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

Asatur Khurshudyan, Ara Avetisyan and Sergey Ohanyan

A chapter in Perusal of the Finite Element Method from IntechOpen

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.

Keywords: morphogenesis; embryonic tissue; adherens junctions; relaxation; quasi-convex energy densities; isometric deformations; short maps; tissue mechanics; ?-convergence; lower semi-continuity; hexagonal elements (search for similar items in EconPapers)
JEL-codes: C60 (search for similar items in EconPapers)
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Persistent link: https://EconPapers.repec.org/RePEc:ito:pchaps:105890

DOI: 10.5772/65027

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