Theoretical nonlinear response of complex single crystal under multi-axial tensile loading

The mechanical properties of single crystals are of interest as they represent the behavior of the basic building blocks. Using the density functional theory based ab initio technique we have devised an approach to analyze the behavior of single crystal so their mechanical properties can be studied beyond linear elasticity. Here we have applied the approach to investigate the mechanical properties of a single stoichiometric hydroxyapatite (HAP) crystal using a large supercell subjected to multi-axial tensile loading. The results reveal a complex nonlinear and loading-path dependent behavior with evolving anisotropy for the HAP crystal. Further, we have introduced a failure envelope index to quantify the strength behavior for comparison of similar materials. We have found that the complexities of the behavior of a single crystal originate from the local structural changes in these multi-component materials.