A structured deformation driven nonlocal macro-meso-scale consistent damage model for the compression/shear dominate failure simulation of quasi-brittle materials

Abstract

The newly proposed nonlocal macro-meso-scale consistent damage model (NMMD) is extended to compression/shear-dominate failure problems. For this purpose, the nonlocal strain of a material point pair in the NMMD is split into elastic strain and structured strain according to the theory of structured deformation. Then the structured part of the deformation of a material point pair, i.e., the structured positive elongation quantity, can be evaluated based on the structured strain. When the structured positive elongation quantity, rather than the original full positive elongation, of a material point pair exceeds a critical value, the material point pair become damaged, leading to mesoscopic damage. The macroscopic topologic damage at one point is then given by the weighted summation of mesoscopic damage of the point pairs connected to this point within its influence domain. Through the energetic degradation function, which bridges the damage in the geometric sense and the damage in the energetic sense, the topologic damage is incorporated into the framework of continuum damage mechanics. This model can be solved numerically. In contrast to the original NMMD for tensile-failure dominate problems, the driving force of topologic damage, i.e., the positive elongation quantity of material point pairs, is modified according to different types of structured strain, and thus the extended model is appropriate for various fracture mechanisms if a proper structured strain is adopted. The proposed model facilitates implementation, and can not only trace the crack path automatically without initial cracks, but also accurately predict the load–deformation curves without mesh sensitivity. The computational efficiency of the proposed model is illustrated via a benchmark problem. Examples verifies that when the masonry-like structured strain is adopted the structured deformation driven NMMD can well capture the vertical crack in quasi-brittle materials under uniaxial compression. In addition, an intuitive interpretation in the principal strain space is given to reveal the underlying physical mechanism for this problem. Alternatively, if the deviatoric structured strain is adopted to modify the driving force of topologic damage, the horizontal crack (true mode II crack) under pure shear can be obtained via NMMD. It is numerically verified that the mode II crack evolves according to the von Mises criterion, i.e., the crack propagates along the direction of the largest distortion energy density. Numerical results also indicate that the key features of the crack patterns from the NMMD and the phase field model are similar when the same structured strain is adopted to decompose the driving force of damage in these two models. This consistency between NMMD and the phase field model is preliminarily interpreted by Green’s function theory. Problems to be further investigated are also discussed, especially for the extension to anisotropic materials.