Multiscale modelling of composite laminates with voids through the direct FE2 method

A concurrent multiscale method, namely the direct FE2, is developed to analyse the mechanical response of fibre-reinforced composites with several void fractions in a nested manner, one at the macro and another one at the microscale. The FE2 is developed through the finite element (FE) mesh at the macro scale, wherein there is a representative volume element (RVE) at every Gauss point where the strains and stresses are evaluated. The RVEs, located at macroscopic FE mesh, with linear boundary conditions applied to the boundary nodes, are linked to macro-scale nodes via Multi-Point Constraints (MPCs). This procedure enables solving a single equilibrium problem, with boundary conditions and loadings at the macro scale and provides data for all defined RVEs. The methodology is applied to a composite laminate under transverse tension. Initially, the method is evaluated to compare the results from the FE2 with those from analyses where the entire domain is discretised (conventional FE full-scale modelling). The stresses obtained from the FE2 method match traditional FE analyses but utilise a significantly lower number of finite elements, resulting in substantial computational cost savings. It follows a parametric study of void distribution effects within the RVE. Afterwards, the stress distribution within the RVE is assessed and then failure of the composites is predicted at the macro scale through the stresses and strains concurrently calculated at the micro-scale.