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Uniform stress fields inside multiple inclusions in an elastic infinite plane under plane deformation
Ming Dai1, Cun-Fa Gao1, C Q Ru2
1State Key Laboratory of Mechanics and Control of Mechanical Structures , Nanjing University of Aeronautics and Astronautics , Nanjing 210016, China.
Proceedings. Mathematical, Physical, and Engineering Sciences
|August 23, 2016
Summary
This study presents a method for determining the shapes of multiple elastic inclusions with uniform internal stress fields. Inclusion shapes are independent of external loads only when their elastic properties match the surrounding matrix.
Area of Science:
- Solid Mechanics
- Materials Science
- Applied Mathematics
Background:
- Understanding stress distribution in composite materials is crucial for predicting material behavior and failure.
- Previous research has limitations in analyzing multiple inclusions with uniform stress fields.
Purpose of the Study:
- To develop a general method for constructing multiple elastic inclusions with uniform internal stress fields.
- To characterize the influence of inclusion shape, elastic properties, and remote loading on stress uniformity.
Main Methods:
- Utilizing complex analysis and conformal mapping to define inclusion shapes.
- Applying boundary value conditions for holomorphic functions in multiply connected regions.
Main Results:
- A broad class of multiple inclusions with uniform internal stress fields is identified.
- Inclusion shapes are independent of remote loading solely when shear moduli match between inclusions and matrix.
- Conditions for the existence of symmetric and rotationally symmetric inclusions are derived.
Conclusions:
- The developed method offers a significant advancement over existing techniques for analyzing multiple elastic inclusions.
- The findings provide critical insights into the relationship between material properties, geometry, and stress fields in composites.
- This research lays the groundwork for designing materials with tailored stress distributions.
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