Date of Award

2026

Degree Type

Thesis

Degree Name

Master of Science in Mechanical Engineering and Applied Mechanics

Department

Mechanical, Industrial and Systems Engineering

First Advisor

Sumanta Das

Abstract

Auxetic materials possess a negative Poisson’s ratio, meaning that they expand laterally when stretched and contract laterally when compressed. The unusual response is created primarily by the geometry and deformation mechanism of the architecture rather than by the chemistry of the base material. Among the available auxetic topologies, the double-arrowhead (DAH) structure is attractive because its behavior can be adjusted through a compact set of geometric parameters. However, the combined relationship between DAH geometry and its finite-deformation tensile Poisson’s ratio has not been characterized using an interpretable data-driven framework.

This thesis develops a finite element analysis and interpretable machine learning workflow for predicting the tensile Poisson’s ratio of two-dimensional DAH lattices. A Python script is used to generate a total of 8,142 geometries by varying four geometric parameters: the apex angle θ1, the re-entrant angle θ2, the cell half-pitch w, and the wall thickness t.  Longitudinal and transverse strains were calculated from interior gauge regions, excluding the plates, and the structural Poisson’s ratio was evaluated. Across the investigated design space, Poisson’s ratio ranged from approximately -2.79 to -0.096, therefore, all designs exhibited an auxetic response at the prescribed tensile displacement.

A feed-forward neural network was trained as a surrogate for the finite element response. Hyperparameter studies considered the hidden-layer neuron count, learning rate, and number of epochs. The selected model used 35 neurons, a learning rate of 10-2, and 200 epochs. Th surrogate reproduced the finite element results with R2 values of 0.9985 for the training data, 0.9985 for the validation data, and 0.9986 for the independent test data. Shapley Additive exPlanations (SHAP) were used to interpret the surrogate. The mean absolute SHAP values ranked θ1 first, θ2 second, w third, and t fourth. Together, the two angles accounted for approximately 90% of the total feature attribution. Increasing θ1 or θ2 generally shifted the predicted response toward less negative Poisson’s ratios, whereas w or t produced smaller shits toward more negative values. The findings establish the two characteristic angles as the principal design levers controlling DAH auxeticity and demonstrate that interpretable surrogate modeling can convert a large simulation database into transparent design guidance.

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