Reducing internal variables and improving efficiency in data-driven modelling of anisotropic damage from RVE simulations

The Data-Driven Harmonic Analysis of Damage (DDHAD) has been proposed recently to construct arbitrarily anisotropic damage models in quasi-brittle heterogeneous materials from calculations on Representative Volume Elements. During preliminary off-line calculations, numerical crack propagations are simulated and the effective damaged elasticity tensor is computed by numerical homogenization. A macroscopic damage model with internal variables is defined using harmonic analysis of the elasticity tensor. The method, called DDHAD, is in this work improved by two key novelties. First, a numerical framework is proposed to evaluate efficiently the model during on-line calculations by computing all the integral terms during off-line calculations and expressing the damage model in a compact matrix form. Second, a reduced model is introduced to further reduce the number of internal variables which is in general large in 3D. It is shown in an application to the damage of 3D printed lattice that even for a complex 3D induced anisotropy, the number of internal variables can drop to a very small number (3 or 4) with the aid of the proposed strategy.