# Computational Homogenisation and Identification of Auxetic Structures with Interval Parameters

## TL;DR

This paper introduces a computational method to model and identify auxetic structures with uncertain material properties, using interval arithmetic and machine learning to improve accuracy and efficiency.

## Contribution

A novel approach combining interval arithmetic and multi-objective optimization for homogenization and identification of uncertain auxetic structures is proposed.

## Key findings

- The methodology effectively captures material behavior under uncertainty using interval parameters.
- Material parameters at the microscopic scale are successfully identified from macroscopic data.
- The use of artificial neural networks and evolutionary algorithms reduces computational effort.

## Abstract

The subject of this paper is the computational homogenisation and identification of heterogeneous materials in the form of auxetic structures made of materials with nonlinear characteristics. It is assumed that some of the material and topological parameters of the auxetic structures are uncertain and are modelled as interval numbers. Directed interval arithmetic is used to minimise the width of the resulting intervals. The finite element method is employed to solve the boundary value problem, and artificial neural network response surfaces are utilised to reduce the computational effort. In order to solve the identification task, the Pareto approach is adopted, and a multi-objective evolutionary algorithm is used as the global optimisation method. The results obtained from computational homogenisation under uncertainty demonstrate the efficacy of the proposed methodology in capturing material behaviour, thereby underscoring the significance of incorporating uncertainty into material properties. The identification results demonstrate the successful identification of material parameters at the microscopic scale from macroscopic data involving the interval description of the process of deformation of auxetic structures in a nonlinear regime.