Nanobeams with Internal Discontinuities: A Local/Nonlocal Approach

Area of Science:

• Solid Mechanics
• Nanotechnology
• Computational Materials Science

Background:

• Existing stress-driven integral models (SDM) do not account for internal discontinuities in nanobeams.
• Nonlocality effects are crucial for accurately modeling nanobeam behavior.

Purpose of the Study:

• To extend the two-phase local/nonlocal stress-driven integral model (SDM) to include internal discontinuities in nanobeams.
• To analyze the size-dependent fracture behavior of cracked nanobeams under Mode I loading.

Main Methods:

• A novel formulation using a convex combination of local and nonlocal phases with a mixture parameter was developed.
• The model was validated using six case studies of uncracked nanobeams with varying constraints and loading.
• Fracture analysis of a centrally-cracked nanobeam was performed.

Main Results:

• The extended SDM successfully models nanobeams with internal discontinuities.
• Nonlocality significantly affects the displacement field of nanobeams.
• Fracture properties (COD, ERR, KIC) of cracked nanobeams show strong dependency on characteristic length and mixture parameter.

Conclusions:

• The proposed model provides a robust framework for analyzing nanobeams with discontinuities.
• The study highlights the importance of considering nonlocal effects and material parameters in nanobeam fracture mechanics.