Brittle fracture on plates governed by topological derivatives

Abstract

Purpose

In the paper an approach for crack nucleation and propagation phenomena in brittle plate structures is presented.

Design/methodology/approach

The Francfort–Marigo damage theory is adapted to the Kirchhoff and Reissner–Mindlin plate bending models. Then, the topological derivative method is used to minimize the associated Francfort–Marigo shape functional. In particular, the whole damaging process is governed by a threshold approach based on the topological derivative field, leading to a notable simple algorithm.

Findings

Numerical simulations are driven in order to verify the applicability of the proposed method in the context of brittle fracture modeling on plates. The obtained results reveal the capability of the method to determine nucleation and propagation including bifurcation of multiple cracks with a minimal number of user-defined algorithmic parameters.

Originality/value

This is the first work concerning brittle fracture modeling of plate structures based on the topological derivative method.

Citation

Xavier, M. and Van Goethem, N. (2022), "Brittle fracture on plates governed by topological derivatives", Engineering Computations, Vol. 39 No. 1, pp. 421-437. https://doi.org/10.1108/EC-07-2021-0375