Extension of incremental sequentially linear analysis to geometrical non-linearity with indirect displacement control. (15th February 2021) - Yu, Chenjie; Hoogenboom, Pierre; Rots, Jan
Highlights: ISLA inherits the robustness from the total scheme and the extensibility from the incremental scheme. ISLA is extended to include geometrical non-linearity in addition to cracking type physical non-linearity for quasi-brittle structures. Indirect displacement control with a control point(s) is introduced into ISLA to stabilise the localised failure process zones or avoid global unloading caused by geometrical and physical non-linearity. Indirect displacement control is applicable when the location or behaviour of the damage process area is not known a priori because the selection of the control point depends on the load positions rather than on the localised failure process zones. ISLA exhibits robustness and accuracy for localising crack propagation in one-way and two-way out-of-plane failures of masonry walls. Abstract: The most widely used method for simulating the non-linear behaviour of concrete and masonry structures is the Newton–Raphson method with arc-length control (N-R method). However, this method may fail to produce converged results because of softening, negative tangent stiffness, bifurcations or snap-back. Sometimes, convergence can be obtained by controlling degrees of freedom in the failure process zone or by applying sequentially linear analysis (SLA). However, the location of the failure is often not known a priori and geometrical non-linearity needs to be included. Recently, incremental sequentially linear analysis (ISLA) has been proposed, which is based on a combination of the N-R method and SLA. 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). The objective of this paper is to demonstrate that ISLA can be applied to problems that behave geometrically nonlinear in addition to physically nonlinear. In this paper, we introduce a method that combines ISLA with indirect displacement control. This method stabilises localised damage process areas and avoids the global unloading caused by geometrical and physical non-linearity. The method uses one or more control points, which are positioned independently of the failure process zones. Two masonry walls were tested and analysed. The load was perpendicular to their planes and evenly distributed. The walls were supported on two or four edges. Stable post-peak results were computed for large geometrical non-linear displacements, and localised crack propagation was computed robustly and correctly.