A unified computational framework for bulk and surface elasticity theory: a curvilinear-coordinate-based finite element methodology

A curvilinear-coordinate-based finite element methodology is presented as a basis for a straightforward computational implementation of the theory of surface elasticity that mimics the underlying mathematical and geometrical concepts. An efficient formulation is obtained by adopting the same methodology for both the bulk and the surface. The key steps to evaluate the hyperelastic constitutive relations at the level of the quadrature point in a finite element scheme using this unified approach are provided. The methodology is illustrated through selected numerical examples.