An incremental-iterative method for modeling damage evolution in voxel-based microstructure models

Numerical methods motivated by rapid advances in image processing techniques have been intensively developed during recent years and increasingly applied to simulate heterogeneous materials with complex microstructure. The present work aims at elaborating an incremental-iterative numerical method for voxel-based modeling of damage evolution in quasi-brittle microstructures. The iterative scheme based on the Lippmann-Schwinger equation in the real space domain (Yvonnet, in Int J Numer Methods Eng 92:178-205, 2012) is first cast into an incremental form so as to implement nonlinear material models efficiently. In the proposed scheme, local strain increments at material grid points are computed iteratively by a mapping operation through a transformation array, while local stresses are determined using a constitutive model that accounts for material degradation by damage. For validation, benchmark studies and numerical simulations using microtomographic data of concrete are performed. For each test, numerical predictions by the incremental-iterative scheme and the finite element method, respectively, are presented and compared for both global responses and local damage distributions. It is emphasized that the proposed incremental-iterative formulation can be straightforwardly applied in the framework of other Lippmann-Schwinger equation-based schemes, like the fast Fourier transform method.