A METHOD FOR QUASI-STATIC ANALYSIS OF TOPOLOGICALLY VARIABLE LATTICE STRUCTURES

The proposed time-independent quasi-static approach for simulations of lattice structures with imperfections is based on integration of the Inverse Broyden's Method suitable for finding the equilibrium state for a large system of atoms interacting through strongly nonlinear potentials and the Recursive Inverse Matrix Algorithm (RIMA) capable of updating the inverse matrix when topological changes (broken or new bonds between the atoms) take place. In this approach, the crystal structure is treated as a truss system while the forces between the atoms situated at the nodes are defined by the inter-atomic potentials. Since both the Broyden's and the RIMA algorithms deal with the inverse matrices of the structure their coupling makes the procedure computationally efficient. In addition, the method allows analysis of lattices subjected to mixed boundary conditions. The developed code was verified by the comparison with an alternative numerical procedure based on energy minimization technique. The model and the code developed were applied to the case of a 2D hexagonal lattice with the mode I crack embedded into the structure. For the cases considered, it was observed that the crack nucleation and growth were accompanied by the dislocation emission.