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Characterizing Dissipative Elastic Metamaterials Produced by Additive Manufacturing
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Elasticity with arbitrarily shaped inhomogeneity.

Joachim Mathiesen1, Itamar Procaccia, Ido Regev

  • 1Physics of Geological Processes, University of Oslo, Postbox 1048 Blindern, N-0316 Oslo, Norway.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 21, 2008
PubMed
Summary
This summary is machine-generated.

This study introduces a semianalytic method for calculating stress in an infinite plate with an embedded inhomogeneity. The technique uses conformal mapping but shows limitations with significant shape distortions.

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Area of Science:

  • Solid Mechanics
  • Continuum Mechanics
  • Materials Science

Background:

  • Classical elasticity problems involve understanding material behavior under stress.
  • An inhomogeneity, a region with different material properties, presents unique challenges in stress analysis.
  • Accurate stress tensor calculation is crucial for predicting material failure and performance.

Purpose of the Study:

  • To develop a semianalytic method for determining the stress tensor in an infinite plate containing an arbitrary-shaped inhomogeneity.
  • To analyze the effectiveness and limitations of a conformal mapping-based approach for this problem.
  • To compare the obtained results with existing solutions in elasticity theory.

Main Methods:

  • Employing two conformal maps to represent the regions inside and outside the inhomogeneity.
  • Matching the conformal maps at the boundary between the inhomogeneity and the surrounding material.
  • Investigating the convergence properties of the method concerning the inhomogeneity's shape.

Main Results:

  • A semianalytic solution for the stress tensor in the specified elastic problem was derived.
  • The method's convergence is sensitive to the degree of distortion of the inhomogeneity's shape.
  • The study provides a comparative analysis against established solutions.

Conclusions:

  • The developed semianalytic method offers a viable approach for stress analysis in plates with inhomogeneities.
  • Limitations in convergence for highly distorted shapes necessitate further research or alternative methods.
  • The findings contribute to the understanding of stress concentrations and material response in heterogeneous media.