A novel sequentially linear approach based on exponential saw-tooth softening in fracture analysis of quasi-brittle material

Abstract

The Newton-Raphson iterative scheme is a widely used technique for modeling the non-linear problems, but it is well known that the scheme is unstable and the convergence may be difficult to obtain in case of snap-back or bifurcation. The sequentially linear approach, which sets a critical integration point and uses a saw-tooth softening approximation, is an alternative approach to address these issues. However, the sequentially linear approach cannot fully solve some drawbacks such as mesh dependency of crack patterns, which is main shortcomings of smeared crack approach. In this paper, the saw-tooth curve based on exponential softening is newly developed and an approach combined it with local crack tracking algorithm is proposed. The crack tip point is chosen by crack tracking algorithm and the fracture behavior is analyzed by sequentially reducing the stiffness and strength in elements within crack path. Several benchmark examples are numerically solved to check the accuracy of crack path, ultimate load and capture of snap-back predicted by the proposed approach and the results are compared with those by traditional sequentially linear approach and experiments.