A Probabilistic Framework for Finite Strain Damage Response of Thick Curved Beams Including the Shear Effect

Area of Science:

• Continuum Mechanics
• Materials Science

Background:

• Curved beams are essential in engineering, but their hyperelastic behavior under cyclic loads, especially with Mullins stress softening and material variability, requires detailed investigation.
• Existing models often simplify bending assumptions, neglecting coupled stress components crucial for finite-thickness, curved beams.

Purpose of the Study:

• To investigate the mechanical response of hyperelastic curved beams under cyclic loading, incorporating Mullins stress-softening and material parameter variability.
• To develop and validate a numerical framework for predicting the behavior of such beams, considering coupled stress components.

Main Methods:

• Utilized a Neo-Hookean hyperelastic model with Ogden-Roxburgh damage formulation for cyclic stress-softening.
• Derived governing partial differential equations in cylindrical coordinates under plane-stress conditions and solved them numerically.
• Validated the model against 2D finite element solutions and performed probabilistic parametric analysis.

Main Results:

• Mullins-induced stress softening is localized near the inner curvature and beam root.
• Inherent material variability significantly influences the distribution of damage.
• The numerical framework accurately captures coupled radial, circumferential, and shear stress components.

Conclusions:

• The proposed model offers a fast and accurate method for predicting hyperelastic curved beam behavior under cyclic loading.
• Accounting for Mullins effect and material variability is crucial for realistic mechanical response prediction.
• The study highlights the importance of considering coupled stresses in finite-thickness curved beam analysis.