A nonlinear finite element formulation for large deflection analysis of 2D composite structures

In this paper, we propose a finite element formulation based on a total Lagrangian approach to analyze two-dimensional (2D) fiber reinforced elastic solids undergoing large displacements. It allows the consideration of discrete short or long fibers embedded in a continuum matrix and the obtained system of equations size is equivalent to that of a non-reinforced medium. The matrix domain is discretized with four-node quadrilateral membrane elements while fibers crossing each matrix element are automatically detected and represented by two-node truss elements. A perfect bonding of fibers to the matrix is assumed and a projection technique is used to express the truss elements variables in terms of their corresponding matrix elements. Five nonlinear examples are presented to validate and demonstrate the capabilities of the proposed finite element formulation.