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Improved Reduced Order Mechanical Model and Finite Element Analysis of Three-Dimensional Deformations of Epithelial Tissues

In: Perusal of the Finite Element Method

Author

Listed:
  • Asatur Khurshudyan
  • Ara Avetisyan
  • Sergey Ohanyan

Abstract

In this chapter, we analyse non-uniform bending of single-layer cell tissues--epithelia, surrounding organs throughout the body. Dimensionally reduced model is suggested, which is equivalent to membranes with bending stiffness: the total elastic energy of the tissue is a combination of stretching and bending energies. The energy, suggested in this chapter, is a piecewise function, the branches of which correspond to a specific deformation regime: compression, pure bending and stretch.

Suggested Citation

  • Asatur Khurshudyan & Ara Avetisyan & Sergey Ohanyan, 2016. "Improved Reduced Order Mechanical Model and Finite Element Analysis of Three-Dimensional Deformations of Epithelial Tissues," Chapters, in: Radostina Vasileva Petrova (ed.), Perusal of the Finite Element Method, IntechOpen.
    • Handle: RePEc:ito:pchaps:105890
    DOI: 10.5772/65027
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    More about this item

    Keywords

    morphogenesis; embryonic tissue; adherens junctions; relaxation; quasi-convex energy densities; isometric deformations; short maps; tissue mechanics; ?-convergence; lower semi-continuity; hexagonal elements;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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