Simulation of failure of structures using dynamics and optimization techniques

Journal article, 2004

Simulation of failure processes requires solution of large sets of non-linear equations, which is an inherently difficult task. Many attempts have been made to stabilize the solution procedures but with limited success. This paper presents a broad review of techniques to stabilize the solution procedures both from the field of structural mechanics (both static and dynamic) and the related field of optimization. In particular two new methods for structural mechanics applications are presented: The arc-length strain constraint and the trust region method (TRM). The TRM uses a step size constraint to ensure the validity of the Taylor expansion. The review finds interesting similarities between arc-length methods, time integration procedures and TRM, providing new insights. The new techniques have been implemented in a FE-code and some numerical examples are presented. The examples show that the results from static arc-length procedures are somewhat artificial and difficult to interpret since they follow a displacement controlled failure. The dynamics must be included to follow the more realistic load controlled failure. The dynamics also to some extent stabilizes the solution process. The convergence test of the TRM shows that it improves robustness allowing larger time increments to be used, but the rate of convergence is decreased why efficiency needs to be further improved.