WIAS Preprint No. 3064, (2023)

An energy-based finite-strain model for 3D heterostructured materials and its validation by curvature analysis


  • Hadjimichael, Yiannis
    ORCID: 0000-0003-3517-8557
  • Merdon, Christian
    ORCID: 0000-0002-3390-2145
  • Liero, Matthias
    ORCID: 0000-0002-0963-2915
  • Farrell, Patricio
    ORCID: 0000-0001-9969-6615

2020 Mathematics Subject Classification

  • 74B20 74G65 74S05

2010 Physics and Astronomy Classification Scheme

  • 46.25.Cc 68.65.-k 62.23.Hj


  • Finite-strain elasticity, energy-based model, heterostructures, bent nanowires, curvature




This paper presents a comprehensive study of the intrinsic strain response of 3D het- erostructures arising from lattice mismatch. Combining materials with different lattice constants induces strain, leading to the bending of these heterostructures. We propose a model for nonlinear elastic heterostructures such as bimetallic beams or nanowires that takes into account local prestrain within each distinct material region. The resulting system of partial differential equations (PDEs) in Lagrangian coordinates incorporates a nonlinear strain and a linear stress-strain relationship governed by Hooke?s law. To validate our model, we apply it to bimetallic beams and hexagonal hetero-nanowires and perform numerical simulations using finite element methods (FEM). Our simulations ex- amine how these structures undergo bending under varying material compositions and cross-sectional geometries. In order to assess the fidelity of the model and the accuracy of simulations, we compare the calculated curvature with analytically derived formula- tions. We derive these analytical expressions through an energy-based approach as well as a kinetic framework, adeptly accounting for the lattice constant mismatch present at each compound material of the heterostructures. The outcomes of our study yield valuable insights into the behavior of strained bent heterostructures. This is particularly significant as the strain has the potential to influence the electronic band structure, piezoelectricity, and the dynamics of charge carriers.

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