Variational Asymptotic Analysis of Beam-Like Cord-Rubber Composites

Amount of engineering applications need steel cord to be embedded in a rubber matrix, which results in beam-like composite materials. Such materials feature a degree of lateral compliance and torsional flexibility while possessing high tensile stiffness. However, the currently available numerical approaches to analyze the effective material properties of such cord-rubber composites are computationally expensive. This paper proposes a novel approach based on an extended Variational Asymptotic Beam Sectional Analysis (VABS) theory which considers finite cross-sectional deformations. In the theory, the three-dimensional (3D) continuum is reduced to a one-dimensional (1D) beam analysis and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities without unnecessary kinematic assumptions. As a result, the modeling and design of cord-rubber composites are dimensionally reduced to a composite beam cross-sectional domain. The present theory is implemented using the finite element method (FEM) in the VABS code, a general-purpose beam cross-sectional analysis tool. An iterative method is applied to solve the finite warping field for the classical-type model using the Euler-Bernoulli beam theory. Hencky strain energy density and Neo-Hookean models describe cord wire and rubber matrix, respectively. Numerical examples demonstrate the capabilities of the present theory to capture the structural features of cord-rubber composites.