The strain-energy density function of the urinary bladder

Area of Science:

• Biomechanics
• Continuum Mechanics
• Biomedical Engineering

Background:

• Finite deformation theory is crucial for understanding hyperelastic materials like the urinary bladder.
• The strain-energy density function (W) is central to this theory but complex to determine.
• Previous work established a foundational theory for urinary bladder deformation.

Purpose of the Study:

• To refine the strain-energy density function (W) for urinary bladder tissue.
• To simplify the mathematical model for hyperelastic continuum.
• To investigate the practical implications of simplifying W.

Main Methods:

• Analysis of the strain-energy density function (W) in a finite deformation context.
• Evaluation of individual terms within the Valanis-Landel type function.
• Comparison of stress-strain relationships under different deformation modes.

Main Results:

• The third term in the Valanis-Landel type strain-energy density function is negligible for most deformations.
• Hook's law applies only in the infinitesimal deformation region.
• The simplified formula for true stress in uniaxial extension matches that of equal-biaxial extension.

Conclusions:

• A simplified strain-energy density function for the urinary bladder is proposed.
• The simplification reduces the complexity of finite deformation analysis for hyperelastic materials.
• The findings offer practical utility in biomechanical applications and modeling.