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On Rate Boundary Conditions for Soft Tissue Bifurcation Analysis
1Faculty of Aerospace Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel e-mail: .
Journal of Biomechanical Engineering
|August 22, 2018
Summary
Understanding soft tissue mechanics is crucial. This study reveals that the type of boundary conditions significantly impacts mechanical instability and critical loads in soft tissues, influencing their function and development.
Area of Science:
- Biomechanics
- Soft Tissue Mechanics
- Computational Biology
Background:
- Mechanical instability in soft tissues can impair function or drive morphogenesis.
- Standard stability analysis is insufficient for large deformations; nonlinearities from load-surface coupling are critical.
- Boundary conditions in soft tissue mechanics are under-explored, with dead-load conditions being prevalent.
Purpose of the Study:
- To investigate the influence of homogeneous rate boundary conditions (RBCs) on critical loads and instability modes in soft tissues.
- To analyze the impact of different RBCs (e.g., dead-load, fluid-pressure) on bifurcation loads.
- To provide universal closed-form solutions for basic spherical patterns.
Main Methods:
- Linear bifurcation analysis of soft tissues undergoing large deformations.
- Modeling material behavior using compressible isotropic hyperelastic strain energy functions (SEFs).
- Examining benchmark problems: full sphere, spherical cavity, and thick spherical shell under hydrostatic states.
Main Results:
- Derived universal closed-form solutions for spherical patterns, highlighting the role of imposed boundary data.
- Demonstrated that rate boundary conditions significantly affect bifurcation load levels and modes.
- Showcased the critical influence of constitutive parameters and RBC type on instability emergence.
Conclusions:
- The choice of homogeneous rate boundary conditions critically impacts bifurcation loads and can prevent instabilities.
- Accurate modeling of boundary conditions is essential for understanding soft tissue mechanical behavior.
- Findings offer insights into growth, morphogenesis, and mechanical failure in soft biological tissues.
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