PSI - Issue 79

Lorenzo Leonetti et al. / Procedia Structural Integrity 79 (2026) 485–492

489

Fig. 3. Flowchart of the proposed data-driven homogenization approach for damaging anisotropic microstructures: on-line phase.

3.1. Off-line phase The first step involves the following operations:

1. Identification of the RUC for periodic homogenization 2. Definition of proportional loading paths for the RUC 3. Execution of crack propagation analyses for all loading paths In particular, the RUC is subjected to a finite set of macrostrain-driven proportional loading histories. The relevant macrostrains are expressed in terms of spherical coordinates:

( ) ( ) ( ) ( ) ( )     

11  =   =  =  12

max

sin cos sin sin cos

22      

11

max

,

(7)

22

max

12

  0,    and

 ) ,     − indicate the macrostrain path direction,

  0,1   is the monotonically increasing

where

max max max 11 22 12 , ,   

are the maximum expected values of these macrostrains.

loading factor, and

The second step involves the following operations: 1. Computation of macroscopic secant moduli 2. Construction of the data-driven damage evolution model A Deep Neural Network (DNN) is used to approximate the damage evolution model

( ) = C C  .

3.2. On-line phase This phase introduces a stress update procedure to handle elastic unloading in compliance with the discrete form of the damage dissipation inequality ( : : ) 2 0 D  =−     C . This procedure adopts an ad hoc predictor-corrector algorithm, which updates the state variable ( 1) n + C at the current macrostrain value ( 1) n +  only when the trial value of the current dissipation increment ( 1) trial n D +  is greater than or equal to zero. 4. Numerical application: homogenized failure behavior of nacre-inspired periodic composites The present numerical application involves a nacre-like microstructure, whose Repeating Unit Cell (RUC) is sketched in the upper left corner of Fig. 2. Plane strain and periodic boundary conditions are assumed for the related microscale problem. The width and height of expanded platelets are equal to 2 and 0.4 μm, respectively. Moreover, the elastic constants of platelets are 60 GPa p E = and 0.3 p  = . Finally, the following values are assumed for the elastic and inelastic interface parameters: 3 6 6 N/mm n s K K e = = , 30 MPa nc sc t t = = , I II 1.575 N/m c c G G = = .