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Stress field around arbitrarily shaped cracks in two-dimensional elastic materials
Eran Bouchbinder1, Joachim Mathiesen, Itamar Procaccia
1Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.
Summary
Calculating stress fields around cracks is complex. This study presents a general solution for arbitrary cracks, offering a superior method for conformal mapping and accurate stress intensity factor calculations.
Area of Science:
- Solid Mechanics
- Fracture Mechanics
- Applied Mathematics
Background:
- Calculating stress fields around arbitrary cracks is a complex mathematical challenge.
- Existing methods often rely on approximations or combined analytic-numerical techniques.
- Exact solutions are limited to specific crack geometries.
Purpose of the Study:
- To provide a general and accurate solution for the stress field around any arbitrarily shaped crack.
- To develop an improved method for conformal mapping.
- To accurately determine stress intensity factors and T-stress for fracture analysis.
Main Methods:
- Developed a general solution for stress field calculation around arbitrary cracks.
- Introduced a novel conformal mapping method as an alternative to the Schwartz-Christoffel transformation.
- Applied the method to accurately estimate stress intensity factors (K(I), K(II)) and T-stress.
Main Results:
- Achieved an accurate estimation of the full stress field for arbitrary crack shapes.
- Demonstrated the effectiveness of the new conformal mapping technique.
- Successfully calculated critical fracture parameters: stress intensity factors and T-stress.
Conclusions:
- The presented general solution simplifies stress field calculations for arbitrary cracks.
- The novel conformal mapping method offers a superior alternative for geometric transformations in elasticity problems.
- This work provides essential tools for accurate fracture mechanics analysis.