TURE MODE II CRACK SIMULATION BASED ON A STRUCTURED DEFORMATION DRIVEN NONLOCAL MACRO-MESO-SCALE CONSISTENT DAMAGE MODEL

The fracture problem in which the crack deformation mode under mode II loading is also mode II is called the true mode II fracture problem. It is challenging to accurately and quantitively capture the whole process of true mode II fracture. In this paper, a structured deformation driven nonlocal macro-meso-scale consistent damage model is adopted to simulate the true mode II fracture problem. The nonlocal strain of a material point pair is decomposed into elastic strain and structured strain based on the theory of structured deformation. Then the structured positive elongation quantity of the material point pair can be evaluated by using the Cauchy-Born rule and the structured strain. In the present paper, the structured strain is taken as the deviatoric part of the nonlocal strain. When the structured positive elongation quantity of a material point pair exceeds the critical elongation quantity, mesoscopic damage starts to emerge at the point-pair level. The topologic damage can be obtained by weighted summing of the mesoscopic damage within the influence domain, then it is embedded into the framework of continuum damage mechanics through the energetic degradation function bridging the geometric damage and energetic damage for numerical solution. Further, the Gauss-Lobatto integration scheme is adopted in this paper to evaluate the nonlocal strain of point pairs, which reduces the number of integral points to 4 and thus considerably reduces the computational cost of preprocessing and nonlinear analysis. The reason for adopting the deviatoric strain as structured strain is revealed based on the analysis of the strain field at the crack tip under mode II loading. Numerical results for two typical true mode II fracture problems indicate that the proposed model can not only well capture the crack deformation pattern of true mode II cracks, but also quantitatively characterize the load-deformation curves without mesh size sensitivity. Problems to be further investigated are also discussed.