Failure criterion for materials with spatially correlated mechanical properties

Area of Science:

• Materials Science
• Statistical Mechanics
• Geophysics

Background:

• Heterogeneous materials exhibit complex failure behaviors influenced by internal structure.
• Fiber bundle models (FBMs) are used to simulate material failure under stress.
• Spatial correlation of mechanical elements and load redistribution rules impact failure modes.

Purpose of the Study:

• To systematically evaluate the role of spatially correlated mechanical elements in FBM failure.
• To investigate the influence of different load redistribution rules on failure characteristics.
• To identify a general failure criterion for heterogeneous systems.

Main Methods:

• Simulations using fiber bundle models (FBMs) with varying degrees of spatial correlation.
• Analysis of failure behavior under different load redistribution rules (e.g., local load sharing).
• Development and validation of a global failure criterion based on macroscopic properties.

Main Results:

• Increasing spatial correlation in FBMs with local load sharing shifts failure from ductile-like to brittle-like.
• A global failure criterion, independent of spatial correlation and load redistribution rules, was identified.
• This criterion is based on macroscopic properties like external load and cumulative damage.

Conclusions:

• Spatial correlation significantly alters failure modes in heterogeneous materials simulated by FBMs.
• A universal macroscopic failure criterion can predict mechanical stability in complex systems.
• This metric holds potential for early warning systems, particularly for geophysical ruptures.