A quasi-static algorithm that includes effects of characteristic time scales for simulating failures in brittle materials

When the brittle heterogeneous material is simulated via lattice models, the quasi-static failure depends on the relative magnitudes of Telem, the characteristic releasing time of the internal forces of the broken elements and Tlattice, the characteristic relaxation time of the lattice, both of which are infinitesimal compared with Tload, the characteristic loading period. The load-unload (L-U) method is used for one extreme, Telem << Tlattice, whereas the force-release (F-R) method is used for the other, Telem T lattice. For cases between the above two extremes, we develop a new algorithm by combining the L-U and the F-R trial displacement fields to construct the new trial field. As a result, our algorithm includes both L-U and F-R failure characteristics, which allows us to observe the influence of the ratio of Telem to Tlattice by adjusting their contributions in the trial displacement field. Therefore, the material dependence of the snap-back instabilities is implemented by introducing one snap-back parameter γ. Although in principle catastrophic failures can hardly be predicted accurately without knowing all microstructural information, effects of γ can be captured by numerical simulations conducted on samples with exactly the same microstructure but different γs. Such a same-specimen-based study shows how the lattice behaves along with the changing ratio of the L-U and F-R components. © 2013 The Author(s).