Computational Homogenisation and Identification of Auxetic Structures with Interval Parameters

Area of Science:

• Materials Science
• Computational Mechanics
• Mechanical Engineering

Background:

• Heterogeneous materials with nonlinear characteristics, such as auxetic structures, present challenges in accurate modeling due to inherent uncertainties in material and topological parameters.
• Traditional methods often struggle to capture the complex behavior of these materials under uncertainty, necessitating advanced computational approaches.

Purpose of the Study:

• To develop and validate a computational homogenization and identification methodology for heterogeneous auxetic materials with uncertain properties.
• To effectively incorporate interval-based uncertainty into the analysis of nonlinear material behavior.
• To accurately identify microscopic material parameters from macroscopic experimental data.

Main Methods:

• Utilized the finite element method (FEM) for solving boundary value problems of auxetic structures.
• Employed artificial neural network (ANN) response surfaces to reduce computational cost.
• Applied directed interval arithmetic to minimize interval widths arising from parameter uncertainty.
• Adopted the Pareto approach and a multi-objective evolutionary algorithm for the material identification task.

Main Results:

• Computational homogenization under uncertainty effectively captured the behavior of heterogeneous auxetic materials.
• The proposed methodology demonstrated the significance of incorporating uncertainty into material property analysis.
• Successful identification of microscopic material parameters was achieved from macroscopic data, including interval descriptions of nonlinear deformation.

Conclusions:

• The developed computational framework provides an effective means to analyze and identify properties of heterogeneous auxetic materials with interval uncertainty.
• The integration of FEM, ANNs, and interval arithmetic offers a robust solution for complex material characterization problems.
• This work highlights the critical importance of accounting for uncertainty in material properties for accurate predictive modeling.