Multiple Crack Growth failure in Cortical Bone under Tension by the eXtended Finite Element Method

A multi-scale analysis for multiple crack growth in unit cell of cortical bone is presented. The cracks are grown until complete failure of the cell. The initial cracks are placed in maximum strain locations. The stress intensity factors are computed at each crack tip and a load parameter is adjusted so that the stress intensity factors remain at the critical value. In the case of competitive crack tips, a stability analysis is performed by computing the second derivative of the potential energy for each crack. The load deflection behavior of the representative volume element is obtained until the point of complete failure. The model is fed with experimental geometrical, mechanical and damage parameters and validated through a comparison with experimental samples. The discretization utilizes the eXtended Finite Element Method and requires no remeshing as the cracks grow. The crack geometries are arbitrary with respect to the mesh, and are described by a vector level set. Special boundary conditions and the algorithm for detecting crack bridging and crack entering Haversian canals which allows the cracks to grow ntil maximum failure and/or percolation is presented.