local spatial biomechanical heterogeneity with sufficient precision from only a few samples. Specifically, it is done by applying the averaging methods to both experimental stress-strain data and constitutive model outputs to accurately predict mechanically untested intermediate regions between adjacent mechanically characterized tissue regions. Having validated the predictive power of the averaged-material-description approach, the fourth objective of this thesis develops a framework for incorporating local spatial mechanical heterogeneity into finite element (FE) simulations of soft biological tissues. Specifically, motivated by functionally graded materials and using an averaging approach to describe local heterogeneity it proposes to model heterogeneous material constants expressed as continuous Fourier functions of spatial positions. Through case studies of aortic aneurysms and skin tissue, it is demonstrated that a continuous heterogeneous material definition leads to a different stress distribution compared with a homogeneous model and avoids stress concentrations associated with a segmental heterogeneous model. Hence, the integration of regional mechanical characterization and the proposed averaging techniques, combined with the developed method for implementing the mechanical heterogeneity into FEM simulations, explored across all objectives of this thesis, sets a new standard for studying soft tissue biomechanics.