DAMAGE SIMULATION OF HETEROGENEOUS SOLIDS BY NONLOCAL FORMULATIONS ON ORTHOGONAL GRIDS
The present paper is part of a comprehensive approach of grid-based modelling. This approach includes geometrical modelling by pixel or voxel models, advanced multiphase B-spline finite elements of variable order and fast iterative solver methods based on the multigrid method. So far, we have only presented these grid-based methods in connection with linear elastic analysis of heterogeneous materials. Damage simulation demands further considerations. The direct stress solution of standard bilinear finite elements is severly defective, especially along material interfaces. Besides achieving objective constitutive modelling, various nonlocal formulations are applied to improve the stress solution. Such a corrective data processing can either refer to input data in terms of Young's modulus or to the attained finite element stress solution, as well as to a combination of both. A damage-controlled sequentially linear analysis is applied in connection with an isotropic damage law. Essentially by a high resolution of the heterogeneous solid, local isotropic damage on the material subscale allows to simulate complex damage topologies such as cracks. Therefore anisotropic degradation of a material sample can be simulated. Based on an effectively secantial global stiffness the analysis is numerically stable. The iteration step size is controlled for an adequate simulation of the damage path. This requires many steps, but in the iterative solution process each new step starts with the solution of the prior step. Therefore this method is quite effective. The present paper provides an introduction of the proposed concept for a stable simulation of damage in heterogeneous solids.