Finite strain crack tip fields in soft incompressible elastic solids

Area of Science:

• Solid Mechanics
• Materials Science
• Computational Mechanics

Background:

• Linear Elastic Fracture Mechanics (LEFM) provides a framework for understanding crack propagation.
• Soft, incompressible materials exhibit complex behaviors under stress, deviating from traditional elastic models.
• Understanding large deformation near crack tips is crucial for predicting material failure.

Purpose of the Study:

• To investigate the large deformation field and stress singularities near a crack tip in soft, incompressible materials under Mode I loading.
• To compare the behavior of a neo-Hookean solid (ideal rubber) with an exponentially hardening hyperelastic solid.
• To contrast the findings with predictions from Linear Elastic Fracture Mechanics (LEFM).

Main Methods:

• Development and application of a finite element model (FEM) for simulating crack tip behavior.
• Analysis of stress and deformation fields for two distinct hyperelastic material models.
• Investigation of singularity behavior (1/R and -1/(R ln R)) in near-tip stress fields.

Main Results:

• Near the crack tip, the opening stress is dominant and exhibits distinct singularities: 1/R for neo-Hookean and -1/(R ln R) for exponential hardening solids.
• Qualitatively similar near-tip stress field behaviors were observed despite significant differences in strain hardening.
• The near-tip opening stress is governed by the far-field energy release rate at high applied loads.

Conclusions:

• The study highlights the limitations of LEFM for soft materials with large deformations.
• Material-specific singularities characterize the near-tip stress fields in hyperelastic solids.
• Energy release rate is a key parameter controlling crack tip stress in these materials under significant loading.