Large strain and 3D stress analysis of laminated fiber-reinforced soft material structures with high order beam finite elements

Abstract

This study explores the capabilities of higher-order beam models within the Carrera Unified Formulation (CUF) framework for the large strain analysis of multilayered hyperelastic structures made of fiber-reinforced material. These materials exhibit complex mechanical behavior described by both geometrical and material nonlinearities. The proposed approach leverages the strengths of CUF, which allows for the definition of higher-order beam finite elements (FE) whose formal expression is an invariant of the structural theory adopted. The governing equations of the nonlinear static analysis are carried out by the Principle of Virtual Displacements (PVD) in a resulting pure displacement-based formulation. The nonlinear governing equations are written in matrix form in terms of Fundamental Nuclei (FN) of the internal and external force vectors and tangent stiffness matrix. The problem is solved through a Newton–Raphson linearization procedure coupled with path-following methods. The results show the capabilities of higher-order models in terms of accuracy and computational costs in predicting accurate displacements, strains, and detailed 3D stress distributions at large strain. The proposed results are compared with the FE solution obtained through classical models available in commercial software.