Membrane Rebar Element considering Rotation of Reinforced Fibers for an Air Spring

Abstract

This paper newly introduces rebar element based on a membrane element for accurate and efficient modeling of thin fiber-reinforced rubber composites. The stiffness matrix of the rebar element consists of two matrices: the first matrix describes the stiffness of the rubber which is a base material of composites; the second matrix adds the stiffness of reinforced fibers by considering only the longitudinal component of elastic modulus. Reinforced fibers embedded into the rubber material are assumed as a virtual continuum layer. During finite element analysis, embedded direction of fibers is determined by the deformed shape of the base material since finite elements of the base material and continuum layer share nodal points. Rotation of fibers is allowed to describe the actual behavior of fibers and is computed at the integration point of an element of the base material. For consideration of the material and geometric nonlinearity, the updated Lagrangian formulation is employed. Validity of proposed rebar element has been investigated with analyses of large deformation problems. Simple tension of an element was analyzed and rotation of reinforced fibers and stiffness change of the composite are thoroughly investigated during deformation. Then, formulated finite element code is applied to simulate two problems such as tensile tests of fiber-reinforced rubber composites and inflation of rolling lobe-type air spring. Simulation results are quantitatively compared with experiment results. Comparisons demonstrate that proposed membrane rebar element describes the behavior of fiber-reinforced rubber composites accurately and effectively.