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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.

Archive for Rational Mechanics and Analysis
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Summary
This summary is machine-generated.

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.

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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.