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A Coupled Experiment-finite Element Modeling Methodology for Assessing High Strain Rate Mechanical Response of Soft Biomaterials
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Matched Interface and Boundary Method for Elasticity Interface Problems.

Bao Wang1, Kelin Xia1, Guo-Wei Wei2

  • 1Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA.

Journal of Computational and Applied Mathematics
|April 28, 2015
PubMed
Summary
This summary is machine-generated.

The matched interface and boundary (MIB) method accurately solves elasticity problems with material interfaces. This new approach handles discontinuous coefficients and complex geometries, achieving second-order accuracy.

Keywords:
Elasticity equationsElasticity interface problemsMatched interface and boundarySpatial-dependent shear modulus

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Area of Science:

  • Continuum Mechanics
  • Solid Mechanics
  • Computational Mechanics

Background:

  • Material interfaces are common in nature and engineering, leading to challenges in elasticity equations due to discontinuous coefficients.
  • Existing methods struggle with discontinuities and complex interface geometries in elasticity problems.

Purpose of the Study:

  • To develop and validate the matched interface and boundary (MIB) method for solving elasticity interface problems.
  • To address both strong (discontinuous solution) and weak (discontinuous derivatives) discontinuities.
  • To handle complex interface geometries and position-dependent material properties.

Main Methods:

  • The matched interface and boundary (MIB) method is employed, utilizing fictitious values to enable standard finite difference schemes across interfaces.
  • Interface jump conditions are enforced to accurately determine fictitious values.
  • New MIB schemes, including secondary fictitious values and geometry-based interpolation, are designed for complex geometries and cross-derivatives.

Main Results:

  • The MIB method accurately models Lamé's parameters with jumps and position dependence.
  • The method effectively handles strong and weak discontinuities.
  • Numerical tests demonstrate second-order accuracy in L∞ and L2 norms for various interface curvatures and material properties.

Conclusions:

  • The developed MIB method provides an accurate, robust, and convergent solution for elasticity interface problems.
  • The approach successfully overcomes challenges posed by complex geometries and discontinuities.
  • This method has broad applicability in science and engineering where material interfaces are prevalent.