# Self-consistent clustering analysis for homogenisation of heterogeneous plates

## TL;DR

This paper presents a novel reduced-order multiscale homogenisation method for heterogeneous plates, combining self-consistent clustering analysis with the Lippmann-Schwinger equation, achieving high accuracy with significantly reduced computational effort.

## Contribution

It introduces a plate-specific SCA scheme with an offline-online strategy and self-consistent updates, enabling efficient multiscale analysis of linear and nonlinear plate problems.

## Key findings

- Matches FFT-based simulation accuracy
- Reduces computational cost by over an order of magnitude
- Handles both linear and nonlinear plate problems

## Abstract

This work introduces a reduced-order model for plate structures with periodic micro-structures by coupling self-consistent clustering analysis (SCA) with the Lippmann-Schwinger equation, enabling rapid multiscale homogenisation of heterogeneous plates. A plate-specific SCA scheme is derived for the first time and features two key elements: (i) an offline-online strategy that combines Green's functions with k-means data compression, and (ii) an online self-consistent update that exploits the weak sensitivity of the reference medium. The framework handles both linear and nonlinear problems in classical plate theory and first-order shear deformation theory, and its performance is verified on linear isotropic perforated plates and woven composites, as well as on non-linear elasto-plastic perforated plates and woven composites with damage. Across all cases the proposed model matches the accuracy of FFT-based direct numerical simulation while reducing computational cost by over an order of magnitude.