DDHADTENS: A program for extracting anisotropic damage variables from tensors using harmonic analysis

The present DDHADTENS program is provided to extract variables characterizing anisotropic damage of elastic tensors. The theory is based on harmonic analysis. The program takes as input: (a) an undamaged elastic tensor and (b) a series of damaged elastic tensors. The output is a series of damage variables, defined as the coefficients of the spherical harmonics describing scalar damage orientation functions, which can be interpreted as the damage of elastic coefficients varying with the direction. These tensors can be obtained externally by numerical fracture simulations in a Representative Volume Element. A 2D version of the code is first provided. In this case, the elastic tensor is given by a 3 × 3 matrix and 6 damage variables are obtained. Second, a 3D version of the code is proposed, where the elastic tensor is given by a 6 × 6 matrix and 21 damage variables are obtained. In both case, a set of reduced variables using PCA is also provided. Numerical examples associated with degradation of elastic properties of Representative Volume Elements (RVE) are described.\ PROGRAM SUMMARY Program Title : DDHADTENS CPC Library link to program files :" https://doi.org/10.17632/2rfbsfjyrg.1 " Developer repository link :" https://github.com/jyvonnet/DDHADtens " Licensing provisions : GPLv3 Program language : Matlab and Python Nature of problems : Given an elastic tensor associated with an undamaged material and a tensor associated with a damage one, the program extracts the relevant damage parameters describing the anisotropic degradation. If a sequence of elastic tensors is provided, the evolution of the damage variables can be plotted. In addition, a PCA procedure is used to extract the most relevant variables. The elastic tensors have to be provided by external simulation results, e.g. Finite Element simulations on representative Volume Elements with damage/fracture evolution. The code can be employed for extracting internal variables in multiscale modelling of materials involving local fracture and apparent (macroscopic) anisotropic damage. Solution method: Uses expansion of orientation-dependent damage functions associated with two elastic tensors into spherical harmonics, with a PCA reduction.