An FFT framework for simulating non-local ductile failure in heterogeneous materials

The simulation of fracture using continuum ductile damage models attains a pathological discretization dependence caused by strain localization, after loss ellipticity the problem, in regions whose size is connected to spatial discretization. Implicit gradient techniques suppress this problem introducing some inelastic non-local fields and solving an enriched formulation where classical balance linear momentum fully coupled with Helmholtz-type equation for each variable. Such equations determine distribution bands width controlled characteristic length, independently on numerical resolution Finite Element method computationally very expensive its use simulate process 3D multi-phase microstructures becomes prohibitive. In work, we propose novel FFT-based iterative algorithm simulating computational homogenization problems. particular, implicit approach properly generalized model regularization media, multiple variables different lengths may come into play. proposed algorithm, two distinct problems are solved staggered fashion: (i) conventional mechanical via FFT-Galerkin solver mixed macroscopic loading control (ii) Krylov-based combined efficient pre-conditioner. implementation firstly validated simple two-dimensional microstructures, showing identical responses discretizations reproducing ductility change dependent length. Finally, robustness efficiency demonstrated failure complex particle reinforced composites characterized millions degrees freedom.