On Rate Boundary Conditions for Soft Tissues Bifurcation Analysis

[+] 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:10.1115/1.4041165 History: Received March 12, 2018; Revised July 29, 2018


Mechanical instability of soft tissues can either risk their normal function, or alternatively trigger patterning mechanisms during growth and morphogenesis processes. Unlike standard stability analysis of linear elastic bodies, for soft tissues undergoing large deformations it is imperative to account for the nonlinearities induced by the coupling between load and surface changes at onset of instability. The related issue of boundary conditions, in context of soft tissues, has hardly been addressed in the literature, with most of available research employing dead-load conditions. This paper is concerned with the influence of imposed homogeneous rate (incremental) surface data on critical loads and associated modes in soft tissues, within the context of linear bifurcation analysis. Material behavior is modeled by compressible isotropic hyperelastic strain energy functions (SEFs), with experimentally validated material parameters for the Fung-Demiray SEF, over a range of constitutive response (including brain and liver tissues). For simplicity we examine benchmark bifurcations of basic spherical patterns: full sphere, spherical cavity, and thick spherical shell. Limiting the analysis to primary hydrostatic states we arrive at universal closed-form solutions, thus providing insight on the role of imposed boundary data. Influence of selected rate boundary conditions like dead-load and fluid-pressure, coupled with constitutive parameters, on the existence and levels of bifurcation loads is compared and discussed. It is argued that the selection of the appropriate type of homogeneous rate boundary condition can have a critical effect on the level of bifurcation loads, and even exclude the emergence of bifurcation instabilities.

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