Abstract Summary
The standard Newton–Raphson scheme suffers from divergence problems due to softening, negative tangent stiffness, bifurcations or snap-back when modelling fracture of quasi-brittle materials, such as masonry and concrete. Convergence can be achieved by applying sequentially linear analysis (SLA) in some cases. However, it has difficulties in dealing with cases in which the displacement history matters such as dynamic damage modelling due to its total approach. Recently, incremental sequentially linear analysis (ISLA) which combines the merits of the N–R method and SLA, has been proposed. The solution search path follows damage cycles sequentially with secant stiffness corresponding to local damage increments, which traces both damage history (explicit) and displacement history (implicit). This work focuses on dynamic damage modelling of quasi-brittle materials accounting for physical non-linearity as well to address the transient effects in the fracture process. The standard ISLA, similar to the large time increment (LATIN) method, the extended finite element method (X-FEM) and strong discontinuity approaches (SDA) which are proposed to capture the crack propagations for quasi-brittle materials, is not suitable for dynamic damage modelling. The objective of this work is therefore to propose a damage integration scheme (damage-driven instead of time integration scheme) based on ISLA for non-linear transient analysis of structures under dynamic loading while retaining the merits of the previous ISLA. The proposed damage integration scheme has been compared with the standard time integration scheme in a dynamically loaded bar example, showing good agreements and sufficient accuracy. The proposed method has been validated further for a notched beam under tension and four-point bending. Since all physical non-linearity is linearized in damage cycles with the explicit secant stiffness of the reduced elastic material model, the algorithm possesses high robustness.
