Iterative solution methods for damage progression analysis

Damage progression is a sequence of damage events. A simulation of it solves a sequence of systems of equations which differ from each other only by the effects of the modelling of the incrementally increasing damage. An initial matrix triangulation, to solve the equations of the virgin structure, provides a preconditioner that can be used for solving the sequence of system equations by approximate or iterative solution techniques. In addition, obtained solutions serve as starting vectors for the next solutions. The numerical efficiency potential of this concept is evaluated by considering a method inspired by the sensitivity formula for finite element models, an iterative method inspired by Jacobiʹs method, and the untransformed preconditioned conjugate gradient method. The ability to reproduce the damage patterns obtained by using exact solution is checked and the efficiency improvements are assessed.