Instability of Incompatible Bilayered Soft Tissues and the Role of Interface Conditions

[+] Author and Article Information
Nir Emuna

Faculty of Aerospace Engineering, Technion|Israel Institute of Technology

David Durban

Faculty of Aerospace Engineering, Technion|Israel Institute of Technology

1Corresponding author.

ASME doi:10.1115/1.4043560 History: Received November 30, 2018; Revised April 14, 2019


Mechanical stability analysis is instructive in explaining biological processes like morphogenesis, organogenesis, and pathogenesis of soft tissues. Consideration of the layered, residually-stressed structure of tissues, requires accounting for the joint effects of interface conditions and layer incompatibility. This paper is concerned with the influence of imposed rate (incremental) interface conditions (RICs) on critical loads in soft tissues, within the context of linear bifurcation analysis. Aiming at simplicity, we analyze a model of bilayered isotropic hyperelastic (neo-Hookean) spherical shells with residual stresses generated by "shrink-fitting" two perfectly bonded layers with radial interfacial incompatibility. This setting allows a comparison between available, seemingly equivalent, interface conditions commonly used in the literature of layered media stability. We analytically determine the circumstances under which the interface conditions are equivalent or not, and numerically demonstrate significant differences between interface conditions with increasing level of layer incompatibility. Differences of more than 10-fold in buckling and 30% in inflation instability critical loads are recorded using the different RICs. Contrasting instability characteristics are also revealed using the different RICs in the presence of incompatibility: inflation instability can occur before pressure maximum, and spontaneous instability may be excluded for thin shells. These findings are relevant to the growing body of stability studies of layered and residually stressed tissues. The impact of interface conditions on critical thresholds is significant in studies that use concepts of instability to draw conclusions about the normal development and the pathologies of tissues like arteries, esophagus, airways, and the brain.

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