Non-linear analysis of bio-structures through refined beam models

A novel approach for the analysis of the non-linear behavior of bio-structures is presented here. This method is developed in the framework of the Carrera Unified Formulation (CUF), a higher-order 1D theory according to which the kinematics of the problem depends on the arbitrary expansion of the generalized unknowns. Taylor-like (TE) and Lagrange-like expansion functions (LE) are employed to describe the kinematic field along the cross-section and, the finite element method (FEM) is used to formulate the governing equations. In this work, the effects of material nonlinearities are investigated and, the problem is solved by using the Newton-Raphson method. An atherosclerotic plaque of an artery is introduced as a typical biostructure with complex geometry and studied for both linear and Non-Linear material cases. The results from the proposed technique highlight the accuracy of the in-plane and out-of-plane stress/strain distributions for different 1D models. The 3D-like accuracy of local effect predictions, the possibility of dealing with complex geometries, and low computational costs of nonlinear analyses make the present formulation appealing for biomechanical applications.