Numerical homogenization of fiber reinforced layer in large elastic deformation using a decoupled iterative method

We propose a procedure to approximate the large elastic deformations of a fiber reinforced layer by a two-scale decoupled homogenization numerical procedure. The nonlinear micro and macroscopic scales are strongly coupled in most homogenization methods which is very costly. Our method consists in decoupling the micro and macro scales by considering separate boundary value problems and an intermediate anisotropic constitutive law optimized over a training set. We propose an iterative procedure based on this method which allows to improve the quality of the approximation to get closer to the coupled homogenization and keeping a reasonable computational cost. We perform representative numerical studies for a layer with heterogeneous hyperelastic material in order to demonstrate the capability and reliability of the proposed method and test several intermediate constitutive laws.