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An Inverse Signorini Obstacle Problem
Maarten V de Hoop1, Matti Lassas2, Jinpeng Lu2
1Computational and Applied Mathematics and Earth Science, Rice University, Houston, TX 77005 USA.
This study uniquely identifies a Signorini obstacle using boundary measurements for isotropic elasticity. The obstacle is determined by single measurements of displacement and stress, advancing inverse problem research.
Area of Science:
- Solid Mechanics
- Inverse Problems
- Mathematical Physics
Background:
- The isotropic elasticity system models material behavior under stress.
- Inverse problems aim to determine system properties from external measurements.
- Signorini boundary conditions arise in contact mechanics problems.
Purpose of the Study:
- To investigate the unique determination of a Signorini obstacle.
- To analyze the inverse problem for the isotropic elasticity system.
- To develop generalizable techniques for differential inequalities.
Main Methods:
- Utilizing boundary measurements of displacement and normal stress.
- Applying techniques from inverse problem theory.
- Analyzing the Signorini boundary value problem.
Main Results:
- Unique determination of the Signorini obstacle is proven.
- A single boundary measurement is sufficient for identification.
- The identification is unique up to a natural obstruction.
Conclusions:
- Boundary measurements can effectively determine Signorini obstacles in elasticity.
- The developed methods offer a framework for broader inverse problem studies.
- This research contributes to understanding contact mechanics and material characterization.
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