FFT-based multiscale scheme for homogenisation of heterogeneous plates including damage and failure

This paper introduces a new approach that combines FFT-based multiscale homogenisation with the Lippman-Schwinger equation to efficiently and accurately analyse plate structures with periodic micro-structures. For the first time, the plate periodic Lippman-Schwinger equation is derived to address the auxiliary cell problem. The proposed method comprises two key components: (i) a 3D plate formulation using a novel finite prism approach, and (ii) solving the Lippman-Schwinger equations by means of Green's functions. Solutions for both the classical and first-order plate theories are derived and implemented for linear and nonlinear problems, completed with an open-source code provided. The efficiency and accuracy of the proposed method are assessed through several case studies, including complex woven composites. It is demonstrated that proposed method achieves a comparable level of accuracy to 3D solid problems while significantly reducing the required computing effort (i.e., milliseconds in computing time as opposed to hours required for 3D solid models). Moreover, nonlinear progressive damage problem involving an actual plate woven composite model is investigated. The results obtained show good agreement with experimental measurements for the progressive damage in plain woven composite, further highlighting the effectiveness of the proposed method. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).