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The aim of this study is three-fold: (i) to present a general higher-ordershell theory to analyze large deformations of thin or thick shell structuresmade of general compressible hyperelastic materials; (ii) to utilize theorthonormal or Cartans moving frame in the formulation of shell theory incontrast to the classical tensorial covariant coordinate system; and (iii) topresent the nonlinear weak-form Galerkin finite element model for the givenshell theory. The displacement field of a point on the line normal to the shellreference surface is approximated by the Taylor series or Legendre polynomials.The kinematics of motion in the assumed coordinate system is derived using thetools of exterior calculus. The use of an orthonormal moving frame makes itpossible to represent kinematic quantities, e.g., determinant of thedeformation gradient, in a far more efficient manner than the classicaltensorial representation of the same with covariant bases. The manipulation ofthe various tensor used in the kinematics and dynamics of the structures can becarried out with ease and a more computationally efficient manner. Thegoverning equation of the shell has been derived in the general surfacecoordinates. The methodology developed herein is very much algorithmic, andhence it can also be applied for any arbitrary interpolated surfaces with equalease. The higher-order nature of the approximation of the displacement fieldmakes the theory suitable for analyzing thick and thin shell structures. Thecompressible hyperelastic material model used as the constitutive relation ofthe material. The formulation presented herein can be specialized for variousnonlinear hyperelastic constitutive models suitable for use, for example, inbio-mechanics and other soft-material problems (e.g., neo-Hookean material,Mooney-Rivlin material, Generalized power-law neo-Hookean material, and so on).

A general higher-order shell theory for compressible isotropic hyperelastic materials using orthonormal moving frame