A computationally efficient coupled multi-scale model for short fiber reinforced composites

A coupled multi-scale (macro–micro) model is developed to predict non-linear elasto-plastic behavior of short fiber reinforced composites. At the microscopic level, a recently proposed micro-mechanical model, developed based on a two-step orientation averaging approach, is used. A wide range of micro-structural parameters, including matrix and fiber constitutive parameters, fiber volume fraction and fiber aspect ratio, can be accommodated in the model. Different interactions including Voigt, Reuss and a self-consistent assumption are considered in the model. This micro-mechanical model is then incorporated in a Finite Element model of the macro-scale problem, enabling coupled macro–micro simulations of real-life structures/specimens. Numerical examples and comparisons with experimental data, taken from literature, show that the model gives good predictions. Besides, several strategies and techniques are employed to improve the computational efficiency of the model. These techniques include replacing originally utilized trapezoidal integration (for fiber orientations and calculation of the Eshelby tensor) with more efficient integration schemes, and using a more efficient method for data storage. Comparisons of the computational efforts shows that these improvements substantially decreased the computational cost of the model.