Hyperelastic Constitutive Modeling of 2D Materials Under In-plane and Flexural Deformations

Author

Serge R. Maalouf, University of MaineFollow

Date of Award

Summer 5-6-2025

Level of Access Assigned by Author

Open-Access Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Mechanical Engineering

First Committee Advisor

Senthil S. Vel

Second Committee Member

Zhihe Jin

Third Committee Member

Masoud Rais-Rohani

Additional Committee Members

Nicholas Bingham

Yingchao Yang

Abstract

Two-dimensional (2D) materials, which consist of one or a few tightly bonded layers of atoms, exhibit remarkable physical properties making them ideal for applications, such as flexible electronics. In many cases, 2D materials are subjected to large in-plane and flexural deformations. In this dissertation, constitutive models are proposed for the nonlinear in-plane and flexural elastic response of 2D materials. A methodology, based on evaluating the strain energies of 2D materials along rays in strain space, has been developed for systematically evaluating the elastic constants of polynomial constitutive models for 2D materials of arbitrary symmetries.

In order to analyze the flexural elastic response of 2D materials, a torus-based parameterization is proposed for simulating different curvature states of 2D materials, including simultaneous bending and twisting. A generalized constitutive model is proposed for the flexural response of 2D materials. Subsequently, a new hyperelastic constitutive model is proposed for 2D materials under simultaneous in-plane and flexural deformations. The in-plane, flexural and coupling elastic constants are evaluated, and the effects of bending and twisting on the in-plane strains are studied. Furthermore, the influence of in-plane strains on the effective flexural rigidities is investigated.

An important contribution of this dissertation is the development of a new invariant-based constitutive model for the in-plane elastic response of hexagonal 2D materials. In order to elucidate the functional dependence of the strain energy density on the deformation, new invariants are introduced to reflect the contributions of dilatational deformations, deviatoric deformations, and deformation-induced anisotropy. A specific form of the constitutive model that consists of a total of seven elastic constants is proposed. Predictions from the proposed constitutive model for the strain energy densities and stresses are compared to those from density functional theory and the Murnaghan polynomial constitutive model.

The proposed models and methodologies in this dissertation are used to study representative materials such as graphene, molybdenum disulfide and black phosphorus, and are applicable to a wide range of 2D materials. The elastic constants of the constitutive models are evaluated for the representative materials, their nonlinear elastic response studied and their linearized elastic properties and flexural rigidities evaluated.

Recommended Citation

Maalouf, Serge R., "Hyperelastic Constitutive Modeling of 2D Materials Under In-plane and Flexural Deformations" (2025). Electronic Theses and Dissertations. 4273.
https://digitalcommons.library.umaine.edu/etd/4273