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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
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Buckling in a rotationally invariant spin-elastic model.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Theoretical Physics

Background:

  • Scanning tunneling microscopy reveals spontaneous rippled-to-buckled transitions in heated graphene.
  • Existing models lack rotational invariance, deviating from classical elasticity theory.

Purpose of the Study:

  • Develop a classical spin-elastic model that preserves rotational invariance.
  • Qualitatively explain the rippled-to-buckled transition in graphene.

Main Methods:

  • Derivation of an effective free energy by integrating over internal degrees of freedom.
  • Analysis of mechanical phases through free energy minimization.
  • Analytical and numerical investigation of thermodynamic stability.

Main Results:

  • The proposed model accounts for the rippled-to-buckled transition.
  • Spatially homogeneous curvature emerges as the order parameter.
  • Different mechanical phases are identified and their stability analyzed.

Conclusions:

  • The spin-elastic model provides a consistent theoretical framework for graphene's phase transitions.
  • Curvature is identified as a critical factor in the rippled-to-buckled transition.
  • The model is applicable to both 1D and 2D systems, with a focus on graphene's honeycomb lattice.