LAUSR

A validated multi-scale computational mechanics framework for progressive failure modeling of composite structures is developed. Zhang and Waas (Acta Mech 225(4–5):1391–1417, 2014) proposed a micromechanics-based two-scale multiscale model which is able to predict the nonlinear response of a composite. Their proposed micromechanics analysis uses the analytical solutions derived from the concentric cylinder model along with the generalized self-consistent model to find the effective properties of the unidirectional fiber reinforced composites, which are dependent on constituent level fiber–matrix mechanical properties and fiber volume fraction. In this model, the composite material is represented by an inner fiber core and an outer matrix annulus. It should be noted that the 2-CYL fiber–matrix concentric cylinder micromechanics model can be extended to a concentric fiber and any number of $$(N-1)$$(N-1) matrix layers in general, keeping the volume fraction constant, hence called the N-cylinder model (NCYL), which can analytically calculate the strain and stress field within the fiber and matrix cylinders for a given applied remote composite strain field, acting on the outer boundary of the matrix cylinder. The spatial variation of strain and stress fields within the cylinder are the key determinants for progressive damage and failure analysis of composite structures and hence, they need to be predicted accurately. The advantage of the NCYL concentric cylinder model is that the matrix strain and stress fields can be found in a discrete manner for each layer and the evolution of damage can be localized at a particular layer of matrix. These results can be used at the sub-scale in a multi-scale analysis to calculate the effective nonlinear composite response at a global scale. This work is based on a full analytical solution, and hence, it delivers a distinct computational advantage in composite failure analysis. That is, high fidelity and computational efficiency are gained at the same time.