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Updated: Jun 8, 2026

A Method for Studying the Temperature Dependence of Dynamic Fracture and Fragmentation

A Method for Studying the Temperature Dependence of Dynamic Fracture and Fragmentation

Published on: June 28, 2015

Autonomy and singularity in dynamic fracture.

Eran Bouchbinder¹

¹Department of Chemical Physics, Weizmann Institute of Science, Rehovot, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 28, 2010

Summary

This summary is machine-generated.

Weakly nonlinear dynamic fracture theory introduces 1/r corrections. Satisfying Newton's equation ensures solution autonomy and vanishing linear momentum, aligning with experimental data.

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Area of Science:

Solid Mechanics
Materials Science
Fracture Mechanics

Background:

Standard linear elastic fracture mechanics describes crack tip fields with a 1/(square root of r) singularity.
Weakly nonlinear theory introduces 1/r corrections to these fields near a dynamic crack tip.
The physical and mathematical implications of these 1/r corrections require thorough investigation.

Purpose of the Study:

To investigate the autonomy and resultant Newton's equation compliance of the 1/r singular fields in dynamic fracture.
To determine the relationship between autonomy and the satisfaction of resultant Newton's equation.
To analyze the linear momentum carried by the 1/r singular fields.

Main Methods:

Theoretical analysis of weakly nonlinear dynamic fracture solutions.
Examination of the mathematical conditions for autonomy.
Verification against resultant Newton's equation in the crack parallel direction.
Calculation of the net linear momentum of the 1/r singular fields.

Main Results:

The 1/r singularity does not inherently guarantee autonomy or satisfy resultant Newton's equation.
Requiring satisfaction of resultant Newton's equation ensures the autonomy of the 1/r singular solution.
The resultant linear momentum associated with the 1/r singular fields is shown to vanish identically.
The theoretical predictions show favorable agreement with recent experimental measurements.

Conclusions:

The study clarifies the physical and mathematical nature of 1/r singularities in dynamic fracture.
Ensuring Newton's equation compliance is crucial for maintaining the autonomy of nonlinear crack tip solutions.
The vanishing linear momentum of 1/r fields has significant implications for understanding dynamic crack propagation.