A corotational flat triangular element for large strain analysis of thin shells with application to soft biological tissues

A flat triangular element for the nonlinear analysis of thin shells is presented. The formulation relies on (i) a polar decomposition based corotational framework and (ii) a core-element kinematic description adopting the multiplicative superposition of membrane and bending actions. The resulting element is a refined yet simple three-node displacement-based triangle accounting for thickness extensibility and initial shell curvature, and equipped with a fully consistent tangent stiffness. Numerical tests involving shell structures made of rubber-like materials or fibred biological tissues show the effectiveness of the proposed element and its suitability to problems characterized by large displacements, large rotations, large membrane strains and bending. A Matlab toolkit implementing the present formulation is provided as supplementary material.